Friday, July 20, 2018

Remembering Peter Christoffersen

This is adapted from remarks read at a memorial service earlier this week:

I'm sad not to be able to be here in person, but I'm simultaneously grateful to Peter Pauly for kindly agreeing to read these academically-focused remarks. His reading is actually wonderful and appropriate, as he played a key role in my training and on my Ph.D. dissertation committee, which means that if Peter Christoffersen was my student, he was also Peter Pauly's "grandstudent". For all that they taught me, I am immensely grateful both to Peter Pauly in early years, and to Peter Christoffersen in later years. I am also grateful to Peter Pauly for another reason -- he was the dean who wisely hired the Christoffersens!

I have been fortunate to have had many wonderful students in various cohorts, but Peter's broad cohort was surely the best: Peter of course, plus (in alphabetical order) Sassan Alizadeh, Filippo Altissimo, Jeremy Berkowitz, Michael Binder, Marcelle Chauvet, Lorenzo Giorgiani, Frank Gong, Atsushi Inoue, Lutz Kilian, Jose Lopez, Anthony Tay, and several others.

The Penn econometrics faculty around that time was similarly strong: Valentina Corradi, Jin Hahn, Bobby Mariano, and eventually Frank Schorfheide, with lots of additional macro-econometrics input from Lee Ohanian and financial econometrics input from Michael Brandt. Hashem Pesaran also visited Penn for a year around then. Peter was well known by all the faculty, not just the econometricians. I recall that the macroeconomists were very disappointed to lose him to econometrics!

Everyone knows Peter's classic 1998 "Evaluating Interval Forecasts" paper, which was part of his Penn dissertation. He uncovered the right notion of the "residual" for a (1-a) x 100% interval forecast, and showed that if all is well then it must be iid Bernoulli(1-a). The paper is one of the International Economic Review's ten most cited papers since its founding in 1960.

Peter and I wrote several papers together, which I consider among my very best, thanks to Peter's lifting me to higher-than-usual levels. They most definitely include our Econometric Theory paper on optimal prediction under asymmetric loss, and our Journal of Business and Economic Statistics paper on multivariate forecast evaluation.

Peter's research style was marked by a wonderful blend of intuition, theoretical rigor, and always, empirical relevance, which took him to heights that few others could reach. And his personality, which simply radiated positivity, made him not only a wonderful person to talk soccer or ski with, but the best imaginable person to talk research with.

Peter was also exceedingly generous and effective with his time as regards teaching & executive education, public service, and conference organization. We used to talk a lot about dynamic volatility models, and their use and abuse in financial risk management. His eventual and now well-known textbook on the topic trained legions of students. He and I were the inaugural speakers at the annual summer school of the Society for Financial Econometrics (SoFiE), that year at Oxford University, where we had a wonderful week lecturing together. He served effectively on many committees, including the U.S. Federal Reserve System's Model Validation Committee, charged with reviewing the models used for bank stress testing. He generously hosted the large annual SoFiE meeting in Toronto, several legendary "ski conferences" at Mont Tremblant, and more. The list goes on and on.

We lost a fine researcher and a fine person, much too soon. One can't even begin to imagine what he might have contributed during the next twenty years. But this much is certain: his legacy lives on, and it shines exceptionally brightly. Rest in peace, my friend.

Thursday, July 19, 2018

Machine Learning, Volatility, and the Interface

Just got back from the NBER Summer Institute. Lots of good stuff happening in the Forecasting and Empirical Methods group. The program, with links to papers, is here.

Lots of room for extensions too. Here's a great example. Consider the interface of the Gu-Kelly-Xiu and Bollerslev-Patton-Quagvleg papers. At first you might think that there is no interface. 

Kelly-Xiu is about using off-the-shelf machine-learning methods to model risk premia in financial markets; that is, to construct portfolios that deliver superior performance. (I had guessed they'd get nothing, but I was massively wrong.) Bollerslev et al. is about predicting realized covariance by exploiting info on past signs (e.g., was yesterday's covariance cross-product pos-pos, neg-neg, pos-neg, or neg-pos?). (They also get tremendous results.)

But there's actually a big interface.

Note that Kelly-Xiu is about conditional mean dynamics -- uncovering the determinants of expected excess returns. You might expect even better results for derivative assets, as the volatility dynamics that drive options prices may be nonlinear in ways missed by standard volatility models. And that's exactly the flavor of the Bollerslev et al. results -- they find that a tree structure conditioning on sign is massively successful.

But Bollerslev et al. don't do any machine learning. Instead they basically stumble upon their result, guided by their fine intuition. So here's a fascinating issue to explore: Hit the Bollerslev et al. realized covariance data with machine learning (in particular, tree methods like random forests) and see what happens. Does it "discover" the Bollerslev et al. result? If not, why not, and what does it discover? Does it improve upon Bollerslev et al.?

Thursday, July 5, 2018

Climate Change and NYU Volatility Institute

There is little doubt that climate change -- tracking, assessment, and hopefully its eventual mitigation -- is the burning issue of our times. Perhaps surprisingly, time-series econometric methods have much to offer for weather and climatological modeling (e.g., here), and several econometric groups in the UK, Denmark, and elsewhere have been pushing the agenda forward.

Now the NYU Volatility Institute is firmly on board. A couple months ago I was at their most recent annual conference, "A Financial Approach to Climate Risk", but it somehow fell through the proverbial (blogging) cracks. The program is here, with links to many papers, slides, and videos. Two highlights, among many, were the presentations by Jim Stock (insights on the climate debate gleaned from econometric tools, slides here) and Bob Litterman (an asset-pricing perspective on the social cost of climate change, paper here). A fine initiative!

Monday, June 25, 2018

Peter Christoffersen and Forecast Evaluation

For obvious reasons Peter Christoffersen has been on my mind. Here's an example of how his influence extended in important ways. Hopefully it's also an entertaining and revealing story.

Everyone knows Peter's classic 1998 "Evaluating Interval Forecasts" paper, which was part of his Penn dissertation. The key insight was that correct conditional calibration requires not only that the 0-1 "hit sequence" of course have the right mean ((1-\(\alpha\)) for a nominal 1-\(\alpha\) percent interval), but also that it be iid (assuming 1-step-ahead forecasts). More precisely, it must be iid Bernoulli(1-\(\alpha\)).

Around the same time I naturally became interested in going all the way to density forecasts and managed to get some more students interested (Todd Gunther and Anthony Tay). Initially it seemed hopeless, as correct density forecast conditional calibration requires correct conditional calibration of all possible intervals that could be constructed from the density, of which there are uncountably infinitely many.

Then it hit us. Peter had effectively found the right notion of an optimal forecast error for interval forecasts. And just as optimal point forecast errors generally must be independent, so too must optimal interval forecast errors (the Christoffersen hit sequence). Both the point and interval versions are manifestations of "the golden rule of forecast evaluation": Errors from optimal forecasts can't be forecastable. The key to moving to density forecasts, then, would be to uncover the right notion of forecast error for a density forecast. That is, to uncover the function of the density forecast and realization that must be independent under correct conditional calibration. The answer turns out to be the Probability Integral Transform, \(PIT_t=\int_{-\infty}^{y_t} p_t(y_t)\), as discussed in Diebold, Gunther and Tay (1998), who show that correct density forecast conditional calibration implies \(PIT \sim iid U(0,1)\). 


The meta-result that emerges is coherent and beautiful: optimality of point, interval, and density forecasts implies, respectively, independence of forecast error, hit, and \(PIT\) sequencesThe overarching point is that a large share of the last two-thirds of the three-part independence result -- not just the middle third -- is due to Peter. He not only cracked the interval forecast evaluation problem, but also supplied key ingredients for cracking the density forecast evaluation problem.

Wonderfully and appropriately, Peter's paper and ours were published together, indeed contiguously, in the International Economic Review. Each is one of the IER's ten most cited since its founding in 1960, but Peter's is clearly in the lead!

Friday, June 22, 2018

In Memoriam Peter Christoffersen

It brings me great sadness to report that Peter Christoffersen passed away this morning after a long and valiant struggle with cancer. (University of Toronto page here, personal page here.) He departed peacefully, surrounded by loving family. I knew Peter and worked closely with him for nearly thirty years. He was the finest husband, father, and friend imaginable. He was also the finest scholar imaginable, certainly among the leading financial economists and financial econometricians of his generation. I will miss him immensely, both personally and professionally.

Monday, June 18, 2018

10th ECB Workshop on Forecasting Techniques, Frankfurt

Starts now, program hereLooks like a great lineup. Most of the papers are posted, and the organizers also plan to post presentation slides following the conference. Presumably in future weeks I'll blog on some of the presentations.

Monday, June 11, 2018

Deep Neural Nets for Volatility Dynamics

There doesn't seem to be much need for nonparametric nonlinear modeling in empirical macro and finance. Not that lots of smart people haven't tried. The two key nonlinearities (volatility dynamics and regime switching) just seem to be remarkably well handled by tightly-parametric customized models (GARCH/SV and Markov-switching, respectively). 

But the popular volatility models are effectively linear (ARMA) in squares. Maybe that's too rigidly constrained. Volatility dynamics seem like something that could be nonlinear in ways much richer than just ARMA in squares. 

Here's an attempt using deep neural nets. I'm not convinced by the paper -- much more thorough analysis and results are required than the 22 numbers reported in the "GARCH" and "stocvol" columns of its Table 1 -- but I'm intrigued.

It's quite striking that neural nets, which have been absolutely transformative in other areas of predictive modeling, have thus far contributed so little in economic / financial contexts. Maybe the "deep" versions will change that, at least for volatility modeling. Or maybe not. 

Thursday, June 7, 2018

Machines Learning Finance

FRB Atlanta recently hosted a meeting on "Machines Learning Finance". Kind of an ominous, threatening (Orwellian?) title, but there were lots of (non-threatening...) pieces. I found the surveys by Ryan Adams and John Cunningham particularly entertaining. A clear theme on display throughout the meeting was that "supervised learning" -- the main strand of machine learning -- is just function estimation, and in particular, conditional mean estimation. That is, regression. It may involve high dimensions, non-linearities, binary variables, etc., but at the end of the day it's still just regression. If you're a regular No Hesitations reader, the "insight" that supervised learning = regression will hardly be novel to you, but still it's good to see it disseminating widely.

Monday, May 21, 2018

Top 100 Economics Blogs

Check out the latest "Top 100 Economics Blogs" here. The blurb for No Hesitations (under "Sub-field Economic Blogs") is pretty funny, issuing a stern warning: 
His blog is primarily focused on statistics and econometrics, and is highly technical. Therefore, it is recommended for those with advanced knowledge of economics and mathematics.
In reality, and as I'm sure you'll agree if you're reading this, it's actually simple and intuitive! I guess it's all relative. Anyway the blurb does get this right: "It is especially recommended for those wanting to learn more about dynamic predictive modeling in economics and finance."

Quite apart from pros and cons of its No Hesitations blurb (surely of much more interest to me than to you...), the list provides an informative and timely snapshot of the vibrant economics blogosphere.

Monday, May 14, 2018

Monetary Policy and Global Spillovers

The Bank of Chile's latest Annual Conference volume, Monetary Policy and Global Spillovers: Mechanisms, Effects, and Policy Measures, is now out, here.  In addition to the research presented in the volume, I love the picture on its front cover. So peaceful.