Very sad to report that Carlo Bianchi, legendary organizer and host of the Bertinoro econometrics summer school (formally the CIDE Summer School of Econometrics) passed away today. His was an absolutely unique and endearing personage.
Whether or not you knew him, check out the testimonials at his retirement a few years ago:
https://carlobianchiandcide.wordpress.com/2015/11/03/20yearsofthecidesummerschoolofeconometrics/
Tuesday, August 4, 2020
Saturday, August 1, 2020
2020 Arnold Zellner Award to Wayne Gao
Absolutely delighted to help spread the word that my young colleague Wayne Gao has won the 2020 Arnold Zellner Thesis Award in Econometrics and Statistics, for his Yale University dissertation "Essays in Network and Panel Modeling." The Zellner Award is given annually for the best Ph.D. thesis dealing with an applied problem in Business and Economic Statistics. It is intended to recognize outstanding work by promising young researchers in the field.
Check out the past recipients below. The list reads like a who's who of the past 25 years!
2019
Max TabordMeehan for the Northwestern University thesis "Essays in Econometrics".
Honorable Mention:
Vishal Kamat for the Northwestern University thesis "Essays in Microeconometrics".
Vira Semenova for the Massachusetts Institute of Technology thesis “Essays in Econometrics and Machine Learning”.
Zifeng Zhao for the University of WisconsinMadison thesis "Modeling Time Series via Copula and Extreme Value Theory”.
2018
Recipient:
Laura Liu for the University of Pennsylvania thesis "Point and Density Forecasts in Panel Data Models".
Honorable Mention:
Daniel R. Kowal for the Cornell University thesis "Bayesian Methods for Functional and Time Series Data".
2017
Recipient:
Rogier Quaedvlieg, for Maastricht University School of Business and Economics thesis "Risk and Uncertainty".
Geert Mesters for the Vrije University thesis "Essays on Nonlinear Panel Time Series Models".
Honorable Mentions:
Mingli Chen for the Boston University thesis "Research Related to HighDimensional Econometrics".
2016
Recipient:
Pedro H. C. Sant'Anna, for the Universidad Carlos III de Madrid thesis "Essays on Duration and Count Data Models".
2015
Recipient:
Tim Christensen, for the Yale University thesis "Essays in Nonparametric Econometrics".
Honorable Mentions:
Rasmus Varneskov, for the Aarhus University thesis "Econometric Analysis of Volatility in Financial Additive Noise Models."
Dong Hwan Oh, for the Duke University thesis, "Copulas for High Dimensions: Models, Estimation, Inference, and Applications."
2014
Recipient:
Joachim Freyberger, for the Northwestern University thesis "Essays on Models with Endogeneity."
Honorable mentions:
Brendan Kline, for the Northwestern University thesis "Essays on the Econometrics of Games"
SeoJeong Lee, for the University of WisconsinMadison thesis "MisspecificationRobust Bootstrap for Moment Condition Models"
Minjing Tao, for the University of WisconsinMadison thesis "Large Volatility Matrix Inference Based on Highfrequency Financial Data"
2013
Recipient:
Xin Tong, for the Princeton University thesis, "Learning with Asymmetry, High Dimension and Social Networks"
Honorable Mention:
Rob Hall, for the Carnegie Mellon University thesis, "New Statistical Applications for Differential Privacy"
2012
Recipient:
Alex Torgovitsky, for the Yale University thesis, "Essays in Econometric Theory."
Honorable Mention:
Zhipeng Liao, for the Yale University thesis, "Shrinkage Methods for Automated Econometric Model Determination."
2011
Recipient:
Kirill Evdokimov, for the Yale University thesis "Essays on Nonparametric and Semiparametric Econometric Models."
Honorable Mention:
Xu Cheng (2010 dissertation from Yale University) and Bryan Kelly (2010 dissertation from New York University)
2010
CoRecipients:
Francesco Bianchi, for the Princeton thesis "Three Essays in Macroeconometrics," (PDF file).
Roopesh Ranjan, for the University of Washington thesis "Combining and Evaluating Probabilistic Forecasts," (PDF file).
2009
Recipient:
Amanda Ellen Kowalski, for the MIT thesis "Essays on Medical Care Using Semiparametric and Structural Econometrics" (PDF file, approx 1.02 Meg).
Honorable Mention:
Xun Tang, for the Northwestern University thesis "Essays in Empirical Auctions and Partially Identified Econometric Models," (PDF file, approx 1.23 Meg).
2008
Recipient:
Victor Todorov, for the Duke thesis "Jump Processes in Finance: Modeling, Simulation, Inference, and Pricings" (PDF file, approx 1.8 Meg).
Honorable Mention:
Andriy Norets, for the University of Iowa thesis "Bayesian Inference for Dynamically Discrete Choice Models".
2007
Recipient:
Panle Jia, for the Yale thesis "Entry and Competition in the Retail and Service Industries" (PDF file, approx 740 KB).
Honorable Mention:
Azeem M. Shaikh, for the Stanford University thesis, "Inference for Partially Identified Econometric Models," (PDF file, approx 980 KB).
2006
Recipient:
Philipp SchmidtDengler, for the Yale thesis "Empirical Analysis of Dynamic Models With Multiple Agents" (PDF file, approx 741 KB).
Honorable Mentions:
Zhongjun Qu for the Boston University thesis "Essays on Structural Change, Long Memory and Cointegration," (PDF file, approx 2.9 Meg).
Stephen P. Ryan for the Duke University thesis "Environmental Regulation in a Concentrated Industry" (PDF file, approx 1.0 Meg).
2005
Recipient:
Motohiro Yogo for the Harvard thesis "Essays on Consumption and Expected Returns" (PDF file, approx 1.0 Meg).
Honorable Mentions:
Morten Ø. Nielsen, for the University of Aarhus (Denmark) thesis, "Multivariate Fractional Integration and Cointegration," (PDF file, approx 2.2 Meg).
Giorgio E. Primiceri, for the Princeton University thesis, "The Effect of Stabilization Policy on U.S. Postwar Business Cycle Fluctuations" (PDF file, approx 1.5 Meg).
2004
Recipient:
Francesca Molinari for the Northwestern University thesis "Contaminated, Corrupted and Missing Data" (PDF file, approx 1.2 Meg).
Honorable Mentions:
Rebecca Hellerstein, for the University of California, Berkely thesis, "Empirical Essays on Vertical Contracts, Exchange Rates, and Monetary Policy," (PDF file, approx 550K).
Andrew Patton, for the University of California, San Diego thesis, "Applications of Copula Theory in Financial Econometrics," (PDF file, approx 1.5 Meg).
2003
Recipient:
Jin Gyo Kim for the University of Toronto thesis "Three Essays on Bayesian Choice Models" (PDF file, approx 4.3 Meg).
2002
Recipient:
Arie Beresteau for the Northwestern University thesis "Nonparametric Estimation of Supermodular Regression Functions with Applications to the Telecommunications Industry" (PDF file, approx 950K).
Honorable Mention:
Govert E. Bijwaard for the Free University (Amsterdam) thesis "Rank Estimation of Duration Models" (PDF file, approx 893K).
2001
CoRecipients:
Mikhail Chernov for the Pennsylvania State University thesis "Essays in Financial Econometrics", available in PDF format, (approx 1.45 Meg).
Monika Piazzesi for the Stanford University thesis "Essays in Monitary Policy and Asset Pricing", available in PDF format, (approx 854K).
2000
Recipient:
Elie T. Tamer, for the Northwestern University thesis "Studies in Incomplete Econometric Models", which includes material from the following papers: "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," available in PDF format (approx 4.93 Meg) and "Inference on Regressions with Interval Data on a Regressor or Outcome," available in PDF format (approx 258K).
Honorable Mentions:
Alberto Abadie, for the MIT thesis "Semiparametric Instrumental Variable Methods for Causal Response Models," available in PostScript format (approx 816K).
Han Hong, for the Stanford University thesis "Equilibrium and Econometric Model of Ascending Auctions," available in PDF format (approx 909K).
1999
CoRecipients:
Qiang Dai, for the Stanford University thesis "Specification Analysis of Affine Term Structure Models," available in PostScript (approx 594K) and PDF (approx 874K) formats.
Keisuke Hirano, for the Harvard University thesis "Essays on the Econometric Analysis of Panel Data," available on his research papers site.
1998
Recipient:
Patrick L. Bajari, for the University of Minnesota thesis "The First Price Sealed Bid Auction with Asymmetric Bidders: Theory with Applications."
Honorable Mentions:
Tong Li, for the University of Southern California thesis "Affiliated Private Values in OCS Wildcat Auctions,"
Ahmet K. Tahmiscioglu, for the University of Southern California thesis "A Bayesian Analysis of Pooling CrossSection and Time Series Data: An Investigation of Company Investment Behavior."
1997
Recipient:
Jeffrey Currie, for the University of Chicago thesis "The Geographic Extent of the Market: Theory and Application to U.S. Petroleum Markets."
Honorable Mentions:
Jason Abrevaya, for the MIT thesis "Semiparametric Estimation Methods for Nonlinear Panel Data Models and Mismeasured Dependent Variables,"
Stephen Gray, for the Stanford thesis "Essays in Financial Economics."
1996
Recipient:
Ekaterina Kyriazidou, for the Northwestern University thesis "Essays in Estimation and Testing of Econometric Models." available in PDF format (approx 1.22 Meg).
Honorable Mention:
Graham Elliot, for the Harvard University thesis "Application of Local to Unity Asymptotic Theory to Time Series Regression."
1995
Recipient:
Marjorie Rosenberg, for the University of Michigan thesis "A Hierarchical Bayesian Model of the Rate of NonAcceptable Inpatient Hospital Utilization.", which led to the paper "A Statistical Control Model for Utilization Management Programs", available in PDF format.
Honorable Mention:
Phillip Braun, for the University of Chicago thesis "Asset Pricing and Capital Investment."
1994
Recipient:
Geert Bekaert, for the Northwestern University thesis "Empirical Analysis of Foreign Exchange Markets: General Equilibrium Perspectives."
Honorable Mention:
Yacine AïtSahalia, for the MIT thesis "Nonparametric Functional Estimation with Applications to Financial Models," which includes material from the following papers: "Nonparametric Pricing of Interest Rate Derivative Structures," available in PDF format (approx 1.66 Meg) and "Testing Continuous Time Models of the Spot Interest Rate" available in PDF format (approx 1.66 Meg)
Check out the past recipients below. The list reads like a who's who of the past 25 years!
2019
Max TabordMeehan for the Northwestern University thesis "Essays in Econometrics".
Honorable Mention:
Vishal Kamat for the Northwestern University thesis "Essays in Microeconometrics".
Vira Semenova for the Massachusetts Institute of Technology thesis “Essays in Econometrics and Machine Learning”.
Zifeng Zhao for the University of WisconsinMadison thesis "Modeling Time Series via Copula and Extreme Value Theory”.
2018
Recipient:
Laura Liu for the University of Pennsylvania thesis "Point and Density Forecasts in Panel Data Models".
Honorable Mention:
Daniel R. Kowal for the Cornell University thesis "Bayesian Methods for Functional and Time Series Data".
2017
Recipient:
Rogier Quaedvlieg, for Maastricht University School of Business and Economics thesis "Risk and Uncertainty".
Geert Mesters for the Vrije University thesis "Essays on Nonlinear Panel Time Series Models".
Honorable Mentions:
Mingli Chen for the Boston University thesis "Research Related to HighDimensional Econometrics".
2016
Recipient:
Pedro H. C. Sant'Anna, for the Universidad Carlos III de Madrid thesis "Essays on Duration and Count Data Models".
2015
Recipient:
Tim Christensen, for the Yale University thesis "Essays in Nonparametric Econometrics".
Honorable Mentions:
Rasmus Varneskov, for the Aarhus University thesis "Econometric Analysis of Volatility in Financial Additive Noise Models."
Dong Hwan Oh, for the Duke University thesis, "Copulas for High Dimensions: Models, Estimation, Inference, and Applications."
2014
Recipient:
Joachim Freyberger, for the Northwestern University thesis "Essays on Models with Endogeneity."
Honorable mentions:
Brendan Kline, for the Northwestern University thesis "Essays on the Econometrics of Games"
SeoJeong Lee, for the University of WisconsinMadison thesis "MisspecificationRobust Bootstrap for Moment Condition Models"
Minjing Tao, for the University of WisconsinMadison thesis "Large Volatility Matrix Inference Based on Highfrequency Financial Data"
2013
Recipient:
Xin Tong, for the Princeton University thesis, "Learning with Asymmetry, High Dimension and Social Networks"
Honorable Mention:
Rob Hall, for the Carnegie Mellon University thesis, "New Statistical Applications for Differential Privacy"
2012
Recipient:
Alex Torgovitsky, for the Yale University thesis, "Essays in Econometric Theory."
Honorable Mention:
Zhipeng Liao, for the Yale University thesis, "Shrinkage Methods for Automated Econometric Model Determination."
2011
Recipient:
Kirill Evdokimov, for the Yale University thesis "Essays on Nonparametric and Semiparametric Econometric Models."
Honorable Mention:
Xu Cheng (2010 dissertation from Yale University) and Bryan Kelly (2010 dissertation from New York University)
2010
CoRecipients:
Francesco Bianchi, for the Princeton thesis "Three Essays in Macroeconometrics," (PDF file).
Roopesh Ranjan, for the University of Washington thesis "Combining and Evaluating Probabilistic Forecasts," (PDF file).
2009
Recipient:
Amanda Ellen Kowalski, for the MIT thesis "Essays on Medical Care Using Semiparametric and Structural Econometrics" (PDF file, approx 1.02 Meg).
Honorable Mention:
Xun Tang, for the Northwestern University thesis "Essays in Empirical Auctions and Partially Identified Econometric Models," (PDF file, approx 1.23 Meg).
2008
Recipient:
Victor Todorov, for the Duke thesis "Jump Processes in Finance: Modeling, Simulation, Inference, and Pricings" (PDF file, approx 1.8 Meg).
Honorable Mention:
Andriy Norets, for the University of Iowa thesis "Bayesian Inference for Dynamically Discrete Choice Models".
2007
Recipient:
Panle Jia, for the Yale thesis "Entry and Competition in the Retail and Service Industries" (PDF file, approx 740 KB).
Honorable Mention:
Azeem M. Shaikh, for the Stanford University thesis, "Inference for Partially Identified Econometric Models," (PDF file, approx 980 KB).
2006
Recipient:
Philipp SchmidtDengler, for the Yale thesis "Empirical Analysis of Dynamic Models With Multiple Agents" (PDF file, approx 741 KB).
Honorable Mentions:
Zhongjun Qu for the Boston University thesis "Essays on Structural Change, Long Memory and Cointegration," (PDF file, approx 2.9 Meg).
Stephen P. Ryan for the Duke University thesis "Environmental Regulation in a Concentrated Industry" (PDF file, approx 1.0 Meg).
2005
Recipient:
Motohiro Yogo for the Harvard thesis "Essays on Consumption and Expected Returns" (PDF file, approx 1.0 Meg).
Honorable Mentions:
Morten Ø. Nielsen, for the University of Aarhus (Denmark) thesis, "Multivariate Fractional Integration and Cointegration," (PDF file, approx 2.2 Meg).
Giorgio E. Primiceri, for the Princeton University thesis, "The Effect of Stabilization Policy on U.S. Postwar Business Cycle Fluctuations" (PDF file, approx 1.5 Meg).
2004
Recipient:
Francesca Molinari for the Northwestern University thesis "Contaminated, Corrupted and Missing Data" (PDF file, approx 1.2 Meg).
Honorable Mentions:
Rebecca Hellerstein, for the University of California, Berkely thesis, "Empirical Essays on Vertical Contracts, Exchange Rates, and Monetary Policy," (PDF file, approx 550K).
Andrew Patton, for the University of California, San Diego thesis, "Applications of Copula Theory in Financial Econometrics," (PDF file, approx 1.5 Meg).
2003
Recipient:
Jin Gyo Kim for the University of Toronto thesis "Three Essays on Bayesian Choice Models" (PDF file, approx 4.3 Meg).
2002
Recipient:
Arie Beresteau for the Northwestern University thesis "Nonparametric Estimation of Supermodular Regression Functions with Applications to the Telecommunications Industry" (PDF file, approx 950K).
Honorable Mention:
Govert E. Bijwaard for the Free University (Amsterdam) thesis "Rank Estimation of Duration Models" (PDF file, approx 893K).
2001
CoRecipients:
Mikhail Chernov for the Pennsylvania State University thesis "Essays in Financial Econometrics", available in PDF format, (approx 1.45 Meg).
Monika Piazzesi for the Stanford University thesis "Essays in Monitary Policy and Asset Pricing", available in PDF format, (approx 854K).
2000
Recipient:
Elie T. Tamer, for the Northwestern University thesis "Studies in Incomplete Econometric Models", which includes material from the following papers: "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," available in PDF format (approx 4.93 Meg) and "Inference on Regressions with Interval Data on a Regressor or Outcome," available in PDF format (approx 258K).
Honorable Mentions:
Alberto Abadie, for the MIT thesis "Semiparametric Instrumental Variable Methods for Causal Response Models," available in PostScript format (approx 816K).
Han Hong, for the Stanford University thesis "Equilibrium and Econometric Model of Ascending Auctions," available in PDF format (approx 909K).
1999
CoRecipients:
Qiang Dai, for the Stanford University thesis "Specification Analysis of Affine Term Structure Models," available in PostScript (approx 594K) and PDF (approx 874K) formats.
Keisuke Hirano, for the Harvard University thesis "Essays on the Econometric Analysis of Panel Data," available on his research papers site.
1998
Recipient:
Patrick L. Bajari, for the University of Minnesota thesis "The First Price Sealed Bid Auction with Asymmetric Bidders: Theory with Applications."
Honorable Mentions:
Tong Li, for the University of Southern California thesis "Affiliated Private Values in OCS Wildcat Auctions,"
Ahmet K. Tahmiscioglu, for the University of Southern California thesis "A Bayesian Analysis of Pooling CrossSection and Time Series Data: An Investigation of Company Investment Behavior."
1997
Recipient:
Jeffrey Currie, for the University of Chicago thesis "The Geographic Extent of the Market: Theory and Application to U.S. Petroleum Markets."
Honorable Mentions:
Jason Abrevaya, for the MIT thesis "Semiparametric Estimation Methods for Nonlinear Panel Data Models and Mismeasured Dependent Variables,"
Stephen Gray, for the Stanford thesis "Essays in Financial Economics."
1996
Recipient:
Ekaterina Kyriazidou, for the Northwestern University thesis "Essays in Estimation and Testing of Econometric Models." available in PDF format (approx 1.22 Meg).
Honorable Mention:
Graham Elliot, for the Harvard University thesis "Application of Local to Unity Asymptotic Theory to Time Series Regression."
1995
Recipient:
Marjorie Rosenberg, for the University of Michigan thesis "A Hierarchical Bayesian Model of the Rate of NonAcceptable Inpatient Hospital Utilization.", which led to the paper "A Statistical Control Model for Utilization Management Programs", available in PDF format.
Honorable Mention:
Phillip Braun, for the University of Chicago thesis "Asset Pricing and Capital Investment."
1994
Recipient:
Geert Bekaert, for the Northwestern University thesis "Empirical Analysis of Foreign Exchange Markets: General Equilibrium Perspectives."
Honorable Mention:
Yacine AïtSahalia, for the MIT thesis "Nonparametric Functional Estimation with Applications to Financial Models," which includes material from the following papers: "Nonparametric Pricing of Interest Rate Derivative Structures," available in PDF format (approx 1.66 Meg) and "Testing Continuous Time Models of the Spot Interest Rate" available in PDF format (approx 1.66 Meg)
Thursday, July 30, 2020
Dirty Secrets of Scientific Peer Review
Is peer review a joke? Surely not. Peer review often makes good papers better and makes bad papers go away. Of course we all wish that "good" and "bad" papers could be so cleanly and cavalierly classified.
Conversely, is peer review something to rely upon as firmly establishing scientific credibility? Now THAT'S the joke. Blind acceptance of "peer reviewed" as "trustworthy" is like blind acceptance of myriad other naive administrative checkthebox "solutions"  a dubious strategy at best. I fear, however, that significant parts of the public have been fooled into thinking that "passing peer review" equals "trustworthy", and that "not yet having passed peer review" equals "not yet trustworthy". The real test is whether a paper influences the course of thought in the medium and long run. Who decides that? The fiercely competitive market for ideas/researchers is highly, if not perfectly, efficient, and it usually sorts things out correctly.
For young researchers:
Immediately put your new paper in a visible working paper series like SSRN or arXiv, and let the market take over. But of course work hard simultaneously to get your paper published in a top place. The refereeing process will (hopefully) improve it, and having the imprimatur of Top Journal X will send a valuable signal to the profession. Just don't be too sad, or too worried, if it doesn't work out as hoped with Top Journal X.
Conversely, is peer review something to rely upon as firmly establishing scientific credibility? Now THAT'S the joke. Blind acceptance of "peer reviewed" as "trustworthy" is like blind acceptance of myriad other naive administrative checkthebox "solutions"  a dubious strategy at best. I fear, however, that significant parts of the public have been fooled into thinking that "passing peer review" equals "trustworthy", and that "not yet having passed peer review" equals "not yet trustworthy". The real test is whether a paper influences the course of thought in the medium and long run. Who decides that? The fiercely competitive market for ideas/researchers is highly, if not perfectly, efficient, and it usually sorts things out correctly.
For young researchers:
Immediately put your new paper in a visible working paper series like SSRN or arXiv, and let the market take over. But of course work hard simultaneously to get your paper published in a top place. The refereeing process will (hopefully) improve it, and having the imprimatur of Top Journal X will send a valuable signal to the profession. Just don't be too sad, or too worried, if it doesn't work out as hoped with Top Journal X.
Monday, July 27, 2020
The Pandemic Recession as a Giant Outlier
When I earlier blogged on Frank Schorfheide and Dongho Song (2020), I was focusing on exact methods for mixedfrequency data in Bayes vs. frequentist forecasting and nowcasting.
Quite apart from that, SchorfheideSong provides eyeopening discussion of a key issue in "forecasting through" the Pandemic Recession (PR), namely how to treat the PR data in estimation. They find that "... forecasts based on a precrisis estimate of the VAR using data up until the end of 2019 appear to be more stable and reasonable than forecasts based on a sequence of recursive estimates that include the most recent observations."
The point is that the PR is in many respects a massive outlier, so that one has to think hard about what to do with it in estimation. That is, as always one wants to fit signal, not noise, and the PR is in certain respects a massive burst of noise, capable of severely distorting parameter estimates and hence forecasts and nowcasts.
Michele Lenza and Giorgio Primiceri address the same issue in another fine new paper, “How to Estimate a VAR after March 2020”. Their focus differs in lots of interesting ways, but the message is the same: One way or another, we need to heavily downweight the PR data.
The emerging message is a big deal: One should be careful before attempting to reestimate forecasting and nowcasting models with data spanning the PR. Of course at this point there remain many open questions, but it's great to see the issues raised.
Quite apart from that, SchorfheideSong provides eyeopening discussion of a key issue in "forecasting through" the Pandemic Recession (PR), namely how to treat the PR data in estimation. They find that "... forecasts based on a precrisis estimate of the VAR using data up until the end of 2019 appear to be more stable and reasonable than forecasts based on a sequence of recursive estimates that include the most recent observations."
The point is that the PR is in many respects a massive outlier, so that one has to think hard about what to do with it in estimation. That is, as always one wants to fit signal, not noise, and the PR is in certain respects a massive burst of noise, capable of severely distorting parameter estimates and hence forecasts and nowcasts.
Michele Lenza and Giorgio Primiceri address the same issue in another fine new paper, “How to Estimate a VAR after March 2020”. Their focus differs in lots of interesting ways, but the message is the same: One way or another, we need to heavily downweight the PR data.
The emerging message is a big deal: One should be careful before attempting to reestimate forecasting and nowcasting models with data spanning the PR. Of course at this point there remain many open questions, but it's great to see the issues raised.
Wednesday, July 22, 2020
Online Econometrics Seminars
In my view it makes little sense for individual university departments to plod forward with their econometrics seminars virtually. (Do we really want to watch twenty seminars from twenty departments each week?) Sponsorship of a few seminars by a few broad umbrella organizations (societies, associations, ...) makes much more sense. The Society for Financial Econometrics (SoFiE) has done it well, here. So has the International Association for Applied Econometrics (IAAE), here, as has the Chamberlain Seminar, here. All those seminars post recordings/slides/papers.
I would like to see a few more. Certainly there should be something explicitly and exclusively on predictive modeling in its relation to time series and machine learning. Also, although there are several online "climate economics" seminars, I would like to see something explicitly "climate econometrics", in the style pioneered here.
I would like to see a few more. Certainly there should be something explicitly and exclusively on predictive modeling in its relation to time series and machine learning. Also, although there are several online "climate economics" seminars, I would like to see something explicitly "climate econometrics", in the style pioneered here.
Tuesday, July 21, 2020
Online Economics Seminars
An interesting and useful (and incomplete but growing) list of online economics seminars is here. Many archive their seminar recordings and slides. The downside is overabundance. (And you thought you were bombarded with too many seminar options before the pandemic!) More on that in a future post.
Thursday, July 16, 2020
Evaluating Interval Forecasts
Evaluation of point and density forecasts is moreorless straightforward. Interval forecasts are another matter entirely. We raised and tried to resolve (some of) the issues here. Now, in a new paper, "Scoring Interval Forecasts: EqualTailed, Shortest, and Modal Interval", Brehmer and Gneiting make major progress. The shortest interval fails to be elicitable! Their eventual conclusion (p. 14) precisely matches my own view: "In many ways, interval forecasts can be seen as an intermediate stage in the
ongoing, transdiciplinary transition from point forecasts to fully probabilistic or
distribution forecasts...Indeed, probabilistic forecasts in the
form of predictive distributions are the gold standard, as they allow for fullfledged decision making and wellunderstood, powerful evaluation methods are available..."
Scoring Interval Forecasts: EqualTailed, Shortest, and Modal Interval
We consider different types of predictive intervals and ask whether they are elicitable, i.e. are unique minimizers of a loss or scoring function in expectation. The equaltailed interval is elicitable, with a rich class of suitable loss functions, though subject to either translation invariance, or positive homogeneity and differentiability, the Winkler interval score becomes a unique choice. The modal interval also is elicitable, with a sole consistent scoring function, up to equivalence. However, the shortest interval fails to be elicitable relative to practically relevant classes of distributions. These results provide guidance in interval forecast evaluation and support recent choices of performance measures in forecast competitions.
Comments:  22 pages 
Subjects:  Statistics Theory (math.ST) 
MSC classes:  62C05, 91B06 
Cite as:  arXiv:2007.05709 [math.ST] 
(or arXiv:2007.05709v1 [math.ST] for this version) 
Tuesday, July 14, 2020
Spurious Factor Analysis
This abstract definitely produced one of those great "ah ha!" moments, at least for me. So obvious once someone points it out. Thanks Alexei and Chen.
I'm hungry for more.
With I(1) regression we have:
Q: When will regressions with I(1) variables not produce spurious results?
A: When the variables are not only integrated but also cointegrated.
What is the analog here, with PCA? That is:
Q: When will PCA with highdim I(1) variables not produce spurious results?
A: ??? (I'm not yet sure. Maybe it's addressed in the paper, which I look forward to reading. Cointegration should again be part of the answer (maybe all of the answer?), as cointegration implies factor structure.)
I'm hungry for more.
With I(1) regression we have:
Q: When will regressions with I(1) variables not produce spurious results?
A: When the variables are not only integrated but also cointegrated.
What is the analog here, with PCA? That is:
Q: When will PCA with highdim I(1) variables not produce spurious results?
A: ??? (I'm not yet sure. Maybe it's addressed in the paper, which I look forward to reading. Cointegration should again be part of the answer (maybe all of the answer?), as cointegration implies factor structure.)
By:  Onatski, A.; Wang, C. 
Abstract:  This paper draws parallels between the Principal Components Analysis of factorless highdimensional nonstationary data and the classical spurious regression. We show that a few of the principal components of such data absorb nearly all the data variation. The corresponding scree plot suggests that the data contain a few factors, which is collaborated by the standard panel information criteria. Furthermore, the DickeyFuller tests of the unit root hypothesis applied to the estimated “idiosyncratic terms” often reject, creating an impression that a few factors are responsible for most of the nonstationarity in the data. We warn empirical researchers of these peculiar effects and suggest to always compare the analysis in levels with that in differences. 
Keywords:  Spurious regression, principal components, factor models, KarhunenLoève expansion. 
Date:  2020–01–13 
URL:  http://d.repec.org/n?u=RePEc:cam:camdae:2003&r=ecm 
Thursday, July 2, 2020
Outstanding New Financial Econometrics Book
Financial Econometric Modelling, by Stan Hurn, Vance L. Martin, Peter C. B. Phillips, and Jun Yu, has now been published by Oxford University Press, here.
It's very, very well done. The depth, breadth, and clarity of coverage are exceptional. It's completely up to date, very "2020". See for yourself; the front and back matter appear below (sans formatting).
Financial Econometric Modelling
Stan Hurn, Vance L. Martin, Peter C. B. Phillips, and Jun Yu
November 12, 2019
Preface
Financial econometrics is an exciting young discipline that began to take on
its present form around the turn of the millennium. The subject brings financial
theory and econometric methods together with the power of data
to advance our understanding of the global financial universe upon which
all modern economies depend. Two major developments underscored its
rapid growth and expanding capabilities. First, the massive importance of
wellfunctioning financial markets to the global economy and to global financial
stability was universally acknowledged following the dotcom bubble of
the late 1990s in the United States and the global financial crisis of 2008 coupled
with its prolonged aftermath. Second, modern methods of econometrics
emerged that proved equal to some of the special challenges presented by financial
data and the ideas of financial theory.
Among the most significant of these challenges are the complex interdependencies
of financial, commodity, and real estate markets, the dynamic and
spatial linkages within financial data, the random wandering behaviour of asset
prices, anomalies such as financial bubbles and market crashes in the data,
the difficulties in modelling rapidly changing volatility in financial returns,
the growth in high dimensional ultrahigh frequency data, and the attention
to market microstructure effects that all such data require. While not entirely
unique to financial data, these challenges presented the econometrics profession
with the need to refashion methods, develop new tools of inference,
and tackle a wide selection of new empirical goals associated with a growing
number of financial instruments and vast data sets being generated in the
financial world.
This book, like the subject itself, is motivated by all of these challenges. We
seek to provide a broad and gentle introduction to this rapidly developing
subject of financial econometrics where theory, measurement, and data play
equal roles in our development and where empirical applications occupy a
central position. Our target audiences are intermediate and advanced undergraduate
students, honours students who wish to learn about financial econometrics,
and postgraduate students with limited backgrounds in econometrics
who are doing masters courses designed to offer an introduction to finance
and its applications. We hope the book will also prove useful to practitioners
in the industry as an introductory reference source for relevant tools and
approaches to modern empirical work in finance.
Throughout the book special emphasis is placed on the exposition of core
concepts, their illustration using relevant financial data sets, and a handson
approach to learning by doing that involves practical implementation. The
guiding principle we have adopted is that only by working through plenty of
applications and exercises can a coherent understanding of the properties of
financial econometric models, interrelationships with the underlying finance
theory, and the role of econometric tools of inference be achieved.
Our philosophy has been to write a book on financial econometrics, not an
econometrics text that illustrates techniques with datasets drawn from finance.
Our goal is centred on the subject of financial econometrics explaining
how evidencedbased research in applied finance is conducted. Econometrics
is viewed as the vehicle that makes the ideas and theories about financial
markets face the reality of observations.
To ensure the book is self contained for a first course in financial econometrics,
some foundational theory and methods of relevant econometric technique
are provided. But the methods covered in this book travel along a customised
path designed to ease the reader’s transition from concepts and methods
to empirical work. The book tracks its way forward from data to modelling
through to estimation, inference, and prediction.
A consistent thematic throughout the book is to motivate each topic with
the presentation of relevant data. The journey begins with data and a simple
grounding in regression and inference. From this foundation, it moves on to
more advanced financial econometric methods that open up empirical applications
with many different types of data from various financial markets. The
path promises to keep readers motivated throughout their journey by means
of many examples and to reinforce their learning by extensive databased exercises.
Several introductory Appendices are included to assist students with
limited mathematics and no econometric background in understanding more
technical aspects of the discussion particularly in the second half of the book.
Organisation of the Book
Part I – Fundamentals – is designed to form the basis of a semester long first
course in financial econometrics directed at an introductory level. Technical
difficulty is kept to an absolute minimum with an emphasis on the data, financial
concepts, appropriate econometric methodology, and the intuition
that draws these essential components of modelling together. Methodology
is largely confined to descriptive methods and ordinary least squares regression,
a choice that limits the extent of the analysis and promotes heuristic discussion
on some topics which are revisited later in the book for a more complete
and rigorous development.
In Part II – Methods – the level of difficulty steps up slightly in treating the
relevant econometric estimation methods of instrumental variables, generalised
method of moments, and maximum likelihood. These core estimators
are used extensively throughout the second half of the book and knowledge
of them is a key asset in working through the later material. Also included in
Part II are methods that deal with panel data and models with latent factors.
A second course in financial econometrics might usefully begin with these
five chapters, taking Part I as a given foundation.
Part III – Topics – introduces a number of special topics in financial econometiv
rics, covering models of volatility, financial market microstructure, the econometrics
of options, and methods relating to extreme values and copulas. One
of the dominant features of financial time series is their volatility. Financial
theory and empirical experience both demonstrate that there is often much
less to explain in the levels of financial returns than there is to explain in their
variation. Accordingly, three chapters of the book are devoted to modelling
volatility. These chapters treat parametric univariate and multivariate models
of volatility and introduce the more recent nonparametric modelling approach
that is based on market realised volatility measured using high frequency
data.
As in any project of this nature, sacrifices were made to keep the length of the
book manageable. Some topics, for instance, are treated by example and illustration
within a chapter rather than by devoting an entire chapter to their
development. As a result the book is rich in real world examples drawn from
financial markets for stocks, fixed income securities, exchange rates, derivatives,
and real estate. As such, the coverage is intended to be extensive while
not treating every topic in the same depth.
Computation
A fundamental principle guiding the inclusion of material in this book is
whether the methods are available for easy implementation. In consequence,
all results reported in the book may be reproduced using existing software
packages like Stata and EViews.1 This choice is intended to enhance the usefulness
of the material for beginning students. In some cases the programming
languages in these packages need to be used to achieve full implementation
of the illustrations. Of course, for those who actively choose to learn by
programming themselves, the results are also reproducible in any of the common
matrix programming languages, such as R2. The numerical computations
reported in the book are primarily rounded versions of the results generated
using Stata.
The data files are all available for download from the book’s companion website
(https://global.oup.com/academic/instructors/finects) in Stata
format (.dta), EViews format (.wf1), comma delimited files (.csv), and as Excel
spreadsheets (.xlsx).
1Stata is the copyright of StataCorp LP www.stata.com and EViews is the copyright of IHSInc.
www.eviews.com.
2R is a free software environment for statistical computation and graphics which is part of the
GNU Project, see www.rproject.org.
Acknowledgements
Many colleagues, students, and research assistants have read and commented
on parts of the book and in some cases even taught from early versions of the
book. We are particularly grateful to Ahmad Bahir, Kit Baum, Jimmy Chan,
Han Chen, Ye Chen, Xiaohong Chen, Jieyang Chong, Adam Clements, Fulvio
Corsi, Mark Doolan, Ren´ee FryMcKibbin, Zhuo Huang, Marko Krause,
Bei Luo, Cheng Liu, Andrew Patton, Shuping Shi, Daniel Smith, Chrismin
Tang, Timo Ter¨asvirta, Stephen Thiele, Tomasz Wo´zniak and Lina Xu. A special
thank you goes to Annastiina Silvennoinen and Glen Wade who were relentless
in picking up typographical errors and factual inconsistencies, as well
as suggesting alternative ways of presenting material. All remaining errors
are the responsibility of the authors.
Stan Hurn, Vance L. Martin, Peter C. B. Phillips and Jun Yu
June 2019
Contents
I Fundamentals 1
1 Prices and Returns 3
1.1 What Is Financial Econometrics? . . . . . . . . . . . . . . . . . . 3
1.2 Financial Assets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Equity Prices and Returns . . . . . . . . . . . . . . . . . . . . . . 8
1.4 Stock Market Indices . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.5 Bond Yields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2 Financial Data 29
2.1 A First Look at the Data . . . . . . . . . . . . . . . . . . . . . . . 30
2.2 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.3 Percentiles and Value at Risk . . . . . . . . . . . . . . . . . . . . 45
2.4 The Efficient Market Hypothesis . . . . . . . . . . . . . . . . . . 48
2.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3 Linear Regression 57
3.1 The Capital Asset Pricing Model . . . . . . . . . . . . . . . . . . 58
3.2 A Multifactor CAPM . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.3 Properties of Ordinary Least Squares . . . . . . . . . . . . . . . . 67
3.4 Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.5 Measuring Portfolio Performance . . . . . . . . . . . . . . . . . . 80
3.6 Minimum Variance Portfolios . . . . . . . . . . . . . . . . . . . . 82
3.7 Event Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4 Stationary Dynamics 95
4.1 Stationarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.2 Univariate Time Series Models . . . . . . . . . . . . . . . . . . . 98
4.3 Autocorrelation and Partial Autocorrelations . . . . . . . . . . . 103
4.4 Mean Aversion and Reversion in Returns . . . . . . . . . . . . . 107
4.5 Vector Autoregressive Models . . . . . . . . . . . . . . . . . . . . 109
4.6 Analysing VARs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.7 DieboldYilmaz Spillover Index . . . . . . . . . . . . . . . . . . . 126
4.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
5 Nonstationarity 133
5.1 The RandomWalk with Drift . . . . . . . . . . . . . . . . . . . . 134
5.2 Characteristics of Financial Data . . . . . . . . . . . . . . . . . . 137
5.3 DickeyFuller Methods and Unit Root Testing . . . . . . . . . . . 140
5.4 Beyond the Simple Unit Root Framework . . . . . . . . . . . . . 147
5.5 Asset Price Bubbles . . . . . . . . . . . . . . . . . . . . . . . . . . 152
5.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
6 Cointegration 161
6.1 The Present Value Model and Cointegration . . . . . . . . . . . . 162
6.2 Vector Error Correction Models . . . . . . . . . . . . . . . . . . . 167
6.3 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
6.4 Cointegration Testing . . . . . . . . . . . . . . . . . . . . . . . . . 180
6.5 Parameter Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
6.6 Cointegration and the Gordon Model . . . . . . . . . . . . . . . 187
6.7 Cointegration and the Yield Curve . . . . . . . . . . . . . . . . . 192
6.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
7 Forecasting 205
7.1 Types of Forecasts . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
7.2 Forecasting Univariate Time Series Models . . . . . . . . . . . . 208
7.3 Forecasting Multivariate Time Series Models . . . . . . . . . . . 212
7.4 Combining Forecasts . . . . . . . . . . . . . . . . . . . . . . . . . 216
7.5 Forecast Evaluation Statistics . . . . . . . . . . . . . . . . . . . . 220
7.6 Evaluating the Density of Forecast Errors . . . . . . . . . . . . . 224
7.7 Regression Model Forecasts . . . . . . . . . . . . . . . . . . . . . 229
7.8 Predicting the Equity Premium . . . . . . . . . . . . . . . . . . . 230
7.9 Stochastic Simulation of Value at Risk . . . . . . . . . . . . . . . 237
7.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
II Methods 247
8 Instrumental Variables 249
8.1 The Exogeneity Assumption . . . . . . . . . . . . . . . . . . . . . 250
8.2 Estimating the RiskReturn Tradeoff . . . . . . . . . . . . . . . . 251
8.3 The General Instrumental Variables Estimator . . . . . . . . . . 255
8.4 Testing for Endogeneity . . . . . . . . . . . . . . . . . . . . . . . 259
8.5 Weak Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
8.6 Consumption CAPM . . . . . . . . . . . . . . . . . . . . . . . . . 266
8.7 Endogeneity and Corporate Finance . . . . . . . . . . . . . . . . 269
8.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
9 Generalised Method of Moments 277
9.1 Single Parameter Models . . . . . . . . . . . . . . . . . . . . . . . 278
9.2 Multiple Parameter Models . . . . . . . . . . . . . . . . . . . . . 281
9.3 OverIdentified Models . . . . . . . . . . . . . . . . . . . . . . . . 288
9.4 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
9.5 Properties of the GMM Estimator . . . . . . . . . . . . . . . . . . 299
9.6 Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
9.7 Consumption CAPM Revisited . . . . . . . . . . . . . . . . . . . 309
9.8 The CKLS Model of Interest Rates . . . . . . . . . . . . . . . . . 312
9.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316
10 Maximum Likelihood 323
10.1 Distributions in Finance . . . . . . . . . . . . . . . . . . . . . . . 324
10.2 Estimation by Maximum Likelihood . . . . . . . . . . . . . . . . 331
10.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334
10.4 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 342
10.5 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344
10.6 Quasi Maximum Likelihood Estimation . . . . . . . . . . . . . . 347
10.7 Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349
10.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357
11 Panel Data Models 365
11.1 Types of Panel Data . . . . . . . . . . . . . . . . . . . . . . . . . . 366
11.2 Reasons for Using Panel Data . . . . . . . . . . . . . . . . . . . . 368
11.3 Two Introductory Panel Models . . . . . . . . . . . . . . . . . . . 372
11.4 Fixed and Random Effects Panel Models . . . . . . . . . . . . . . 377
11.5 Dynamic Panel Models . . . . . . . . . . . . . . . . . . . . . . . . 386
11.6 Nonstationary Panel Models . . . . . . . . . . . . . . . . . . . . . 394
11.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400
12 Latent Factor Models 409
12.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410
12.2 Principal Components . . . . . . . . . . . . . . . . . . . . . . . . 412
12.3 A Latent Factor CAPM . . . . . . . . . . . . . . . . . . . . . . . . 420
12.4 Dynamic Factor Models: the Kalman Filter . . . . . . . . . . . . 423
12.5 A Parametric Approach to Factors . . . . . . . . . . . . . . . . . 431
12.6 Stochastic Volatility . . . . . . . . . . . . . . . . . . . . . . . . . . 434
12.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437
III Topics 445
13 Univariate GARCH Models 447
13.1 Volatility Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . 448
13.2 The GARCH Model . . . . . . . . . . . . . . . . . . . . . . . . . . 450
13.3 Asymmetric Volatility Effects . . . . . . . . . . . . . . . . . . . . 458
13.4 Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460
CONTENTS xi
13.5 The RiskReturn Tradeoff . . . . . . . . . . . . . . . . . . . . . . 465
13.6 Heatwaves and Meteor Showers . . . . . . . . . . . . . . . . . . 467
13.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470
14 Multivariate GARCH Models 477
14.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478
14.2 Early Covariance Estimators . . . . . . . . . . . . . . . . . . . . . 480
14.3 The BEKK Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 482
14.4 The DCC Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487
14.5 Optimal Hedge Ratios . . . . . . . . . . . . . . . . . . . . . . . . 493
14.6 Capital Ratios and Financial Crises . . . . . . . . . . . . . . . . . 495
14.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498
15 Realised Variance and Covariance 505
15.1 High Frequency Data . . . . . . . . . . . . . . . . . . . . . . . . . 506
15.2 Realised Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . 509
15.3 Integrated Variance . . . . . . . . . . . . . . . . . . . . . . . . . . 512
15.4 Microstructure Noise . . . . . . . . . . . . . . . . . . . . . . . . . 515
15.5 Bipower Variation and Jumps . . . . . . . . . . . . . . . . . . . . 518
15.6 Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522
15.7 The Realised GARCH Model . . . . . . . . . . . . . . . . . . . . 525
15.8 Realised Covariance . . . . . . . . . . . . . . . . . . . . . . . . . 527
15.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532
16 Microstructure Models 537
16.1 Characteristics of High Frequency Data . . . . . . . . . . . . . . 537
16.2 Limit Order Book . . . . . . . . . . . . . . . . . . . . . . . . . . . 538
16.3 Bid Ask Bounce . . . . . . . . . . . . . . . . . . . . . . . . . . . . 540
16.4 Information Content of Trades . . . . . . . . . . . . . . . . . . . . 543
16.5 Modelling Price Movements in Trades . . . . . . . . . . . . . . . 545
16.6 Modelling Durations . . . . . . . . . . . . . . . . . . . . . . . . . 551
16.7 Modelling Volatility in Transactions Time . . . . . . . . . . . . . 555
16.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558
17 Options 565
17.1 Option Pricing Basics . . . . . . . . . . . . . . . . . . . . . . . . . 566
17.2 The BlackScholes Option Price Model . . . . . . . . . . . . . . . 569
17.3 A First Look at Options Data . . . . . . . . . . . . . . . . . . . . 573
17.4 Estimating the BlackScholes Model . . . . . . . . . . . . . . . . 574
17.5 Testing the BlackScholes Model . . . . . . . . . . . . . . . . . . 581
17.6 Option Pricing and GARCH Volatility . . . . . . . . . . . . . . . 583
17.7 The MelickThomas Option Price Model . . . . . . . . . . . . . . 585
17.8 Nonlinear Option Pricing . . . . . . . . . . . . . . . . . . . . . . 587
17.9 Using Options to Estimate GARCH Models . . . . . . . . . . . . 588
17.10Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591
18 Extreme Values and Copulas 599
18.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 600
18.2 Evidence of Heavy Tails . . . . . . . . . . . . . . . . . . . . . . . 602
18.3 Extreme Value Theory . . . . . . . . . . . . . . . . . . . . . . . . 605
18.4 Modelling Dependence using Copulas . . . . . . . . . . . . . . . 611
18.5 Properties of Copulas . . . . . . . . . . . . . . . . . . . . . . . . . 614
18.6 Estimating Copula Models . . . . . . . . . . . . . . . . . . . . . . 621
18.7 MGARCH Model Using Copulas . . . . . . . . . . . . . . . . . . 624
18.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626
19 Concluding Remarks 633
A Mathematical Preliminaries 635
A.1 Summation Notation . . . . . . . . . . . . . . . . . . . . . . . . . 635
A.2 Expectations Operator . . . . . . . . . . . . . . . . . . . . . . . . 638
A.3 Differentiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 639
A.4 Taylor Series Expansions . . . . . . . . . . . . . . . . . . . . . . . 641
A.5 Matrix Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646
A.6 Transposition of a Matrix . . . . . . . . . . . . . . . . . . . . . . . 650
A.7 Symmetric Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . 651
B Properties of Estimators 661
B.1 Finite Sample Properties . . . . . . . . . . . . . . . . . . . . . . . 661
B.2 Asymptotic Properties . . . . . . . . . . . . . . . . . . . . . . . . 663
C Linear Regression Model in Matrix Notation 669
D Numerical Optimisation 673
E Simulating Copulas 677
Author index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 698
Subject index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 702
Author index
A¨ıtSahalia, Y., 341, 517, 518
Adams, R., 269, 270, 382
Akaike, H., 113
Aldrich, J., 323
Almeida, H., 269, 270, 382
Amenc, N., 477
Andersen, T.G, 517
Anderson, D.R., 218
Anderson, R.C., 269
Anderson, T.W., 390
Andreou, E., 237
Arellano, M., 390
Augustin, N.H., 218
Bae, K.H., 599
Bai, J., 419
Baillie, R.T., 493, 494
Baker, R., 262
Bali, T.G., 255
Baltagi, B.H, 400
Banerjee, A., 203
BarndorffNielsen, O.E., 508, 515,
518, 520, 521, 529, 538
Bartlett, M.S., 175, 349
Bates, J., 218, 235
Becker, R., 224
Bekaert, G., 67
Bera, A.K., 79, 229
Bergstrom, A.R., 161
Black, F., 569
Blundell, R., 390
Bollerslev, T., 448, 450, 457, 517,
525, 589
Bond, S., 390
Bonhomme, S., 372
Bouchard, JP., 544
Bound, J., 262
Bover, O., 390
Brennan, M.J., 315
Brockwell, P.J., 98, 106
Brownlees, C., 495, 498
Buckland, S.T., 218
Burnham, K.P., 218
Bykhovskaya, A., 150
Campbell, J.Y., 131, 154, 237
Carhart, M.M., 65
Chan, K.C., 313
Chao, J.C., 179
Cheng, X., 179
Chiang, M.H., 400
Choi, I., 399
Christoffersen, P.F., 464
Chu, C.J., 397
Clemen, R.T., 219
Clements, A.E., 224, 469
Clements, M.P., 219
Cochrane, J.H., 48, 237
Colacito, R., 224
Corbae, D., 199
Corsi, F., 522
Cox, J.C., 315, 329
Cram´er, H., 345
Davidson, R., 260
Davis, R.A., 98, 106
Diba, B.T., 154
Dickey, D.A., 140, 141, 146
Diebold, F.X., 24, 126, 132, 223, 229,
431, 441, 517
Dolado, J.J., 203
Doolan, M.B., 224
Dungey, M., 362, 467
Durbin, J., 129, 298
Eisler, Z., 544
Elliott, G., 149, 217, 219, 224
Engle, R.F., 78, 161, 173, 174, 224,
448–450, 467, 471, 487,
489, 495, 498, 542, 552,
555, 556
Epps, T.W., 528
Evans, G.W., 154
Fakhrutdinova, L., 467
Fama, E.F., 48, 64, 107, 403
AUTHOR INDEX 699
Fan, Y., 612
Ferreira, D., 269, 270, 382
Ferson, W.E., 268, 269
Fisher, R.A., 398
Flannery, M.J., 388, 406
Flemming, J., 224
French, K.R., 64, 107
Fuller, W.A., 140, 141
Galbraith, J.W., 203
Garratt, A., 219
Ghosh, A., 229
Ghysels, E., 255
Gibbons, M., 403
Gibson, M., 589
Glosten, L.R., 458
Goltz, F., 477
Goodhart, C.A.E., 467
Gordon, M.J., 187, 190, 201
Goyal, A., 231, 244
Granger, C.W.J., 115, 161, 174, 203,
218, 235
Grossman, H.I., 154
Gunther, T.A., 229
Haldane, A.G., 442
Hall, A.D., 544
Hall, A.R., 300
Hall, S.G., 442
Hamilton, J.D., 98
Hankins, K.W., 388, 406
Hannan, E.J., 113
Hansen, B.E., 174
Hansen, L.P., 298, 300, 302, 303, 311
Hansen, P.R., 462, 508, 518, 525,
529, 538
Harris, D., 98, 122, 292, 350, 427,
548, 587, 662
Harvey, A.C., 427, 493
Harvey, C.R., 268, 269
Hasbrouck, J., 543, 559
Hausman, J.A., 385, 545
Hautsch, N., 544
Heaton, J., 298
Hendry, D.F., 203, 219
Hodrick, R.J., 54
Hoerova, M., 67
Hoyem, K., 67
Hsiao, C., 390
Hu, WY., 67
Huang, R., 544
Huang, Z., 525
Hurn, A.S., 98, 122, 224, 292, 350,
427, 469, 548, 587, 662
Hwang, J., 173
Im, K.S., 397
Ingersoll, J.E., 315, 329
Ito, T., 467
Jacobs, J.P.A.M., 362
Jacod, J., 518
Jaeger, D., 262
Jaganathan, R., 458
Jarque, C.M., 79
Jensen, M.C., 80
Johansen, S., 174, 177, 184
Judson, R.A., 388
Kanniainen, J., 588, 589
Kao, C., 400
Kapetanious, G., 219
Karolyi, G.A., 313, 599
Kasparis, I., 237
Kelly, B., 489
Kim, M.J., 107
Kirby, C., 224
Kiviet, J., 388
Kockelkoren, J., 544
Koop, G., 219
Kwiatkowski, D.P., 151
L¨ utkepohl, H., 113, 122
Labhard, V., 219
Labys, P., 517
Lee, C.C., 150
Lee, J.H., 237
Levin, A., 397
Li, C., 24, 431, 441
Li, D.X., 600
Lim, KG., 199
Lin, B., 588, 589
700 BIBLIOGRAPHY
Lin, C.F., 397
Lin, W.L., 467
Liu, L., 517
Lo, A.W., 154, 545
Lo, D.K., 544
Longstaff, F.A., 313
Loretan, M., 173
Lunde, A., 462, 508, 518, 525, 529,
538
MacBeth, J.D., 403
MacKenzie, D., 600
MacKinlay, A.C., 154, 545
MacKinnon, J.G., 144, 181, 260
Maddala, G.S., 399
Malmendier, U., 67
Mann, H.B., 95, 109
Manresa, E., 372
Mariano, R.S., 223
Martin, V.L., 98, 122, 292, 350, 427,
548, 587, 662
Melick, W.R., 586
Merton, R.C., 251, 473, 536
Millar, R.B., 345
Mincer, J., 462
Moon, H.R., 400
Myers, R.J., 493, 494
Mykland, P.A., 517, 518
Nagel, S., 67
Nelson, C.R., 107, 431
Nelson, D.B., 459
Newbold, P., 203
Newey, W.K., 175, 349
Ng, S., 147, 419
Nickell, S., 387, 388
Ostdiek, B., 224
Ouliaris, S., 181, 199
Owen, A.L., 388
P´erignon, C., 45
Patton, A.J., 224, 471, 517, 525, 612
Peng, L., 255
Perron, P., 147, 150
Pesaran, M.H., 397
Phillips, P.C.B., 140, 150–152, 156,
173, 174, 179–181, 203,
237, 264, 372, 400
Poterba, J.M., 108
Pratt, J.W., 323
Prescott, E.C., 54
Price, S., 219
Quaedvlieg, R., 525
Quinn, B.G., 113
Rajan, R.G., 393, 406
Ramanathan, R., 218
Reeb, D.M., 269
Reinhart, C.M., 362
Rogoff, K.S., 362
Roley, V.V., 467
Roll, R., 541, 558
Ross, S.A., 315, 329, 403
Rothenberg, T.J., 149
Roulet, J., 54
Runkle, D, 458
Russell, J.R., 542, 552
Said, S.E., 146
Saikkonen, P., 173
Samuelson, P., 48
Sanders, A.B., 313
SantaClara, P., 255
Schmidt, P., 151
Scholes, M., 569
Schwartz, E.S., 315
Schwarz, G., 113
Shanken, J., 403
Sharpe,W.F., 80
Shek, H.H., 525
Shephard, N., 508, 515, 518, 520,
521, 529, 538
Sheppard, K., 224, 517
Shi, S., 156
Shi, Z., 372
Shiller, R.J., 67, 131
Shin, Y., 151, 397
Siegel, A.F., 431
Silvennoinen, A., 488, 493
Sims, C.A., 109
Singleton, K.J., 311
Smith, D.R., 45
Smith, J., 219
Solnik, B., 54
Spears, T., 600
Staiger, D., 262, 264
Stambaugh, R.F., 236
Startz, B., 107
Stigler, S.M., 323
Stock, J.H., 149, 173, 219, 262, 264,
274
Stulz, R.M., 599
Su, L., 372
Summers, L.H., 108
Sun, Y., 173
Tang, L., 477
Taylor, S.J., 435
Ter¨asvirta, T., 488, 493
Thiele, S., 493
Thomas, C.P., 586
Timmerman, A., 217, 224
Toda, H.Y., 180
Treynor, J.L., 80
Trivedi, P.K., 612, 678
Tsay, R.S., 229
Tse, Y.K., 488
Tsui, A.K.C., 488
Vahey, S.P., 219
Vaidyanathan, V., 477
Valkanov, R., 255
Van der Vaart, A.W., 345
Van der Waart, J.W., 301
Vasicek, O., 341
Volkov, V.V., 469
Wald, A., 95, 109
Wallis, K.F., 219
Watson, M.W., 173, 219
Welch, I., 231, 244
Wellner, J.A., 301
West, K.D., 175, 349
White, H., 78, 349
Winkler, R.L., 219
Wooldridge, J.M., 457
Wright, J.H., 274
Wu, S., 399
Wu, Y., 152
Yamamoto, Y., 180
Yang, H., 588, 589
Yaron, A., 298
Yilmaz, K., 126, 132
Yogo, M., 237, 264, 274
Yoo, B.S., 173
Yu, J., 152, 156
Zako¨ıan, J.M., 458
Zarnowitz, V., 462
Zhang, L., 517, 518
Zhou, H., 589
Zimmer, D.M., 612, 678
Zingales, L., 393, 406
Subject index
F test of significance, 74
t test of significance, 73
Adjusted coefficient of determination
(R2), 72
Akaike information criterion (AIC),
113
Asset returns
volatility clustering, 448–450
Asymptotic efficiency
GMM, 301
maximum likelihood, 345
ordinary least squares, 69
Asymptotic normality
GMM, 303
maximum likelihood, 346
ordinary least squares, 70
Augmented DickeyFuller test,
145–147
GLS detrending, 149
lag length selection, 147
Autocorrelation function, 103
Autocovariance, 103
Autoregressive (AR) model
estimation, 99
specification, 98
Autoregressive conditional duration
model, 551–555
Autoregressive moving average
(ARMA) model
estimation, 102
specification, 101
BFGS algorithm, 675
BHHH algorithm, 674
Bid ask bounce, 540–542
Bipower variation, 518–522
BlackScholes option pricing model
currency option, 573
equity option, 573
European call option, 569–572
European put option, 572
testing bias, 581
testing heteroskedasticity, 582
testing smiles and smirks, 582
BollerslevWooldridge standard
errors, 457
Bond yields, 36
term structure, 24
yield curve, 24
yield to maturity, 23
Capital asset pricing model (CAPM),
58–63
consumption (CCAPM), 309
Coefficient of determination (R2),
72
Cointegration, 163
fully modified estimation,
174–177
estimation, 173–180
Gordon model, 187–192
Johansen reduced rank regression
estimator, 177–180
modelling the yield curve,
192–198
present value model, 163–167
testing, 180–187
testing hypotheses on cointegrating
parameters, 186
Consistency
GMM, 301
instrumental variables, 259
maximum likelihood, 345
ordinary least squares, 68
Consumption capital asset pricing
model (CCAPM), 266–
269
Copulas
t copula, 616
Clayton copula, 617
estimating copula models,
621–624
Frank copula, 618
SUBJECT INDEX 703
Gaussian copula, 614
Gumbel copula, 618
measuring tail dependence,
618–621
modelling dependence using
copulas, 611–614
properties of copulas, 614–621
Diagnostic tests on disturbances
ARCH, 78
autocorrelation, 76
heteroskedasticity, 77
normality, 79
DickeyFuller test, 140–145
DieboldMariano test, 223
DieboldYilmaz Spillover Index,
125–128
Dividends
discounted future stream of,
34
dividend yield, 34
Durations, 39
Dynamic factor models, 423–429
Efficient market hypothesis, 48–51,
134
return predictability, 48
variance ratio, 50
Endogeneity and corporate finance,
269–272
Equilibrium dynamics, 164
Equity prices, 30–32
effect of dividends, 10
effect of stock splits, 11
quoted prices, 8
Event analysis, 85–87
Extreme value distribution
distribution types, 606–607
Hill estimator, 608
maximum likelihood estimation,
609–610
VaR calculation, 611
Extreme value theory, 605–611
Financial assets
cash, 6
derivatives, 7
equities, 7
Eurodollar deposits, 6
fixedincome securities, 6
Treasury bills, 6
Forecasting
AR(1) model, 208–211
AR(2) model, 211
bivariate VAR(1) model, 213–
214
bivariate VECM(1) model,
214–216
combining forecasts, 216–219
density forecast evaluation,
224–229
ex ante forecasts, 206
ex post forecasts, 207
forecast evaluation, 220–224
predictive regressions, 229–
237
properties, 212
Fully modified estimation OLS,
174–177
GibbonsRossShanken test, 371,
403
Gordon model, 187–192
Granger causality, 115
Hannan information criterion
(HIC), 113
HansenSargan J test, 306
High frequency data
characteristics, 537–538
cleaning, 507–508
limit order book, 538–540
transactions data, 506–509
Idiosyncratic risk, 59
Impulse response analysis, 116
Instrumental variables estimator
multiple endogenous regressors,
258–259
twovariable regression model,
254
Integrated process, 137
704 BIBLIOGRAPHY
Integrated variance, 512–515
Intertemporal CAPM, 251–255
Invariance
maximum likelihood, 346
Jensen’s alpha, 80
Johansen reduced rank regression
estimator, 177–180
Johansen tests of cointegration,
182–185
Kalman filter
estimation, 428
factor extraction, 428–429
multivariate, 427
univariate, 424–426
Lag length selection
information criteria, 113–114
Lagrange multiplier (LM) test
test for ARCH, 470
Lagrange multiplier test, 351–352
Leptokurtosis, 38
Likelihood ratio test, 351
Limited dependent variables, 545–
551
linear probability model, 547
ordered probit, 549–551
probit, 546–549
Linear regression model, 58
disturbance term diagnostics,
76–80
explanatory variable diagnostics,
73–75
matrix notation, 669–670
Marginal expected shortfall, 495–
498
Mean absolute error (MAE), 221
Mean absolute percentage error
(MAPE), 221
Mean square error (MSE), 221
Measuring portfolio performance
Jensen’s alpha, 80
Sharpe ratio, 80
Treynor ratio, 80
MelickThomas option pricing
model, 585–587
Microstructure noise, 515–518
Minimum variance portfolio, 82–
85
Modelling the yield curve, 192–198
Moving average (MA) model
estimation, 100
specification, 100
Multifactor CAPM
instrumental variables estimation,
255–258
Multifactor CAPM, 63–67
Multiple regression model, 63
NelsonSiegel parametric factor
model, 431–434
News impact curve (NIC), 459
NewtonRaphson algorithm, 674
Nonlinear option pricing model,
587–588
Nonstationary process, 137
Optimal hedge ratio, 493–495
Options
BlackScholes option pricing
model, 569–573
data, 573–574
GARCH volatility, 583–585
Greeks, 578–581
historical volatility, 575–576
implied volatility, 576–578
pricing basics, 566–569
Order of integration, 137
Order statistics, 602–603
Ordinary least squares estimator,
60–61
Panel data
ArellanoBond estimator, 390
common effects model, 374–
377
fixed effects model, 378–380
Hausman test, 383–385
Nickell bias, 386
no common effects model,
372–374
SUBJECT INDEX 705
panel cointegration, 398–400
panel unit roots, 396–398
random effects model, 380–
382
system GMM estimator, 390
Partial autocorrelation function,
106
Percentiles, 45
Predicting the equity premium,
230–237
Principal component analysis,
412–420
estimation, 413–417
factor extraction, 417–418
model specification, 412–413
testing, 419–420
Probability integral transform
(PIT), 224
Properties of GMM estimators,
299–305
Properties of instrumental variable
estimators, 259
Properties of instrumental variables
estimators, 254
Properties of maximum likelihood
estimators, 344–347
Properties of ordinary least squares
estimators, 67–71
Quasi maximum likelihood estimator,
347
Random walk with drift model,
134–137
Realised covariance, 527–531
refresh time synchronisation,
529–531
Realised variance
computing, 509–511
forecasting, 522–525
Residualbased tests of cointegration,
180–182
Returns
effect of dividends, 15
excess returns, 16
continuous compounded returns,
13
dollar returns, 11
log returns, 13, 32
mean aversion and reversion,
107
simple returns, 12
Riskreturn tradeoff, 251–255, 465–
467
Root mean square error (RMSE),
221
Safe capital ratio, 495–498
Schwarz information criterion
(SIC), 113
Sharpe ratio, 80
Signature plot, 511
Spurious regression problem, 203
Stationary process
introduced, 96
Stock market index
Deutscher Aktien Index (DAX),
19
Dow Jones Industrial Average
Index (DJIA), 19
Financial Times Stock Exchange
100 Index (FTSE),
19
Hang Seng Index (HSX), 19
Nikkei 225 Index (NKX), 19
price weighted, 19
Standard and Poors Composite
500 Index (S&P 500),
19
value weighted, 19
Strong exogeneity, 187
Summary statistics, 41–45
sample correlation, 44
sample covariance, 44
sample kurtosis, 43
sample mean, 41
sample skewness, 43
sample standard deviation, 42
sample variance, 41
Systematic risk, 59
706 BIBLIOGRAPHY
Term structure of interest rates, 24,
192
Testing for bubbles, 152–157
Testing for endogeneity, 259–261
Transactions data, 39
Treynor ratio, 80
Unit root tests
Augmented DickeyFuller
test, 145–147
DickeyFuller test, 140–145
GLS detrending, 149–150
KPSS test, 151
PhillipsPeron test, 150
Righttailed tests, 152–157
Structural breaks, 147
Univariate GARCH model
BollerslevWooldridge standard
errors, 457
estimation, 455–457
forecasting, 460–465
heatwaves and meteor showers,
467–470
normal distribution, 455
t distribution, 456
Value at risk, 45–47, 237–240
Variance decomposition, 122
Vector autoregressive models (VAR),
109–125
DieboldYilmaz spillover index,
125
estimation, 111
Granger causality, 115
impulse response analysis,
116
lag length selection, 113–114
specification, 110
transactions time, 543–544
variance decomposition, 122
Vector error correction model
(VECM), 167–173
Relationship with VARs, 171–
173
Volatility
defined, 42
Volatility models
EGARCH, 458
GARCH, 453–460
GARCHM, 465–467
TARCH, 458
BEKK, 482–486
DCC, 487–493
DECO, 488
exponentially weighted moving
average, 452, 480
historical volatility, 451, 480
IGARCH, 454
in transactions time, 555–558
options data and GARCH,
588–591
realised GARCH, 525–527
stochastic volatility, 434–437
Wald test, 351
Weak exogeneity, 186
Weak instruments, 261–266
White standard errors, 348
It's very, very well done. The depth, breadth, and clarity of coverage are exceptional. It's completely up to date, very "2020". See for yourself; the front and back matter appear below (sans formatting).
Financial Econometric Modelling
Stan Hurn, Vance L. Martin, Peter C. B. Phillips, and Jun Yu
November 12, 2019
Preface
Financial econometrics is an exciting young discipline that began to take on
its present form around the turn of the millennium. The subject brings financial
theory and econometric methods together with the power of data
to advance our understanding of the global financial universe upon which
all modern economies depend. Two major developments underscored its
rapid growth and expanding capabilities. First, the massive importance of
wellfunctioning financial markets to the global economy and to global financial
stability was universally acknowledged following the dotcom bubble of
the late 1990s in the United States and the global financial crisis of 2008 coupled
with its prolonged aftermath. Second, modern methods of econometrics
emerged that proved equal to some of the special challenges presented by financial
data and the ideas of financial theory.
Among the most significant of these challenges are the complex interdependencies
of financial, commodity, and real estate markets, the dynamic and
spatial linkages within financial data, the random wandering behaviour of asset
prices, anomalies such as financial bubbles and market crashes in the data,
the difficulties in modelling rapidly changing volatility in financial returns,
the growth in high dimensional ultrahigh frequency data, and the attention
to market microstructure effects that all such data require. While not entirely
unique to financial data, these challenges presented the econometrics profession
with the need to refashion methods, develop new tools of inference,
and tackle a wide selection of new empirical goals associated with a growing
number of financial instruments and vast data sets being generated in the
financial world.
This book, like the subject itself, is motivated by all of these challenges. We
seek to provide a broad and gentle introduction to this rapidly developing
subject of financial econometrics where theory, measurement, and data play
equal roles in our development and where empirical applications occupy a
central position. Our target audiences are intermediate and advanced undergraduate
students, honours students who wish to learn about financial econometrics,
and postgraduate students with limited backgrounds in econometrics
who are doing masters courses designed to offer an introduction to finance
and its applications. We hope the book will also prove useful to practitioners
in the industry as an introductory reference source for relevant tools and
approaches to modern empirical work in finance.
Throughout the book special emphasis is placed on the exposition of core
concepts, their illustration using relevant financial data sets, and a handson
approach to learning by doing that involves practical implementation. The
guiding principle we have adopted is that only by working through plenty of
applications and exercises can a coherent understanding of the properties of
financial econometric models, interrelationships with the underlying finance
theory, and the role of econometric tools of inference be achieved.
Our philosophy has been to write a book on financial econometrics, not an
econometrics text that illustrates techniques with datasets drawn from finance.
Our goal is centred on the subject of financial econometrics explaining
how evidencedbased research in applied finance is conducted. Econometrics
is viewed as the vehicle that makes the ideas and theories about financial
markets face the reality of observations.
To ensure the book is self contained for a first course in financial econometrics,
some foundational theory and methods of relevant econometric technique
are provided. But the methods covered in this book travel along a customised
path designed to ease the reader’s transition from concepts and methods
to empirical work. The book tracks its way forward from data to modelling
through to estimation, inference, and prediction.
A consistent thematic throughout the book is to motivate each topic with
the presentation of relevant data. The journey begins with data and a simple
grounding in regression and inference. From this foundation, it moves on to
more advanced financial econometric methods that open up empirical applications
with many different types of data from various financial markets. The
path promises to keep readers motivated throughout their journey by means
of many examples and to reinforce their learning by extensive databased exercises.
Several introductory Appendices are included to assist students with
limited mathematics and no econometric background in understanding more
technical aspects of the discussion particularly in the second half of the book.
Organisation of the Book
Part I – Fundamentals – is designed to form the basis of a semester long first
course in financial econometrics directed at an introductory level. Technical
difficulty is kept to an absolute minimum with an emphasis on the data, financial
concepts, appropriate econometric methodology, and the intuition
that draws these essential components of modelling together. Methodology
is largely confined to descriptive methods and ordinary least squares regression,
a choice that limits the extent of the analysis and promotes heuristic discussion
on some topics which are revisited later in the book for a more complete
and rigorous development.
In Part II – Methods – the level of difficulty steps up slightly in treating the
relevant econometric estimation methods of instrumental variables, generalised
method of moments, and maximum likelihood. These core estimators
are used extensively throughout the second half of the book and knowledge
of them is a key asset in working through the later material. Also included in
Part II are methods that deal with panel data and models with latent factors.
A second course in financial econometrics might usefully begin with these
five chapters, taking Part I as a given foundation.
Part III – Topics – introduces a number of special topics in financial econometiv
rics, covering models of volatility, financial market microstructure, the econometrics
of options, and methods relating to extreme values and copulas. One
of the dominant features of financial time series is their volatility. Financial
theory and empirical experience both demonstrate that there is often much
less to explain in the levels of financial returns than there is to explain in their
variation. Accordingly, three chapters of the book are devoted to modelling
volatility. These chapters treat parametric univariate and multivariate models
of volatility and introduce the more recent nonparametric modelling approach
that is based on market realised volatility measured using high frequency
data.
As in any project of this nature, sacrifices were made to keep the length of the
book manageable. Some topics, for instance, are treated by example and illustration
within a chapter rather than by devoting an entire chapter to their
development. As a result the book is rich in real world examples drawn from
financial markets for stocks, fixed income securities, exchange rates, derivatives,
and real estate. As such, the coverage is intended to be extensive while
not treating every topic in the same depth.
Computation
A fundamental principle guiding the inclusion of material in this book is
whether the methods are available for easy implementation. In consequence,
all results reported in the book may be reproduced using existing software
packages like Stata and EViews.1 This choice is intended to enhance the usefulness
of the material for beginning students. In some cases the programming
languages in these packages need to be used to achieve full implementation
of the illustrations. Of course, for those who actively choose to learn by
programming themselves, the results are also reproducible in any of the common
matrix programming languages, such as R2. The numerical computations
reported in the book are primarily rounded versions of the results generated
using Stata.
The data files are all available for download from the book’s companion website
(https://global.oup.com/academic/instructors/finects) in Stata
format (.dta), EViews format (.wf1), comma delimited files (.csv), and as Excel
spreadsheets (.xlsx).
1Stata is the copyright of StataCorp LP www.stata.com and EViews is the copyright of IHSInc.
www.eviews.com.
2R is a free software environment for statistical computation and graphics which is part of the
GNU Project, see www.rproject.org.
Acknowledgements
Many colleagues, students, and research assistants have read and commented
on parts of the book and in some cases even taught from early versions of the
book. We are particularly grateful to Ahmad Bahir, Kit Baum, Jimmy Chan,
Han Chen, Ye Chen, Xiaohong Chen, Jieyang Chong, Adam Clements, Fulvio
Corsi, Mark Doolan, Ren´ee FryMcKibbin, Zhuo Huang, Marko Krause,
Bei Luo, Cheng Liu, Andrew Patton, Shuping Shi, Daniel Smith, Chrismin
Tang, Timo Ter¨asvirta, Stephen Thiele, Tomasz Wo´zniak and Lina Xu. A special
thank you goes to Annastiina Silvennoinen and Glen Wade who were relentless
in picking up typographical errors and factual inconsistencies, as well
as suggesting alternative ways of presenting material. All remaining errors
are the responsibility of the authors.
Stan Hurn, Vance L. Martin, Peter C. B. Phillips and Jun Yu
June 2019
Contents
I Fundamentals 1
1 Prices and Returns 3
1.1 What Is Financial Econometrics? . . . . . . . . . . . . . . . . . . 3
1.2 Financial Assets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Equity Prices and Returns . . . . . . . . . . . . . . . . . . . . . . 8
1.4 Stock Market Indices . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.5 Bond Yields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2 Financial Data 29
2.1 A First Look at the Data . . . . . . . . . . . . . . . . . . . . . . . 30
2.2 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.3 Percentiles and Value at Risk . . . . . . . . . . . . . . . . . . . . 45
2.4 The Efficient Market Hypothesis . . . . . . . . . . . . . . . . . . 48
2.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3 Linear Regression 57
3.1 The Capital Asset Pricing Model . . . . . . . . . . . . . . . . . . 58
3.2 A Multifactor CAPM . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.3 Properties of Ordinary Least Squares . . . . . . . . . . . . . . . . 67
3.4 Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.5 Measuring Portfolio Performance . . . . . . . . . . . . . . . . . . 80
3.6 Minimum Variance Portfolios . . . . . . . . . . . . . . . . . . . . 82
3.7 Event Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4 Stationary Dynamics 95
4.1 Stationarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.2 Univariate Time Series Models . . . . . . . . . . . . . . . . . . . 98
4.3 Autocorrelation and Partial Autocorrelations . . . . . . . . . . . 103
4.4 Mean Aversion and Reversion in Returns . . . . . . . . . . . . . 107
4.5 Vector Autoregressive Models . . . . . . . . . . . . . . . . . . . . 109
4.6 Analysing VARs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.7 DieboldYilmaz Spillover Index . . . . . . . . . . . . . . . . . . . 126
4.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
5 Nonstationarity 133
5.1 The RandomWalk with Drift . . . . . . . . . . . . . . . . . . . . 134
5.2 Characteristics of Financial Data . . . . . . . . . . . . . . . . . . 137
5.3 DickeyFuller Methods and Unit Root Testing . . . . . . . . . . . 140
5.4 Beyond the Simple Unit Root Framework . . . . . . . . . . . . . 147
5.5 Asset Price Bubbles . . . . . . . . . . . . . . . . . . . . . . . . . . 152
5.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
6 Cointegration 161
6.1 The Present Value Model and Cointegration . . . . . . . . . . . . 162
6.2 Vector Error Correction Models . . . . . . . . . . . . . . . . . . . 167
6.3 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
6.4 Cointegration Testing . . . . . . . . . . . . . . . . . . . . . . . . . 180
6.5 Parameter Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
6.6 Cointegration and the Gordon Model . . . . . . . . . . . . . . . 187
6.7 Cointegration and the Yield Curve . . . . . . . . . . . . . . . . . 192
6.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
7 Forecasting 205
7.1 Types of Forecasts . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
7.2 Forecasting Univariate Time Series Models . . . . . . . . . . . . 208
7.3 Forecasting Multivariate Time Series Models . . . . . . . . . . . 212
7.4 Combining Forecasts . . . . . . . . . . . . . . . . . . . . . . . . . 216
7.5 Forecast Evaluation Statistics . . . . . . . . . . . . . . . . . . . . 220
7.6 Evaluating the Density of Forecast Errors . . . . . . . . . . . . . 224
7.7 Regression Model Forecasts . . . . . . . . . . . . . . . . . . . . . 229
7.8 Predicting the Equity Premium . . . . . . . . . . . . . . . . . . . 230
7.9 Stochastic Simulation of Value at Risk . . . . . . . . . . . . . . . 237
7.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
II Methods 247
8 Instrumental Variables 249
8.1 The Exogeneity Assumption . . . . . . . . . . . . . . . . . . . . . 250
8.2 Estimating the RiskReturn Tradeoff . . . . . . . . . . . . . . . . 251
8.3 The General Instrumental Variables Estimator . . . . . . . . . . 255
8.4 Testing for Endogeneity . . . . . . . . . . . . . . . . . . . . . . . 259
8.5 Weak Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
8.6 Consumption CAPM . . . . . . . . . . . . . . . . . . . . . . . . . 266
8.7 Endogeneity and Corporate Finance . . . . . . . . . . . . . . . . 269
8.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
9 Generalised Method of Moments 277
9.1 Single Parameter Models . . . . . . . . . . . . . . . . . . . . . . . 278
9.2 Multiple Parameter Models . . . . . . . . . . . . . . . . . . . . . 281
9.3 OverIdentified Models . . . . . . . . . . . . . . . . . . . . . . . . 288
9.4 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
9.5 Properties of the GMM Estimator . . . . . . . . . . . . . . . . . . 299
9.6 Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
9.7 Consumption CAPM Revisited . . . . . . . . . . . . . . . . . . . 309
9.8 The CKLS Model of Interest Rates . . . . . . . . . . . . . . . . . 312
9.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316
10 Maximum Likelihood 323
10.1 Distributions in Finance . . . . . . . . . . . . . . . . . . . . . . . 324
10.2 Estimation by Maximum Likelihood . . . . . . . . . . . . . . . . 331
10.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334
10.4 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 342
10.5 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344
10.6 Quasi Maximum Likelihood Estimation . . . . . . . . . . . . . . 347
10.7 Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349
10.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357
11 Panel Data Models 365
11.1 Types of Panel Data . . . . . . . . . . . . . . . . . . . . . . . . . . 366
11.2 Reasons for Using Panel Data . . . . . . . . . . . . . . . . . . . . 368
11.3 Two Introductory Panel Models . . . . . . . . . . . . . . . . . . . 372
11.4 Fixed and Random Effects Panel Models . . . . . . . . . . . . . . 377
11.5 Dynamic Panel Models . . . . . . . . . . . . . . . . . . . . . . . . 386
11.6 Nonstationary Panel Models . . . . . . . . . . . . . . . . . . . . . 394
11.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400
12 Latent Factor Models 409
12.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410
12.2 Principal Components . . . . . . . . . . . . . . . . . . . . . . . . 412
12.3 A Latent Factor CAPM . . . . . . . . . . . . . . . . . . . . . . . . 420
12.4 Dynamic Factor Models: the Kalman Filter . . . . . . . . . . . . 423
12.5 A Parametric Approach to Factors . . . . . . . . . . . . . . . . . 431
12.6 Stochastic Volatility . . . . . . . . . . . . . . . . . . . . . . . . . . 434
12.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437
III Topics 445
13 Univariate GARCH Models 447
13.1 Volatility Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . 448
13.2 The GARCH Model . . . . . . . . . . . . . . . . . . . . . . . . . . 450
13.3 Asymmetric Volatility Effects . . . . . . . . . . . . . . . . . . . . 458
13.4 Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460
CONTENTS xi
13.5 The RiskReturn Tradeoff . . . . . . . . . . . . . . . . . . . . . . 465
13.6 Heatwaves and Meteor Showers . . . . . . . . . . . . . . . . . . 467
13.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470
14 Multivariate GARCH Models 477
14.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478
14.2 Early Covariance Estimators . . . . . . . . . . . . . . . . . . . . . 480
14.3 The BEKK Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 482
14.4 The DCC Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487
14.5 Optimal Hedge Ratios . . . . . . . . . . . . . . . . . . . . . . . . 493
14.6 Capital Ratios and Financial Crises . . . . . . . . . . . . . . . . . 495
14.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498
15 Realised Variance and Covariance 505
15.1 High Frequency Data . . . . . . . . . . . . . . . . . . . . . . . . . 506
15.2 Realised Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . 509
15.3 Integrated Variance . . . . . . . . . . . . . . . . . . . . . . . . . . 512
15.4 Microstructure Noise . . . . . . . . . . . . . . . . . . . . . . . . . 515
15.5 Bipower Variation and Jumps . . . . . . . . . . . . . . . . . . . . 518
15.6 Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522
15.7 The Realised GARCH Model . . . . . . . . . . . . . . . . . . . . 525
15.8 Realised Covariance . . . . . . . . . . . . . . . . . . . . . . . . . 527
15.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532
16 Microstructure Models 537
16.1 Characteristics of High Frequency Data . . . . . . . . . . . . . . 537
16.2 Limit Order Book . . . . . . . . . . . . . . . . . . . . . . . . . . . 538
16.3 Bid Ask Bounce . . . . . . . . . . . . . . . . . . . . . . . . . . . . 540
16.4 Information Content of Trades . . . . . . . . . . . . . . . . . . . . 543
16.5 Modelling Price Movements in Trades . . . . . . . . . . . . . . . 545
16.6 Modelling Durations . . . . . . . . . . . . . . . . . . . . . . . . . 551
16.7 Modelling Volatility in Transactions Time . . . . . . . . . . . . . 555
16.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558
17 Options 565
17.1 Option Pricing Basics . . . . . . . . . . . . . . . . . . . . . . . . . 566
17.2 The BlackScholes Option Price Model . . . . . . . . . . . . . . . 569
17.3 A First Look at Options Data . . . . . . . . . . . . . . . . . . . . 573
17.4 Estimating the BlackScholes Model . . . . . . . . . . . . . . . . 574
17.5 Testing the BlackScholes Model . . . . . . . . . . . . . . . . . . 581
17.6 Option Pricing and GARCH Volatility . . . . . . . . . . . . . . . 583
17.7 The MelickThomas Option Price Model . . . . . . . . . . . . . . 585
17.8 Nonlinear Option Pricing . . . . . . . . . . . . . . . . . . . . . . 587
17.9 Using Options to Estimate GARCH Models . . . . . . . . . . . . 588
17.10Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591
18 Extreme Values and Copulas 599
18.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 600
18.2 Evidence of Heavy Tails . . . . . . . . . . . . . . . . . . . . . . . 602
18.3 Extreme Value Theory . . . . . . . . . . . . . . . . . . . . . . . . 605
18.4 Modelling Dependence using Copulas . . . . . . . . . . . . . . . 611
18.5 Properties of Copulas . . . . . . . . . . . . . . . . . . . . . . . . . 614
18.6 Estimating Copula Models . . . . . . . . . . . . . . . . . . . . . . 621
18.7 MGARCH Model Using Copulas . . . . . . . . . . . . . . . . . . 624
18.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626
19 Concluding Remarks 633
A Mathematical Preliminaries 635
A.1 Summation Notation . . . . . . . . . . . . . . . . . . . . . . . . . 635
A.2 Expectations Operator . . . . . . . . . . . . . . . . . . . . . . . . 638
A.3 Differentiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 639
A.4 Taylor Series Expansions . . . . . . . . . . . . . . . . . . . . . . . 641
A.5 Matrix Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646
A.6 Transposition of a Matrix . . . . . . . . . . . . . . . . . . . . . . . 650
A.7 Symmetric Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . 651
B Properties of Estimators 661
B.1 Finite Sample Properties . . . . . . . . . . . . . . . . . . . . . . . 661
B.2 Asymptotic Properties . . . . . . . . . . . . . . . . . . . . . . . . 663
C Linear Regression Model in Matrix Notation 669
D Numerical Optimisation 673
E Simulating Copulas 677
Author index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 698
Subject index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 702
Author index
A¨ıtSahalia, Y., 341, 517, 518
Adams, R., 269, 270, 382
Akaike, H., 113
Aldrich, J., 323
Almeida, H., 269, 270, 382
Amenc, N., 477
Andersen, T.G, 517
Anderson, D.R., 218
Anderson, R.C., 269
Anderson, T.W., 390
Andreou, E., 237
Arellano, M., 390
Augustin, N.H., 218
Bae, K.H., 599
Bai, J., 419
Baillie, R.T., 493, 494
Baker, R., 262
Bali, T.G., 255
Baltagi, B.H, 400
Banerjee, A., 203
BarndorffNielsen, O.E., 508, 515,
518, 520, 521, 529, 538
Bartlett, M.S., 175, 349
Bates, J., 218, 235
Becker, R., 224
Bekaert, G., 67
Bera, A.K., 79, 229
Bergstrom, A.R., 161
Black, F., 569
Blundell, R., 390
Bollerslev, T., 448, 450, 457, 517,
525, 589
Bond, S., 390
Bonhomme, S., 372
Bouchard, JP., 544
Bound, J., 262
Bover, O., 390
Brennan, M.J., 315
Brockwell, P.J., 98, 106
Brownlees, C., 495, 498
Buckland, S.T., 218
Burnham, K.P., 218
Bykhovskaya, A., 150
Campbell, J.Y., 131, 154, 237
Carhart, M.M., 65
Chan, K.C., 313
Chao, J.C., 179
Cheng, X., 179
Chiang, M.H., 400
Choi, I., 399
Christoffersen, P.F., 464
Chu, C.J., 397
Clemen, R.T., 219
Clements, A.E., 224, 469
Clements, M.P., 219
Cochrane, J.H., 48, 237
Colacito, R., 224
Corbae, D., 199
Corsi, F., 522
Cox, J.C., 315, 329
Cram´er, H., 345
Davidson, R., 260
Davis, R.A., 98, 106
Diba, B.T., 154
Dickey, D.A., 140, 141, 146
Diebold, F.X., 24, 126, 132, 223, 229,
431, 441, 517
Dolado, J.J., 203
Doolan, M.B., 224
Dungey, M., 362, 467
Durbin, J., 129, 298
Eisler, Z., 544
Elliott, G., 149, 217, 219, 224
Engle, R.F., 78, 161, 173, 174, 224,
448–450, 467, 471, 487,
489, 495, 498, 542, 552,
555, 556
Epps, T.W., 528
Evans, G.W., 154
Fakhrutdinova, L., 467
Fama, E.F., 48, 64, 107, 403
AUTHOR INDEX 699
Fan, Y., 612
Ferreira, D., 269, 270, 382
Ferson, W.E., 268, 269
Fisher, R.A., 398
Flannery, M.J., 388, 406
Flemming, J., 224
French, K.R., 64, 107
Fuller, W.A., 140, 141
Galbraith, J.W., 203
Garratt, A., 219
Ghosh, A., 229
Ghysels, E., 255
Gibbons, M., 403
Gibson, M., 589
Glosten, L.R., 458
Goltz, F., 477
Goodhart, C.A.E., 467
Gordon, M.J., 187, 190, 201
Goyal, A., 231, 244
Granger, C.W.J., 115, 161, 174, 203,
218, 235
Grossman, H.I., 154
Gunther, T.A., 229
Haldane, A.G., 442
Hall, A.D., 544
Hall, A.R., 300
Hall, S.G., 442
Hamilton, J.D., 98
Hankins, K.W., 388, 406
Hannan, E.J., 113
Hansen, B.E., 174
Hansen, L.P., 298, 300, 302, 303, 311
Hansen, P.R., 462, 508, 518, 525,
529, 538
Harris, D., 98, 122, 292, 350, 427,
548, 587, 662
Harvey, A.C., 427, 493
Harvey, C.R., 268, 269
Hasbrouck, J., 543, 559
Hausman, J.A., 385, 545
Hautsch, N., 544
Heaton, J., 298
Hendry, D.F., 203, 219
Hodrick, R.J., 54
Hoerova, M., 67
Hoyem, K., 67
Hsiao, C., 390
Hu, WY., 67
Huang, R., 544
Huang, Z., 525
Hurn, A.S., 98, 122, 224, 292, 350,
427, 469, 548, 587, 662
Hwang, J., 173
Im, K.S., 397
Ingersoll, J.E., 315, 329
Ito, T., 467
Jacobs, J.P.A.M., 362
Jacod, J., 518
Jaeger, D., 262
Jaganathan, R., 458
Jarque, C.M., 79
Jensen, M.C., 80
Johansen, S., 174, 177, 184
Judson, R.A., 388
Kanniainen, J., 588, 589
Kao, C., 400
Kapetanious, G., 219
Karolyi, G.A., 313, 599
Kasparis, I., 237
Kelly, B., 489
Kim, M.J., 107
Kirby, C., 224
Kiviet, J., 388
Kockelkoren, J., 544
Koop, G., 219
Kwiatkowski, D.P., 151
L¨ utkepohl, H., 113, 122
Labhard, V., 219
Labys, P., 517
Lee, C.C., 150
Lee, J.H., 237
Levin, A., 397
Li, C., 24, 431, 441
Li, D.X., 600
Lim, KG., 199
Lin, B., 588, 589
700 BIBLIOGRAPHY
Lin, C.F., 397
Lin, W.L., 467
Liu, L., 517
Lo, A.W., 154, 545
Lo, D.K., 544
Longstaff, F.A., 313
Loretan, M., 173
Lunde, A., 462, 508, 518, 525, 529,
538
MacBeth, J.D., 403
MacKenzie, D., 600
MacKinlay, A.C., 154, 545
MacKinnon, J.G., 144, 181, 260
Maddala, G.S., 399
Malmendier, U., 67
Mann, H.B., 95, 109
Manresa, E., 372
Mariano, R.S., 223
Martin, V.L., 98, 122, 292, 350, 427,
548, 587, 662
Melick, W.R., 586
Merton, R.C., 251, 473, 536
Millar, R.B., 345
Mincer, J., 462
Moon, H.R., 400
Myers, R.J., 493, 494
Mykland, P.A., 517, 518
Nagel, S., 67
Nelson, C.R., 107, 431
Nelson, D.B., 459
Newbold, P., 203
Newey, W.K., 175, 349
Ng, S., 147, 419
Nickell, S., 387, 388
Ostdiek, B., 224
Ouliaris, S., 181, 199
Owen, A.L., 388
P´erignon, C., 45
Patton, A.J., 224, 471, 517, 525, 612
Peng, L., 255
Perron, P., 147, 150
Pesaran, M.H., 397
Phillips, P.C.B., 140, 150–152, 156,
173, 174, 179–181, 203,
237, 264, 372, 400
Poterba, J.M., 108
Pratt, J.W., 323
Prescott, E.C., 54
Price, S., 219
Quaedvlieg, R., 525
Quinn, B.G., 113
Rajan, R.G., 393, 406
Ramanathan, R., 218
Reeb, D.M., 269
Reinhart, C.M., 362
Rogoff, K.S., 362
Roley, V.V., 467
Roll, R., 541, 558
Ross, S.A., 315, 329, 403
Rothenberg, T.J., 149
Roulet, J., 54
Runkle, D, 458
Russell, J.R., 542, 552
Said, S.E., 146
Saikkonen, P., 173
Samuelson, P., 48
Sanders, A.B., 313
SantaClara, P., 255
Schmidt, P., 151
Scholes, M., 569
Schwartz, E.S., 315
Schwarz, G., 113
Shanken, J., 403
Sharpe,W.F., 80
Shek, H.H., 525
Shephard, N., 508, 515, 518, 520,
521, 529, 538
Sheppard, K., 224, 517
Shi, S., 156
Shi, Z., 372
Shiller, R.J., 67, 131
Shin, Y., 151, 397
Siegel, A.F., 431
Silvennoinen, A., 488, 493
Sims, C.A., 109
Singleton, K.J., 311
Smith, D.R., 45
Smith, J., 219
Solnik, B., 54
Spears, T., 600
Staiger, D., 262, 264
Stambaugh, R.F., 236
Startz, B., 107
Stigler, S.M., 323
Stock, J.H., 149, 173, 219, 262, 264,
274
Stulz, R.M., 599
Su, L., 372
Summers, L.H., 108
Sun, Y., 173
Tang, L., 477
Taylor, S.J., 435
Ter¨asvirta, T., 488, 493
Thiele, S., 493
Thomas, C.P., 586
Timmerman, A., 217, 224
Toda, H.Y., 180
Treynor, J.L., 80
Trivedi, P.K., 612, 678
Tsay, R.S., 229
Tse, Y.K., 488
Tsui, A.K.C., 488
Vahey, S.P., 219
Vaidyanathan, V., 477
Valkanov, R., 255
Van der Vaart, A.W., 345
Van der Waart, J.W., 301
Vasicek, O., 341
Volkov, V.V., 469
Wald, A., 95, 109
Wallis, K.F., 219
Watson, M.W., 173, 219
Welch, I., 231, 244
Wellner, J.A., 301
West, K.D., 175, 349
White, H., 78, 349
Winkler, R.L., 219
Wooldridge, J.M., 457
Wright, J.H., 274
Wu, S., 399
Wu, Y., 152
Yamamoto, Y., 180
Yang, H., 588, 589
Yaron, A., 298
Yilmaz, K., 126, 132
Yogo, M., 237, 264, 274
Yoo, B.S., 173
Yu, J., 152, 156
Zako¨ıan, J.M., 458
Zarnowitz, V., 462
Zhang, L., 517, 518
Zhou, H., 589
Zimmer, D.M., 612, 678
Zingales, L., 393, 406
Subject index
F test of significance, 74
t test of significance, 73
Adjusted coefficient of determination
(R2), 72
Akaike information criterion (AIC),
113
Asset returns
volatility clustering, 448–450
Asymptotic efficiency
GMM, 301
maximum likelihood, 345
ordinary least squares, 69
Asymptotic normality
GMM, 303
maximum likelihood, 346
ordinary least squares, 70
Augmented DickeyFuller test,
145–147
GLS detrending, 149
lag length selection, 147
Autocorrelation function, 103
Autocovariance, 103
Autoregressive (AR) model
estimation, 99
specification, 98
Autoregressive conditional duration
model, 551–555
Autoregressive moving average
(ARMA) model
estimation, 102
specification, 101
BFGS algorithm, 675
BHHH algorithm, 674
Bid ask bounce, 540–542
Bipower variation, 518–522
BlackScholes option pricing model
currency option, 573
equity option, 573
European call option, 569–572
European put option, 572
testing bias, 581
testing heteroskedasticity, 582
testing smiles and smirks, 582
BollerslevWooldridge standard
errors, 457
Bond yields, 36
term structure, 24
yield curve, 24
yield to maturity, 23
Capital asset pricing model (CAPM),
58–63
consumption (CCAPM), 309
Coefficient of determination (R2),
72
Cointegration, 163
fully modified estimation,
174–177
estimation, 173–180
Gordon model, 187–192
Johansen reduced rank regression
estimator, 177–180
modelling the yield curve,
192–198
present value model, 163–167
testing, 180–187
testing hypotheses on cointegrating
parameters, 186
Consistency
GMM, 301
instrumental variables, 259
maximum likelihood, 345
ordinary least squares, 68
Consumption capital asset pricing
model (CCAPM), 266–
269
Copulas
t copula, 616
Clayton copula, 617
estimating copula models,
621–624
Frank copula, 618
SUBJECT INDEX 703
Gaussian copula, 614
Gumbel copula, 618
measuring tail dependence,
618–621
modelling dependence using
copulas, 611–614
properties of copulas, 614–621
Diagnostic tests on disturbances
ARCH, 78
autocorrelation, 76
heteroskedasticity, 77
normality, 79
DickeyFuller test, 140–145
DieboldMariano test, 223
DieboldYilmaz Spillover Index,
125–128
Dividends
discounted future stream of,
34
dividend yield, 34
Durations, 39
Dynamic factor models, 423–429
Efficient market hypothesis, 48–51,
134
return predictability, 48
variance ratio, 50
Endogeneity and corporate finance,
269–272
Equilibrium dynamics, 164
Equity prices, 30–32
effect of dividends, 10
effect of stock splits, 11
quoted prices, 8
Event analysis, 85–87
Extreme value distribution
distribution types, 606–607
Hill estimator, 608
maximum likelihood estimation,
609–610
VaR calculation, 611
Extreme value theory, 605–611
Financial assets
cash, 6
derivatives, 7
equities, 7
Eurodollar deposits, 6
fixedincome securities, 6
Treasury bills, 6
Forecasting
AR(1) model, 208–211
AR(2) model, 211
bivariate VAR(1) model, 213–
214
bivariate VECM(1) model,
214–216
combining forecasts, 216–219
density forecast evaluation,
224–229
ex ante forecasts, 206
ex post forecasts, 207
forecast evaluation, 220–224
predictive regressions, 229–
237
properties, 212
Fully modified estimation OLS,
174–177
GibbonsRossShanken test, 371,
403
Gordon model, 187–192
Granger causality, 115
Hannan information criterion
(HIC), 113
HansenSargan J test, 306
High frequency data
characteristics, 537–538
cleaning, 507–508
limit order book, 538–540
transactions data, 506–509
Idiosyncratic risk, 59
Impulse response analysis, 116
Instrumental variables estimator
multiple endogenous regressors,
258–259
twovariable regression model,
254
Integrated process, 137
704 BIBLIOGRAPHY
Integrated variance, 512–515
Intertemporal CAPM, 251–255
Invariance
maximum likelihood, 346
Jensen’s alpha, 80
Johansen reduced rank regression
estimator, 177–180
Johansen tests of cointegration,
182–185
Kalman filter
estimation, 428
factor extraction, 428–429
multivariate, 427
univariate, 424–426
Lag length selection
information criteria, 113–114
Lagrange multiplier (LM) test
test for ARCH, 470
Lagrange multiplier test, 351–352
Leptokurtosis, 38
Likelihood ratio test, 351
Limited dependent variables, 545–
551
linear probability model, 547
ordered probit, 549–551
probit, 546–549
Linear regression model, 58
disturbance term diagnostics,
76–80
explanatory variable diagnostics,
73–75
matrix notation, 669–670
Marginal expected shortfall, 495–
498
Mean absolute error (MAE), 221
Mean absolute percentage error
(MAPE), 221
Mean square error (MSE), 221
Measuring portfolio performance
Jensen’s alpha, 80
Sharpe ratio, 80
Treynor ratio, 80
MelickThomas option pricing
model, 585–587
Microstructure noise, 515–518
Minimum variance portfolio, 82–
85
Modelling the yield curve, 192–198
Moving average (MA) model
estimation, 100
specification, 100
Multifactor CAPM
instrumental variables estimation,
255–258
Multifactor CAPM, 63–67
Multiple regression model, 63
NelsonSiegel parametric factor
model, 431–434
News impact curve (NIC), 459
NewtonRaphson algorithm, 674
Nonlinear option pricing model,
587–588
Nonstationary process, 137
Optimal hedge ratio, 493–495
Options
BlackScholes option pricing
model, 569–573
data, 573–574
GARCH volatility, 583–585
Greeks, 578–581
historical volatility, 575–576
implied volatility, 576–578
pricing basics, 566–569
Order of integration, 137
Order statistics, 602–603
Ordinary least squares estimator,
60–61
Panel data
ArellanoBond estimator, 390
common effects model, 374–
377
fixed effects model, 378–380
Hausman test, 383–385
Nickell bias, 386
no common effects model,
372–374
SUBJECT INDEX 705
panel cointegration, 398–400
panel unit roots, 396–398
random effects model, 380–
382
system GMM estimator, 390
Partial autocorrelation function,
106
Percentiles, 45
Predicting the equity premium,
230–237
Principal component analysis,
412–420
estimation, 413–417
factor extraction, 417–418
model specification, 412–413
testing, 419–420
Probability integral transform
(PIT), 224
Properties of GMM estimators,
299–305
Properties of instrumental variable
estimators, 259
Properties of instrumental variables
estimators, 254
Properties of maximum likelihood
estimators, 344–347
Properties of ordinary least squares
estimators, 67–71
Quasi maximum likelihood estimator,
347
Random walk with drift model,
134–137
Realised covariance, 527–531
refresh time synchronisation,
529–531
Realised variance
computing, 509–511
forecasting, 522–525
Residualbased tests of cointegration,
180–182
Returns
effect of dividends, 15
excess returns, 16
continuous compounded returns,
13
dollar returns, 11
log returns, 13, 32
mean aversion and reversion,
107
simple returns, 12
Riskreturn tradeoff, 251–255, 465–
467
Root mean square error (RMSE),
221
Safe capital ratio, 495–498
Schwarz information criterion
(SIC), 113
Sharpe ratio, 80
Signature plot, 511
Spurious regression problem, 203
Stationary process
introduced, 96
Stock market index
Deutscher Aktien Index (DAX),
19
Dow Jones Industrial Average
Index (DJIA), 19
Financial Times Stock Exchange
100 Index (FTSE),
19
Hang Seng Index (HSX), 19
Nikkei 225 Index (NKX), 19
price weighted, 19
Standard and Poors Composite
500 Index (S&P 500),
19
value weighted, 19
Strong exogeneity, 187
Summary statistics, 41–45
sample correlation, 44
sample covariance, 44
sample kurtosis, 43
sample mean, 41
sample skewness, 43
sample standard deviation, 42
sample variance, 41
Systematic risk, 59
706 BIBLIOGRAPHY
Term structure of interest rates, 24,
192
Testing for bubbles, 152–157
Testing for endogeneity, 259–261
Transactions data, 39
Treynor ratio, 80
Unit root tests
Augmented DickeyFuller
test, 145–147
DickeyFuller test, 140–145
GLS detrending, 149–150
KPSS test, 151
PhillipsPeron test, 150
Righttailed tests, 152–157
Structural breaks, 147
Univariate GARCH model
BollerslevWooldridge standard
errors, 457
estimation, 455–457
forecasting, 460–465
heatwaves and meteor showers,
467–470
normal distribution, 455
t distribution, 456
Value at risk, 45–47, 237–240
Variance decomposition, 122
Vector autoregressive models (VAR),
109–125
DieboldYilmaz spillover index,
125
estimation, 111
Granger causality, 115
impulse response analysis,
116
lag length selection, 113–114
specification, 110
transactions time, 543–544
variance decomposition, 122
Vector error correction model
(VECM), 167–173
Relationship with VARs, 171–
173
Volatility
defined, 42
Volatility models
EGARCH, 458
GARCH, 453–460
GARCHM, 465–467
TARCH, 458
BEKK, 482–486
DCC, 487–493
DECO, 488
exponentially weighted moving
average, 452, 480
historical volatility, 451, 480
IGARCH, 454
in transactions time, 555–558
options data and GARCH,
588–591
realised GARCH, 525–527
stochastic volatility, 434–437
Wald test, 351
Weak exogeneity, 186
Weak instruments, 261–266
White standard errors, 348
Tuesday, June 30, 2020
Entering (and Trying to Exit) the Pandemic Recession
econ.EM econ.GN
RealTime Real Economic Activity: Exiting the Great Recession and Entering the Pandemic Recession
Authors: Francis X. Diebold
Abstract: We study the realtime signals provided by the AruobaDieboldScotti Index of Business conditions (ADS) for tracking economic activity at high frequency. We start with exit from the Great Recession, comparing the evolution of realtime vintage beliefs to a "final" latevintage chronology. We then consider entry into the Pandemic Recession, again tracking the evolution of realtime vintage beliefs. ADS swings widely as its underlying economic indicators swing widely, but the emerging ADS path as of this writing (late June) indicates a return to growth in May. The trajectory of the nascent recovery, however, is massively uncertain, particularly as COVID19 spreads in the South and West, and could be reversed as quickly as it started.
Submitted 26 June, 2020; originally announced June 2020.
Monday, June 29, 2020
Causality and Generalized Impulse Response Functions
Neil Shephard just gave a fine talk, "Econometric analysis of potential outcomes time series:
instruments, shocks, linearity and the causal response function". Recording here (soon).
Slides here. The key result is on slide 11: If the conditions (Assns 13 on slides p. 5) for a potential outcome time series are satisfied, then the KoopPesaranPotter (1996) "generalized impulse response function" (GIRF) has a direct causal interpretation. Neil pitched the paper as providing deeper understanding and firmer foundations for the GIRF, which it certainly does.
Wow! This is wonderful in general, and for me personally: Throughout almost all my work with Kamil Yilmaz on measuring network connectedness (e.g., here), we work in a GIRF framework for the underlying vector autoregression (actually generalized variance decomposition, but it's the same thing). We liked the GIRF for a pragmatic reason  its invariance to variable ordering, unlike Cholesky factor identification  but we always wanted to understand it more deeply.
instruments, shocks, linearity and the causal response function". Recording here (soon).
Slides here. The key result is on slide 11: If the conditions (Assns 13 on slides p. 5) for a potential outcome time series are satisfied, then the KoopPesaranPotter (1996) "generalized impulse response function" (GIRF) has a direct causal interpretation. Neil pitched the paper as providing deeper understanding and firmer foundations for the GIRF, which it certainly does.
Wow! This is wonderful in general, and for me personally: Throughout almost all my work with Kamil Yilmaz on measuring network connectedness (e.g., here), we work in a GIRF framework for the underlying vector autoregression (actually generalized variance decomposition, but it's the same thing). We liked the GIRF for a pragmatic reason  its invariance to variable ordering, unlike Cholesky factor identification  but we always wanted to understand it more deeply.
Thursday, June 25, 2020
Pandemic Economic Forecasting with MixedFrequency Data
Nice SchorfheideSong (SS) Bayesian realtime pandemic economic forecasting with mixedfrequency data here. They simulate exact posteriors. ADS nowcasting is also based on exact mixedfrequency estimation (MLE). So both SS and ADS get things right in principle (SS Bayesian forecasting, ADS frequentist nowcasting), and both are easily implemented in practice. That is, both are intellectually pure, yet practically relevant.
Monday, June 22, 2020
COVID, Economic Activity, and Climate
Everyone talks about COVID helping reduce warming:
COVID up > economic activity down > CO2 down > temperature down.
But there's a flip side:
COVID up > activity down > atmospheric sulphate aerosols down > temperature UP!
(Sulphate aerosols reflect solar heat, so if they're down, temp is up.)
See https://news.mongabay.com/2020/06/climateconundrumcouldcovid19belinkedtoearlyarcticicemelt/.
It would be interesting to assess the the competing effects of CO2 vs. sulphate aerosols, dynamically. One might start with impulseresponse analysis of an economic activity shock in a predictive model containing economic activity, CO2, sulphate aerosols, and temperature.
COVID up > economic activity down > CO2 down > temperature down.
But there's a flip side:
COVID up > activity down > atmospheric sulphate aerosols down > temperature UP!
(Sulphate aerosols reflect solar heat, so if they're down, temp is up.)
See https://news.mongabay.com/2020/06/climateconundrumcouldcovid19belinkedtoearlyarcticicemelt/.
It would be interesting to assess the the competing effects of CO2 vs. sulphate aerosols, dynamically. One might start with impulseresponse analysis of an economic activity shock in a predictive model containing economic activity, CO2, sulphate aerosols, and temperature.
Wednesday, June 17, 2020
Time Series Modeling of COVID19 Paths
Check out the refreshing new paper by Andrew Harvey and Paul Kattuman "Time series models based on growth curves with applications to forecasting coronavirus", pp. 126156 here.
For noncausal forecasting, reducedform approaches like those of HarveyKattuman are almost always the way to go, from traditional time series modeling to more recent extensions in machine learning. To paraphrase a longago No Hesitations post: We generally don't need deep structural understanding to succeed at forecasting, which is wonderful, because we typically don't have deep structural understanding. (Admit it.)
Forecasting COVID progression (cases, deaths, etc.) is a fine example. The leading structural ("SIR") model is a toy model, an intentionally strippeddown abstraction of a much more complex reality. There's nothing wrong with that  that's what all structural models are, and good structural models can yield invaluable insights. But good forecasting requires capturing the complex reality more fully, with its model uncertainty, measurement uncertainty, parameter uncertainty, innovation uncertainty, structural change uncertainty, etc. That's where reducedform approaches shine.
On the other hand, because structural models can in principle illuminate the causal mechanisms that underlie reducedform correlations, they may help with analysis of conterfactuals. That is, structural models may facilitate causal forecasting in addition to noncausal forecasting.
Of course it doesn't have to be an either/or choice. One can attempt to blend the structural and reducedform approaches, hoping to achieve the best of both worlds. To that end, see the alsorefreshing new paper by Andrew Atkeson et al., "Estimating and forecasting disease scenarios for COVID19 with an SIR model", here.
Tuesday, June 16, 2020
SoFiE 2021 San Diego and 2022 Cambridge
Happy to help spread the word that the Society for Financial Econometrics annual conference 2021 will be in San Diego (UCSD) June 1517, and 2022 will be in Cambridge England (University of Cambridge) June 2729. Finally some real inperson meetings, and each location is perfect. Quite a big deal. Zoom is hardly a substitute. See you there!
Monday, June 15, 2020
Did the U.S. Recession Start in February or March?
Some seem to think that the NBER declared a February recession start. It did not; rather, it declared a February cyclical peak.
So when did the recession start? It's a bit ambiguous, since a peak is an apex atop both the upward expansion path and the downward contraction path. Indeed the NBER's press release states that "The [February 2020] peak marks the end of the expansion that began in June 2009 and the beginning of a recession."
Nevertheless, when measuring expansion and contraction durations, the NBER convention is that peak months are taken as part of expansions ("the last month of good times"), and trough months are taken as part of contractions ("the last month of bad times"), as in the NBER table here.
So when did the recession start? It's a bit ambiguous, since a peak is an apex atop both the upward expansion path and the downward contraction path. Indeed the NBER's press release states that "The [February 2020] peak marks the end of the expansion that began in June 2009 and the beginning of a recession."
Nevertheless, when measuring expansion and contraction durations, the NBER convention is that peak months are taken as part of expansions ("the last month of good times"), and trough months are taken as part of contractions ("the last month of bad times"), as in the NBER table here.
Friday, June 12, 2020
Real Economics in Business Strategy Simulation
This spam somehow made it through my filters. But it looks pretty cool, not really spam. Maybe my filters are smarter than I thought.
https://scientificstrategy.com
I am certainly not expert in micro / IO / marketing, so maybe I'm far behind the curve, but at any rate the practitioner in me was intrigued by the tools described in the email below. I have no idea whether they're any good, but it's certainly interesting to see real economics evidently getting in closer touch with the nittygritty of practical business decision making.
https://scientificstrategy.com
I am certainly not expert in micro / IO / marketing, so maybe I'm far behind the curve, but at any rate the practitioner in me was intrigued by the tools described in the email below. I have no idea whether they're any good, but it's certainly interesting to see real economics evidently getting in closer touch with the nittygritty of practical business decision making.
Hi Professor Diebold:
Model the dynamics of your market with Market Simulation:
Our 100+ example models include:
 Cournot / Bertrand / Edgeworth / Giffen / Hotelling / Nash
 Stackelberg LeaderFollower Price Competition
 WholesalerRetailer Double Marginalization / M&A
 eCommerce / Brick & Mortar
 Good / Better / Best Product Pricing
 Learning Curves / Search Costs / Bundling
 Capacity Limitations / Switching Costs / Cannibalization
 Conjoint Analysis / New Product Development
Our case studies include:
 Android vs iOS
 Microbrews (6parts)
 Cola Wars (7parts)
 SUV Market (2parts)
 Competitive Strategy Game CSG (2parts)
 Porter’s Five Forces (5parts)
Model, analyze, and solve your pricing / product / positioning / placement. Or send in your problem for us to solve.
Happy Simulations!
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Ted Hartnell  CTO
Phone: +14158004454
LinkedIn: https://www.linkedin.com/in/tedhartnell
Address: 25 Pond Court, Milpitas, CA 95035
More on Conditional Predictive Accuracy Assessment
I recently blogged on the new ZhuTimmermann paper. I mentioned that they end on a constructive note for unconditional predictive accuracy comparisons, even if they raise issues for conditional comparisons. I forgot (until now) about Li, Liao, and Quaedvlieg (2020), one of my favorite recent papers. (We discussed it at length in my Ph.D. class in April.) Their setup avoids the ZhuTimmermann critique and provides an appealing route forward for conditional assessments.
Thursday, June 11, 2020
Monthly vs. Quarterly Recession Dating
The peak delineating the U.S. Pandemic Recession is Feb 2020 if you measure monthly (sure), but 2019Q4 if you measure quarterly (huh?). See the NBER's explanation below. Actually I find the explanation compelling: if you must measure quarterly, 2019Q4 is the right date.
The broader question is why look at a quarterly chronology when you have monthly? You might argue that our science is inexact, so that a monthly chronology may convey a false appearance of precision, like reporting econometric parameter estimates to ten decimal places. Surely I have some sympathy for that view.
But I think the monthly chronology is generally reliable, and there is no doubt that, if I could have access only to monthly or quarterly, I'd take monthly. Nevertheless quarterly is a useful complement, because you DON'T determine the peak quarter simply as the one containing the peak month, as the recent episode illustrates, so the quarterly chronology contains information not in the monthly chronology. The (fairly rare) situations when the peak quarter does not contain the peak month provide useful flags for situations deserving extra thought.
From NBER:
The broader question is why look at a quarterly chronology when you have monthly? You might argue that our science is inexact, so that a monthly chronology may convey a false appearance of precision, like reporting econometric parameter estimates to ten decimal places. Surely I have some sympathy for that view.
But I think the monthly chronology is generally reliable, and there is no doubt that, if I could have access only to monthly or quarterly, I'd take monthly. Nevertheless quarterly is a useful complement, because you DON'T determine the peak quarter simply as the one containing the peak month, as the recent episode illustrates, so the quarterly chronology contains information not in the monthly chronology. The (fairly rare) situations when the peak quarter does not contain the peak month provide useful flags for situations deserving extra thought.
From NBER:
Determination of the February 2020 Peak in US Economic Activity
This report is also available as a PDF.
Cambridge, June 8, 2020  The Business Cycle Dating Committee of the National Bureau of Economic Research maintains a chronology of the peaks and troughs of U.S. business cycles. The committee has determined that a peak in monthly economic activity occurred in the U.S. economy in February 2020. The peak marks the end of the expansion that began in June 2009 and the beginning of a recession. The expansion lasted 128 months, the longest in the history of U.S. business cycles dating back to 1854. The previous record was held by the business expansion that lasted for 120 months from March 1991 to March 2001.
The committee also determined that a peak in quarterly economic activity occurred in 2019Q4. Note that the monthly peak (February 2020) occurred in a different quarter (2020Q1) than the quarterly peak. The committee determined these peak dates in accord with its longstanding policy of identifying the months and quarters of peak activity separately, without requiring that the monthly peak lie in the same quarter as the quarterly peak. Further comments on the difference between the quarterly and monthly dates are provided below.
A recession is a significant decline in economic activity spread across the economy, normally visible in production, employment, and other indicators. A recession begins when the economy reaches a peak of economic activity and ends when the economy reaches its trough. Between trough and peak, the economy is in an expansion.
Because a recession is a broad contraction of the economy, not confined to one sector, the committee emphasizes economywide indicators of economic activity. The committee believes that domestic production and employment are the primary conceptual measures of economic activity.
The Month of the Peak
In determining the date of the monthly peak, the committee considers a number of indicators of employment and production. The committee normally views the payroll employment measure, which is based on a large survey of employers, as the most reliable comprehensive estimate of employment. This series reached a clear peak in February. The committee recognized that this survey was affected by special circumstances associated with the pandemic of early 2020. In the survey, individuals who are paid but not at work are counted as employed, even though they are not in fact working or producing. Workers on paid furlough, who became more numerous during the pandemic, thus resulted in an overcount of people working in recent months. Accordingly, the committee also considered the employment measure from the Bureau of Labor Statistics household survey, which excludes individuals who are paid but on furlough. This series plateaued from December 2019 through February 2020, and then fell steeply from February to March. Because both series measure employment during the week or pay period containing the 12th of the month, they understate the collapse of employment during the second half of March, as indicated by unprecedented levels of new claims for unemployment insurance. The committee concluded that both employment series were thus consistent with a business cycle peak in February.
The committee believes that the two most reliable comprehensive estimates of aggregate production are the quarterly estimates of real Gross Domestic Product (GDP) and of real Gross Domestic Income (GDI), both produced by the Bureau of Economic Analysis (BEA). These measures estimate production that occurred over an entire quarter and are not available monthly. The most comprehensive monthly measure of aggregate expenditures, which includes roughly 70 percent of real GDP, is monthly real personal consumption expenditures (PCE), published by the BEA. This series reached a clear peak in February 2020. The most comprehensive monthly measure of aggregate real income is real personal income less transfers, from the BEA. The deduction of transfers is necessary because transfers are included in personal income but do not arise from production. This measure also reached a welldefined peak in February 2020.
The Quarter of the PeakThe committee believes that the two most reliable comprehensive estimates of aggregate production are the quarterly estimates of real Gross Domestic Product (GDP) and of real Gross Domestic Income (GDI), both produced by the Bureau of Economic Analysis (BEA). These measures estimate production that occurred over an entire quarter and are not available monthly. The most comprehensive monthly measure of aggregate expenditures, which includes roughly 70 percent of real GDP, is monthly real personal consumption expenditures (PCE), published by the BEA. This series reached a clear peak in February 2020. The most comprehensive monthly measure of aggregate real income is real personal income less transfers, from the BEA. The deduction of transfers is necessary because transfers are included in personal income but do not arise from production. This measure also reached a welldefined peak in February 2020.
In dating the quarterly peak, the committee relies on real GDP and real GDI as published by the BEA, and on quarterly averages of key monthly indicators. Quarterly real GDP and real GDI peaked in 2019Q4.
The quarterly average of employment as measured by the payroll series rose from 2019Q4 to 2020Q1. However, the committee concluded that the special factor noted above implies that the series should not play a significant role in determining the quarterly peak. The quarterly average as measured by the household survey reached a clear peak in 2019Q4. The committee concluded that like GDP and GDI, the number of people working also reached its quarterly peak in 2019Q4.
The fact that the monthly peak of February occurred in the middle of 2020Q1 while the quarterly peak occurred in 2019Q4 reflects the unusual nature of this recession. The economy contracted so sharply in March (the final month of the quarter) that in 2020Q1, GDP, GDI, and employment were significantly below their levels of 2019Q4.
Further CommentsThe quarterly average of employment as measured by the payroll series rose from 2019Q4 to 2020Q1. However, the committee concluded that the special factor noted above implies that the series should not play a significant role in determining the quarterly peak. The quarterly average as measured by the household survey reached a clear peak in 2019Q4. The committee concluded that like GDP and GDI, the number of people working also reached its quarterly peak in 2019Q4.
The fact that the monthly peak of February occurred in the middle of 2020Q1 while the quarterly peak occurred in 2019Q4 reflects the unusual nature of this recession. The economy contracted so sharply in March (the final month of the quarter) that in 2020Q1, GDP, GDI, and employment were significantly below their levels of 2019Q4.
The usual definition of a recession involves “a decline in economic activity that lasts more than a few months.” However, in deciding whether to identify a recession, the committee weighs the depth of the contraction, its duration, and whether economic activity declined broadly across the economy (the diffusion of the downturn). The committee recognizes that the pandemic and the public health response have resulted in a downturn with different characteristics and dynamics than prior recessions. Nonetheless, it concluded that the unprecedented magnitude of the decline in employment and production, and its broad reach across the entire economy, warrants the designation of this episode as a recession, even if it turns out to be briefer than earlier contractions.
Committee members participating in the decision were: Robert Hall, Stanford University (chair); Robert Gordon, Northwestern University; James Poterba, MIT and NBER President; Valerie Ramey, University of California, San Diego; Christina Romer, University of California, Berkeley; David Romer, University of California, Berkeley; James Stock, Harvard University; Mark Watson, Princeton University.
Committee members participating in the decision were: Robert Hall, Stanford University (chair); Robert Gordon, Northwestern University; James Poterba, MIT and NBER President; Valerie Ramey, University of California, San Diego; Christina Romer, University of California, Berkeley; David Romer, University of California, Berkeley; James Stock, Harvard University; Mark Watson, Princeton University.
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