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!