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/2015/11/03/20-years-of-the-cide-summer-school-of-econometrics/

## 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 Tabord-Meehan 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 Wisconsin-Madison 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 High-Dimensional 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 Wisconsin--Madison thesis "Misspecification-Robust Bootstrap for Moment Condition Models"

Minjing Tao, for the University of Wisconsin--Madison thesis "Large Volatility Matrix Inference Based on High-frequency 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

Co-Recipients:

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 Schmidt-Dengler, 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

Co-Recipients:

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

Co-Recipients:

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 Cross-Section 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 Non-Acceptable In-patient 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 Aït-Sahalia, 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 Tabord-Meehan 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 Wisconsin-Madison 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 High-Dimensional 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 Wisconsin--Madison thesis "Misspecification-Robust Bootstrap for Moment Condition Models"

Minjing Tao, for the University of Wisconsin--Madison thesis "Large Volatility Matrix Inference Based on High-frequency 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

Co-Recipients:

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 Schmidt-Dengler, 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

Co-Recipients:

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

Co-Recipients:

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 Cross-Section 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 Non-Acceptable In-patient 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 Aït-Sahalia, 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 check-the-box "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 check-the-box "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 mixed-frequency data in Bayes vs. frequentist forecasting and nowcasting.

Quite apart from that, Schorfheide-Song provides eye-opening 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 pre-crisis 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 re-estimate 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, Schorfheide-Song provides eye-opening 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 pre-crisis 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 re-estimate 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 more-or-less 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: Equal-Tailed, 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 full-fledged decision making and well-understood, powerful evaluation methods are available..."

# Scoring Interval Forecasts: Equal-Tailed, 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 equal-tailed 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

A: When the variables are not only integrated but also

What is the analog here, with PCA? That is:

Q: When will PCA with high-dim I(1) variables

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

*co*integrated.What is the analog here, with PCA? That is:

Q: When will PCA with high-dim 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 high-dimensional 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 Dickey-Fuller 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 non-stationarity 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, Karhunen-Loève 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

well-functioning financial markets to the global economy and to global financial

stability was universally acknowledged following the dot-com 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 ultra-high 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 re-fashion 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 hands-on

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 evidenced-based 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 data-based 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.r-project.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 Fry-McKibbin, 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 Diebold-Yilmaz 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 Dickey-Fuller 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 Risk-Return 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 Over-Identified 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 Risk-Return 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 Black-Scholes Option Price Model . . . . . . . . . . . . . . . 569

17.3 A First Look at Options Data . . . . . . . . . . . . . . . . . . . . 573

17.4 Estimating the Black-Scholes Model . . . . . . . . . . . . . . . . 574

17.5 Testing the Black-Scholes Model . . . . . . . . . . . . . . . . . . 581

17.6 Option Pricing and GARCH Volatility . . . . . . . . . . . . . . . 583

17.7 The Melick-Thomas 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¨ıt-Sahalia, 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

Barndorff-Nielsen, 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, J-P., 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, W-Y., 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, K-G., 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

Santa-Clara, 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 Dickey-Fuller 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

Black-Scholes 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

Bollerslev-Wooldridge standard

errors, 457

Bond yields, 36

term structure, 24

yield curve, 24

yield to maturity, 23

Capital asset pricing model (CAPM),

58–63

consumption (C-CAPM), 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 (C-CAPM), 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

Dickey-Fuller test, 140–145

Diebold-Mariano test, 223

Diebold-Yilmaz 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

fixed-income 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

Gibbons-Ross-Shanken test, 371,

403

Gordon model, 187–192

Granger causality, 115

Hannan information criterion

(HIC), 113

Hansen-Sargan 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

two-variable regression model,

254

Integrated process, 137

704 BIBLIOGRAPHY

Integrated variance, 512–515

Inter-temporal 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

Melick-Thomas 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

Multi-factor CAPM

instrumental variables estimation,

255–258

Multifactor CAPM, 63–67

Multiple regression model, 63

Nelson-Siegel parametric factor

model, 431–434

News impact curve (NIC), 459

Newton-Raphson algorithm, 674

Nonlinear option pricing model,

587–588

Nonstationary process, 137

Optimal hedge ratio, 493–495

Options

Black-Scholes 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

Arellano-Bond 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

Residual-based 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

Risk-return 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 Dickey-Fuller

test, 145–147

Dickey-Fuller test, 140–145

GLS detrending, 149–150

KPSS test, 151

Phillips-Peron test, 150

Right-tailed tests, 152–157

Structural breaks, 147

Univariate GARCH model

Bollerslev-Wooldridge 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

Diebold-Yilmaz 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

GARCH-M, 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

Real-Time Real Economic Activity: Exiting the Great Recession and Entering the Pandemic Recession

Authors: Francis X. Diebold

Abstract: We study the real-time signals provided by the Aruoba-Diebold-Scotti Index of Business conditions (ADS) for tracking economic activity at high frequency. We start with exit from the Great Recession, comparing the evolution of real-time vintage beliefs to a "final" late-vintage chronology. We then consider entry into the Pandemic Recession, again tracking the evolution of real-time 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 COVID-19 spreads in the South and West, and could be reversed as quickly as it started.

Submitted 26 June, 2020; originally announced June 2020.

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