On Assessing Convergence to a Steady State

I recently listened to a stimulating statistics talk, "Discerning a Steady State Sequentially," by Moshe Pollak (with Tom Hope), presently visiting Penn. Of course it's impossible to know with certainty whether we're in steady state based on a finite sample path, but the point is that we may nevertheless be able to make probabilistic statements, effectively "testing the hypothesis" that we're in steady state.

Moshe takes a sequential analytic approach. Here's his abstract: "In many contexts one observes a stochastic process with the goal of learning steady-state characteristics. This talk addresses the question of how to declare with confidence that steady-state has been reached. We focus on a sequence of independent observations that tends in a stochastically monotone fashion to a constant distribution."

Moshe's obvious limitation is independence, as steady states of simulated Markov chains, not independent sequences, are the object of interest in many important applications (posterior simulation, global optimization, etc.).

In the Markov chain case, why not do something like the following. Whenever time \(t\) is a multiple of \(m\), use a distribution-free non-parametric (randomization) test for equality of distributions to test whether the unknown distribution \(f_1\) of \(x_t, ..., x_{t-(m/2)}\) equals the unknown distribution \(f_2\) of \(x_{t-(m/2)+1}, ..., x_{t-m}\). If, for example, we pick \(m=20,000\), then whenever time \(t\) is a multiple of 20,000 we would test equality of the distributions of \(x_t, ..., x_{t-10000}\) and \(x_{t-10001}, ..., x_{t-20000}\). We declare arrival at the steady state when the null is not rejected. Or something like that.

Of course the Markov chain is serially correlated, but who cares, as we're only trying to assess equality of unconditional distributions. That is, randomizations of \(x_t, ..., x_{t-(m/2)}\) and of \(x_{t-(m/2)+1}, ..., x_{t-m}\) destroy the serial correlation, but so what?

My suggestion is either misguided for some reason that I'm missing, or someone must have done it. (It's just too obvious.)

More on Factor-Augmented VAR's (Principal Components Regression)

Here's a sampling of emails that I received on my recent "Factor-Augmented VAR" post.

Serena Ng at Columbia notes that her "Targeted Predictors" paper (with Jushan Bai) is motivated by considerations similar to those that motivate partial least squares (PLS). She also notes that she has a discussion of this in a Handbook of Forecasting overview paper (sections 4 and 5), and that it's not clear that PLS is systematically dominant. I look forward to reading the Handbook piece, which, embarrassingly, I have not yet done.

George Kapetanios at Queen Mary, University of London, echoes Serena's view. He sent his new paper, "Revisiting Useful Approaches to Data-Rich Macroeconomic Forecasting" (with Jan Groen), in the PLS-Kelly-Pruitt tradition but considering more general settings (e.g., weak factors) and considering alternative methods such as ridge regression. His upshot is that forecasting is of course complex and "best" procedures depend on a variety of settings and choices (and the "best" may not be PLS), but that in any event principal-component regression (PCR) appears robustly sub-optimal.

Not least, Frank DiTraglia at Penn sent some interesting links to the chemometrics literature, which prominently features PLS and has some interesting probabilistic perspectives on it.

So it's interesting. PCR appears robustly sub-optimal, but there's a feeling that PLS at least as traditionally implemented does not appear robustly dominant. Other emails, not reported in detail here, echoed that theme,

So much for the PCR vs. PLS issue. What about the PCR vs. ridge regression (RR) issue? Enter Paramveer Dhillon, a Penn Computer Science (machine learning) Ph.D. student, who sent his paper, "A Risk Comparison of Ordinary Least Squares vs Ridge Regression" (with Dean Foster, Sham Kakade and Lyle Ungar). Paramveer et al. show that PCR risk is always within a factor of four of RR risk, but that the converse is not true; that is, RR can be arbitrarily worse than PCR. So from a different perspective PCR suddenly looks appealing. (And from the Blogger-Abusing-His-Position-to-Pat-Himself-on-the-Back Department: Paramveer also notes that he enjoyed my Ph.D. time-series course, which he audited last year!)

[Finally, my friends, just in case you missed the weekend post I'll repeat it: Please don't hesitate to post comments. Instead what usually happens is that people email me directly, and I can't respond, and I feel bad that I can't respond, and the sender feels bad that I didn't respond, and most importantly, people who would benefit from reading the comment (and perhaps reading comments on the comment, or themselves commenting on the comment) never get to see it. A bad equilibrium all around.]

Check Out the Society of Quantitative Analysts (SQA)

If you're in or around Manhattan, in industry or interested in academic-industry crossover (and who wouldn't be?), the Society of Quantitative Analysts is for you. A totally class act.  Check out, for example, Director Jonathan Reiss and and next week's speaker Clara Vega.

About SQA | Contact SQA | Amazon Books

February 24, 2014 You are invited to attend the free-of-charge research symposium "Quantitative Investing with News and Sentiment Analytics" sponsored by RavenPack and Deltix, on February 24, 2014, from 10am to 5pm, at The Cornell Club (6 East 44th Street, New York, NY).  The organizers have invited several leading quantitative finance practitioners and academics to present work they have been doing on equities, credit and macro with news analytics. Confirmed Speakers •Nicholas Colas, Chief Market Strategist, ConvergEx Group •Clara Vega, Senior Economist, Federal Reserve •Sasha Migdal, CEO, MigdalResearch LLC •Andrea Ghiringhelli, Director R&D, Fitch Solutions •Ian Watt, Economist & Country Insights Specialist, Roubini Global Economics •Jeremiah Green, Assistant Professor, Penn State University •David Marra, CEO, Arialytics •Ilya Gorelik, CEO, Deltix •Peter Hafez, Director of Quant Research, RavenPack March 5, 2014 Dr. Merav Ozair (SQA board member) will be holding a webinar on March 5th at 12pm for PRMIA on "FOREX Markets: Trading, Regulations and Risk". About the Presenter: Dr. Merav Ozair has over 12 years’ of business and consulting experience.  Currently her work and expertise center on volatility modeling, market microstructure and developing statistical (econometric) investing and trading strategies. Her previous business experience includes developing business strategies to enhance business growth; evaluating the viability of potential public offerings; estimating the market value of business for M&A; performing fundamental and valuation analysis; developing models for performance attribution, and; analyzing operating risk and risk management on a company’s level. Dr. Ozair has over 15 years’ teaching experience and currently she has been teaching at the Finance and Risk Engineering (FRE) program at NYU – Market Microstructure, Financial Econometrics and Portfolio Management.  She has earned her PhD in Accounting and Finance from Stern Business School at NYU, and her research interests include market microstructure, volatility modeling and financial econometrics.  She is also the founder of Mackabie Capital a financial service provider which bridges fundamental and quantitative methods to enable money managers in their pursuit for better alpha generating strategies, risk control and execution.  She also holds a CPA and a CQF.  For further information visit: www.mackabiecapital.com March 20-22, 2014 Professionals are welcome to attend the Quinnipiac Global Asset Management Education (G.A.M.E.) IV Forum on Thursday March 20, 2014 at the Sheraton New York Times Square Hotel to hear keynote speaker panels discuss the:  Global Economy, Alternative Assets versus Equities, Corporate Governance, Global Markets and provide a Fed & Washington Perspective.  Last year, more than 1000 college students, faculty and investment professionals participated in this very dynamic investment conference, representing 43 countries, 44 states, Puerto Rico and the District of Columbia.  Pre-registration is required and on-site registration will not be available.  Members and friends of SQA are able to save $200 per professional registration by using the Promotion Code SQA14.  In addition, professional group registrations of five or more will save an additional $50 per registration.  Our online registration is open with a link provided below. ADDITIONAL INFORMATION: Registration: http://www.regonline.com/eventinfo.asp?eventid=1277206 Web Site:       http://game.quinnipiac.edu Email:               game@quinnipiac.edu Phone:            203-582-5400 Overview YouTube Video:  http://youtu.be/GTjETSW73Qo Confirmed Keynote Speakers Include: Keynote Panels: •           Global Economy Douglas Coté, CFA, Chief Market Strategist & Senior Portfolio Manager, ING Investment Management Bob Doll, CFA, Chief Equity Strategist & Senior Portfolio Manager, Nuveen Asset Management LLC Dr. John Silvia, Managing Director & Chief Economist, Wells Fargo Securities Richard Yamarone, Senior Economist, Bloomberg Brief •           Alternatives vs. Equities Rich Bernstein, Chief Executive Officer, Richard Bernstein Advisors LLC Michael Khouw, Managing Director & Primary Strategist, DASH Financial Joe Kinahan, Chief Strategist, TD Ameritrade Benjamin A. Pace III, Managing Director & Chief Investment Officer, Deutsche Bank Private Wealth Management •           Fed & Washington Perspective Tom Keene, Editor-At-Larger, Bloomberg News •           Corporate Governance Al Angrisani, President & Chief Investment Officer, Harris Interactive Gary Katz, President & Chief Investment Officer, International Securities Exchange Edward Knight, JD, Executive Vice President, General Counsel & Regulatory Officer, NASDAQ OMX Group Inc John D. Rogers, CFA, President & Chief Executive Officer, CFA Institute •           Global Markets Ralph Acampora, CMT, Senior Managing Director, Altaira Ltd Guy Adami, Managing Director, Drakon Capital & Fast Money Contributor, CNBC Abby Joseph Cohen, CFA, Senior Investment Strategist & President Global Markets Institute, Goldman Sachs Dr. David Kelly, CFA, Managing Director & Chief Global Strategist, J.P. Morgan Funds August 11-16, 2014 The SQA is once again proud to partner with SYMMYS and Attilio Meucci for the 6-day annual intensive course "Advanced Risk and Portfolio Management Bootcamp" at New York University.  The course is worth 40 CE units of CFA Institute and 40 CPE units of GARP.  The ARPM Bootcamp (http://symmys.com/ arpm-bootcamp) provides in-depth understanding of buy-side modeling from the foundations to the latest advanced statistical and optimization techniques, in nine intense, heavily quantitative hours each day, with theory, live simulations, review sessions and exercises.  Topics include portfolio construction, factor modeling, copulas, liquidity, risk modeling, and much more. Also features Gala Dinner with world-renowned speakers such as Rob Almgren, Peter Carr, Bruno Dupire, Jim Gatheral, Bob Litterman, Bob Litzenberger, Andrew Lo, Fabio Mercurio, Steven Shreve. See a short video http://www.youtube.com/watch?v=BUnrgjNxBWk To register with the SQA discounted partner rate go to http://www.symmys.com/arpm-bootcamp/registration, then see 1) "Registration Type", select "Partner"; 2) go to "Specify", select "Other"; 3) go to "Specify", type "SQA", or contact ARPM at arpm.bootcamp@symmys.com

Don't Hesitate to Post Comments

A brief plea: PLEASE don't hesitate to post comments. Instead what usually happens is that people email me directly, and I can't respond, and I feel bad that I can't respond, and the sender feels bad that I didn't respond, and most importantly, people who would benefit from reading the comment (and perhaps reading comments on the comment, or themselves commenting on the comment) never get to see it. A bad equilibrium all around.

My next post will collect a few of the email comments that I got on the last post, Thoughts on Factor-Augmented VAR's. But again, that's a terribly inefficient way to proceed. Please just post your comments directly.

Maybe after that I'll post a few provocative rants to see what you have to say.

Related, some of you get my posts via Twitter or Facebook and occasionally comment, which is great, but society would benefit if you would post comments directly on the blog, in addition to Facebook or whatever, as most people access the blog directly and hence will never see your Facebook comments.

Thanks for your consideration. And of course many, many thanks for reading.

New posts coming soon!

Thoughts on "Factor-Augmented VAR's"

Let's use the standard term, principal-components regression (PCR). It's irrelevant whether it's a "regular" regression or an autoregression, univariate or multivariate. Econometricians have always liked PCR. (I am no exception.) In this "data-rich" age it's more useful than ever, and things like Bernanke and Boivin's factor-augmented vector autoregressions have taken PCR to new heights of popularity.

But PCR has some awkward aspects, well-known in some circles (see, e.g., Hastie and Tibshirani, Elements of Statistical Learning, Chapter 3) but curiously little-known in others.

In particular:

(1) First-step PC extraction is "unsupervised" (in machine-learning jargon). Hence the x-variable linear combinations given by the PC's may differ importantly from the best x-variable linear combinations for predictive purposes. This is unfortunate because second-step PCR typically is used for prediction!

(2) PCR shrinks in rather awkward/extreme directions/amounts. PCR shrinks the excluded PC's completely to 0 (by construction), and moreover, it shrinks the included PC's equally toward 0, regardless of the relative sizes of their associated eigenvalues.

So, what to do?

(1) Wold's partial least squares (PLS) attempts to address issue (1). Recent interesting work, moreover, extends PLS in powerful ways, as with the Kelly-Pruitt three-pass regression filter and its amazing apparent success in predicting aggregate equity returns.

(2) Ridge regression (among others) addresses issue (2). It includes all PC's and shrinks them toward 0 according to the relative sizes of their associated eigenvalues.

SoFiE Facebook Group and More

The next Society for Financial Econometrics (SoFiE) Facebbok Group member will be our 1000th!  If you're not a member of the Facebook group, simply go to https://www.facebook.com/groups/sofienyu/ to join. Related, may I please ask you to take a minute and think of a single friend/colleague who might benefit from joining the Facebook group, and send her/him a quick email? If you help, we can move closer to 2000 members in one discrete jump. Finally, and again related, please consider joining SoFiE (the Society, not just the Facebook group). There are many benefits, and your formal support would be much appreciated. Just go to the SoFiE homepage and click on "membership information."

Congratulations to Loretta Mester, New President of The Federal Reserve Bank of Cleveland

Loretta is presently the Director of Research at the Philadelphia Fed, and she will replace Cleveland's Sandra Pianalto effective June 1. She has been a stunningly effective research director in Philadelphia; indeed her loss is a terrible blow to FRB Philadelphia and a massive gain for FRB Cleveland.  Not least I'm personally grateful for her enthusiastic support of FRB Philadelphia's ADS index and GDPplus series.  I will miss her, and I wish her every success in her new role.  

For additional information, see the Reuters article.

NBER Econonometrics "Methods Lectures" Videos

For nearly a decade, the National Bureau of Economic Research has been holding a day of econometrics "Methods Lectures" during the Summer Institute, with the speakers and sub-topic changing each year.


Evidently it's not widely known that the lecture videos and slides are available online -- just click on any of the links below.

[Warning: Certain of the links reveal that audio/video recording/delivery is not the NBER's strong suit, but all the videos are there if you take a few minutes to figure things out.]


Summer Institute 2013
Econometric Methods for High-Dimensional Data
Victor Chernozhukov, Massachusetts Institute of Technology, Matthew Gentzkow, University of Chicago and NBER, Christian Hansen, University of Chicago , Jesse Shapiro, University of Chicago and NBER, Matthew Taddy, University of Chicago

Summer Institute 2012
Econometric Methods for Demand Estimation
Ariel Pakes, Harvard University and NBER and Aviv Nevo, Northwestern University and NBER

Summer Institute 2011
Computational Tools & Macroeconomic Applications
Lawrence Christiano, Northwestern University and NBER and Jesus Fernandez-Villaverde, University of Pennsylvania and NBER

Summer Institute 2010
Financial Econometrics
Sydney Ludvigson, New York University and NBER , Yacine Ait-Sahalia, Princeton University and NBER, Michael Brandt, Duke University and NBER and Andrew Lo, MIT and NBER

Summer Institute 2009
Using Field Experiments in Economics: An Introduction, and Conducting Field Research in Developing Countries
John List, University of Chicago and NBER and Michael Kremer, Harvard University and NBER

Summer Institute 2008
Whats New in Econometrics – Time Series
James H. Stock, Harvard University and NBER and Mark W. Watson, Princeton University and NBER

Summer Institute 2007
Whats New in Econometrics?
Guido Imbens, Harvard University and NBER and Jeffrey Wooldridge, Michigan State University

2014 SoFiE Financial Econometrics Summer School at Harvard

The 2014 Society for Financial Econometrics (SoFiE) Summer School in Financial Econometrics will take place July 28 - August 1 at Harvard University. This is the third annual edition; 2012 and 2013 were highly successful, and I'm certain that 2014 will be as well. The topic is the econometrics of option pricing, and the lecturers are Patrick Gagliardini (University of Lugano and the Swiss Finance Institute) and Eric Renault (Brown University). Students are typically drawn from top Ph.D. programs, world-wide. For additional information, and to apply for admission, go to http://www.stat.harvard.edu/SoFiE/index.html. Application deadline is March 25!

The event has an interesting history that traces largely to the vision and energy of Neil Shephard. While still at Oxford running the Oxford-Man Institute of Quantitative Finance, he had the idea, he asked SoFiE to partner with him (I was SoFiE President at the time), and he generously donated Oxford's beautiful facilities and fine administrative services. Now that he's moved to Harvard, the summer school has moved with him. Thanks, Neil, for your many wonderful ongoing contributions to econometrics education.



Here's a detailed 2014 course outline:
1. Stochastic-volatility option pricing. Options prices as expected Black-Scholes price. Volatility smiles.
2. Non-linear State-Space models.
3. GMM with latent variables: Indirect Inference and Implied-States GMM.
4. Nonparametric fitting of implied volatility surfaces. Implied binomial trees and maximum entropy
5. High-frequency data and option pricing
6. Extended Method of Moments (XMM).
7. Volatility risk premium and long memory in volatility.
8. VIX computation and methods for American options.

Research Credibility, Bayes, and "Searching for Asterisks"

Is there really a "credibility crisis" in the sciences that use statistics, as some seem to fear these days? I think not; generally I'm on board with Demming's "In God we trust, all others bring data." Of course there are issues, but they're hardly new. Some simply reflect poor understanding of statistics. For example, a Bayesian calculation of post-study probability, \( P(H_0 ~ true ~|~ data ) \), is very different from a classical \(p\)-value, \( P(data ~|~ H_0 ~ true) \). The former can be large even when the latter is very small -- notwithstanding the fact that the two are often naively confused. Other issues are real -- like the effects of "searching for asterisks" (data mining, in the bad sense) and the corresponding "file-drawer problem" in which "insignificant" results languish in file drawers, unsubmitted, unpublished and unseen -- but lots of existing and ongoing work is helping us to confront them.

It's important, however, always to be on alert. Here's some reading on the issue of \( P(H_0 ~ true ~|~ data ) \) vs. \( P(data ~|~ H_0 ~ true) \), which has gotten fresh attention recently. Cohen (1994) is classic, as is its title, "The Earth Is Round (\(p < .05\))." Fast-forwarding twenty years, the Maniadis et al. (2014) AER piece is very interesting (also see the January 2014 Issue of Econ Journal Watch, which arrived as spam but turned out to contain an interesting comment with a rejoinder by Maniadis et al.). Last and not least, see Dick Startz's 2013 working paper.