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.

Monday, May 7, 2018

Fourth Penn Quantitative Policy Workshop

Some years ago I blogged on the first Workshop on Quantitative Tools for Macroeconomic Policy Analysis hosted by the Penn Institute for Economic Research (PIER). We just completed the fourth! It was a great group as usual, with approximately 25 participants from around the globe, mostly economists at country central banks, ECB, etc. Some of the happy campers, along with yours truly, appear in the photo. You can find all sorts of information on the workshop site. Information / registration for the next Workshop (May 2019) will presumably be posted in fall. Please consider joining us, and tell your friends!

Monday, April 30, 2018

Pockets of Predictability

Some months ago I blogged on "Pockets of Predictability," here. The Farmer-Schmidt-Timmermann paper that I mentioned is now available, here.