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 is my student, he is 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 places where few others could go. And his personality, which simply radiated positivity, made him not only a wonderful person to talk soccer or ski with, but also to do 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 supervision and regulation. 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 imagine what he might have contributed during the next twenty years. But his legacy lives on, and it shines very 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.

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.

Monday, April 23, 2018

Ghysels and Marcellino on Time-Series Forecasting

If you're teaching a forecasting course and want a good text, or if you're just looking for an informative and modern treatment, see Applied Economic Forecasting Using Time Series Methods, by Eric Ghysels and Massimilliano Marcellino. It will be published this week by Oxford University Press. It has a very nice modern awareness of Big Data with emphasis on reduced-rank structure, regularization methods -- LASSO appears as early as p. 23! -- , structural change, mixed-frequencies, etc. It's also very tastefully done in terms of what's included and what's excluded, emphasizing what's most important and de-emphasizing the rest. As regards non-linearity, for example, volatility dynamics and regime-switching are in, and most of the rest is out.

Monday, April 16, 2018

The History of Forecasting Competitions

Check out Rob Hyndman's "Brief History of Time Series Forecasting Competitions". I'm not certain whether the title's parallel to Hawking's Brief History of Time is intentional. At any rate, even if Hyndman's focus is rather more narrow than the origin and fate of the universe, his post is still fascinating and informative. Thanks to Ross Askanasi for bring it to my attention.

Monday, April 9, 2018

An Art Market Return Index

Rare and collectible goods, from fine art to fine wine, have many interesting and special aspects. Some are shared and some are idiosyncratic.

From the vantage point of alternative investments (among other things), it would be useful to have high-frequency indices for those asset markets, just as we do for traditional "financial" asset markets like equities.

Along those lines, in "Monthly Art Market Returns" Bocart, Ghysels, and Hafner develop a high-frequency measurement approach, despite the fact that art sales generally occur very infrequently. Effectively they develop a mixed-frequency 
repeat-sales model, which captures the correlation between art prices and other liquid asset prices that are observed much more frequently. They use the model to extract a monthly art market return index, as well as sub-indices for contemporary art, impressionist art, etc.

Quite fascinating and refreshingly novel.

Monday, April 2, 2018

Econometrics, Machine Learning, and Big Data

Here's a useful slide deck by Greg Duncan at Amazon, from a recent seminar at FRB San Francisco (powerpoint, ughhh, sorry...). It's basically a superset of the keynote talk he gave at Penn's summer 2017 conference, Big Data in Predictive Dynamic Econometric Modeling. Greg understands better than most the close connection between "machine learning" and econometrics / statistics, especially between machine learning and the predictive perspective emphasized in time series for a century or so.

Monday, March 26, 2018

Classic Jacod (1994) Paper

J. Financial Econometrics will soon publish Jean Jacod's brilliant and beautiful 1994 paper, "Limit of Random Measures Associated with the Increments of a Brownian Semimartingale", which I just had the pleasure of reading for the first time. (Ungated version here.) Along with several others, I was asked to supply some comments for the issue's introduction. What follows is adapted from those comments, providing some historical background. (Except that it's not really historical background -- keep reading...)

Jacod's paper effectively lays the foundation for the vast subsequent econometric "realized volatility" (empirical quadratic variation) literature of the past twenty years.  Reading it leads me to recall my early realized volatility work with Torben Andersen and Tim Bollerslev in the late 1990's and early 2000's. It started in the mid-1990's at a meeting of the NBER Asset Pricing Program, where I was the discussant for a paper of theirs, eventually published as Andersen and Bollerslev (1998). They were using realized volatility as the "realization" in a study of GARCH volatility forecast accuracy, and my discussion was along the lines of, "That's interesting, but I think you've struck gold without realizing it -- why not skip the GARCH and instead simply characterize, model, and forecast realized volatility directly?".

So we decided to explore realized volatility directly. Things really took off with Andersen et al. (2001) and Andersen et al. (2003). The research program was primarily empirical, but of course we also wanted to advance the theoretical foundations. We knew some relevant stochastic integration theory, and we made progress culminating in Theorem 2 of Andersen et al. (2003). Around the same time, Ole Bardorff-Nielsen and Neil Shephard were also producing penetrating and closely-related results (most notably Barndorff-Nielsen and Shephard, 2002). Very exciting early times.

Now let's return to Jacod's 1994 paper, and consider it against the above historical background of early econometric realized volatility papers. Doing so reveals not only its elegance and generality, but also its prescience: It was written well before the "historical background"!! One wonders how it went unknown and unpublished for so long.

References

Andersen, T. G. and T. Bollerslev (1998), "Answering the Skeptics: Yes, Standard Volatility Models do Provide Accurate Forecasts," International Economic Review, 39, 885-905.

Andersen, T.G., T. Bollerslev, F.X. Diebold, and P. Labys (2001), "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, 96, 42-55.

Andersen, T.G., T. Bollerslev, F.X. Diebold, and P. Labys (2003), "Modeling and Forecasting Realized Volatility," Econometrica, 71, 579-625.

Barndorff-Nielsen, O. and N. Shephard (2002), "Econometric Analysis of Realized Volatility and its Use in Estimating Stochastic Volatility Models," Journal of the Royal Statistical Society, 64,
253-280.

Jacod, J. (1994), "Limit of Random Measures Associated with the Increments of a Brownian Semimartingale," Manuscript, Institute de Mathematiques de Jussieu, Universite Pierre et Marie Curie, Paris.

Monday, March 19, 2018

Big Data and Economic Nowcasting

Check out this informative paper from the Federal Reserve Bank of New York: "Macroeconomic Nowcasting and Forecasting with Big Data", by Brandyn Bok, Daniele Caratelli, Domenico Giannone, Argia Sbordone, and Andrea Tambalotti.

Key methods for confronting big data include (1) imposition of restrictions (for example, (a) zero restrictions correspond to "sparsity", (b) reduced-rank restrictions correspond to factor structure, etc.), and (2) shrinkage (whether by formal Bayesian approaches or otherwise).

Bok et al. provide historical perspective on use of (1)(b) for macroeconomic nowcasting; that is, for real-time analysis and interpretation of hundreds of business-cycle indicators using dynamic factor models. They also provide a useful description of FRBNY's implementation and use of such models in policy deliberations.

It is important to note that the Bok et al. approach nowcasts current-quarter GDP, which is different from nowcasting "the business cycle" (as done using dynamic factor models at FRB Philadelphia, for example), because GDP alone is not the business cycle. Hence the two approaches are complements, not substitutes, and both are useful.

Monday, March 12, 2018

Sims on Bayes

Here's a complementary and little-known set of slide decks from Chris Sims, deeply insightful as always. Together they address some tensions associated with Bayesian analysis and sketch some resolutions. The titles are nice, and revealing. The first is "Why Econometrics Should Always and Everywhere Be Bayesian". The second is "Limits to Probability Modeling" (with Chris' suggested possible sub-title: "Why are There no Real Bayesians?").

Thursday, March 8, 2018

H-Index for Journals

In an earlier rant, I suggested that journals move from tracking inane citation "impact factors" to citation "H indexes" or similar, just as routinely done when evaluating individual authors. It turns out that RePEc already does it, here. There are literally many thousands of journals ranked. I show the top 25 below. Interestingly, four "field" journals actually make the top 10, effectively making them "super (uber?) field journals" (J. Finance, J. Financial Economics, J. Monetary Economics, and J. Econometrics). For example, J. Econometrics is basically indistinguishable from Review of Economic Studies. 

The rankings

RankJournalFactorAdjusted
citations
ItemsAll
citations
1American Economic Review, American Economic Association2623897539641395549
2Journal of Political Economy, University of Chicago Press2352275342978229129
3Econometrica, Econometric Society (also covers Econometrica, Econometric Society )2332660313530267883
4The Quarterly Journal of Economics, Oxford University Press2312116382311212892
5Journal of Finance, American Finance Association2102130764558215655
6Journal of Financial Economics, Elsevier1651380732654149337
7Journal of Monetary Economics, Elsevier (also covers Carnegie-Rochester Conference Series on Public Policy, Elsevier )1581237053334128056
8Review of Economic Studies, Oxford University Press1571143592317115072
9Journal of Econometrics, Elsevier1491318234160141376
10Journal of Economic Literature, American Economic Association1457291689173201
11Journal of Economic Perspectives, American Economic Association14577073167377758
12The Review of Economics and Statistics, MIT Press1401093303953109953
13Economic Journal, Royal Economic Society (also covers Economic Journal, Royal Economic Society )1371037633663104399
14Journal of International Economics, Elsevier12276446298381228
15Review of Financial Studies, Society for Financial Studies11966261165767063
16Journal of Public Economics, Elsevier11790038372295659
17Journal of Development Economics, Elsevier11365314311168204
18European Economic Review, Elsevier11174123387075847
19Journal of Economic Theory, Elsevier10883540423890223
20Journal of Business & Economic Statistics, Taylor & Francis Journals (also covers Journal of Business & Economic Statistics, American Statistical Association )10544499172644729
21Journal of Money, Credit and Banking, Blackwell Publishing (also covers Journal of Money, Credit and Banking, Blackwell Publishing )10451991295552610
22Management Science, INFORMS9570575689176945
23Journal of Banking & Finance, Elsevier9361760482972982
24International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association (also covers International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association )9148542253748823
25Journal of Labor Economics, University of Chicago Press9137921108438993

Wednesday, February 28, 2018

The Rate of Return on Everything

Jorda, Knoll, Kuvshinov, Schularick and Taylor deliver more than just a memorable title, "The Rate of Return on Everything, 1870-2015". (Dec 2017 NBER version here; earlier ungated June 2017 version here.) Their paper is a fascinating exercise in data construction and analysis. It goes well beyond, say, the earlier and also-fascinating Dimson et al. (2002) book, by including housing, among other things.

Caveat emptor: In this case two words suffice -- survivorship bias. Jorda et al. are well aware of it, and they work hard to assess and address it. But still.

Monday, February 26, 2018

STILL MORE on NN's and ML

I recently discussed how the nonparametric consistency of wide NN's proved underwhelming, which is partly why econometricians lost interest in NN's in the 1990s.

The other thing was the realization that NN objective surfaces are notoriously bumpy, so that arrival at a local optimum (e.g., by the stochastic gradient descent popular in NN circles) offered little comfort.

So econometricians' interest declined on both counts. But now both issues are being addressed. The new focus on NN depth as opposed to width is bearing much fruit. And recent advances in "reinforcement learning" methods effectively promote global as opposed to just local optimization, by experimenting (injecting randomness) in clever ways. (See, e.g., Taddy section 6, here.)

All told, it seems like quite an exciting new time for NN's. I've been away for 15 years. Time to start following again...

Wednesday, February 21, 2018

Larry Brown

Larry Brown has passed away.  Larry was a giant of modern statistics and a towering presence at Penn.  Simultaneously, everyone who knew him liked him, immensely. He will be missed dearly, both professionally and personally.

I received the obituary below from Penn's Statistics Department.

Lawrence David Brown Lawrence D. Brown died peacefully at 6:30 a.m. on Feb. 21, 2018, at the age of 77. Larry preserved his unfailing fortitude and good humor to his last day. Larry was born on Dec. 16, 1940, in Los Angeles, California. His parents moved to Alexandria, VA, during World War II, then returned to California. His father, Louis Brown, was a successful tax lawyer and later a professor of law at the University of Southern California, where he worked tirelessly on behalf of client services and conflict prevention, for which he coined the phrase preventive law. His mother, Hermione Kopp Brown, studied law in Virginia and then in Los Angeles and became one of the leading women lawyers in Los Angeles in the field of entertainment law, with emphasis on estate planning. Larry inherited their dedication for service, their mental acuity and resourcefulness, and their selfless good spirits. Larry graduated from Beverly Hills High School in 1957 and from the California Institute of Technology in 1961 and earned his Ph.D. in mathematics from Cornell University three years later. Initially hired at the University of California, Berkeley, he then taught in the mathematics department at Cornell University from 1966-72 and 1978-94 and in the statistics department at Rutgers University from 1972-78; he moved to the Wharton School at the University of Pennsylvania in 1994 and taught his last course there as the Miers Busch Professor of Statistics in the fall of 2017. One of the leading statisticians of his generation, he was the recipient of many honors, including devoted service as a member of the National Academy of Sciences, election to the American Academy of Arts and Sciences, the presidency of the Institute of Mathematical Statistics, and an honorary doctorate from Purdue University. He was much loved by his colleagues and his students, many of whom hold leading positions in the United States and abroad. His passion for his work was matched by his devotion to his family. His wife Linda Zhao survives him, as do their sons Frank and Louie, their daughter Yiwen Zhao, his daughters from his first marriage, Yona Alpers and Sarah Ackman, his brothers Marshall and Harold and their wives Jane and Eileen, and 19 grandchildren.

Monday, February 19, 2018

More on Neural Nets and ML

I earlier mentioned Matt Taddy's "The Technological Elements of Artificial Intelligence" (ungated version here).

Among other things the paper has good perspective on the past and present of neural nets. (Read:  his views mostly, if not exactly, match mine...)  

Here's my personal take on some of the history vis a vis econometrics:

Econometricians lost interest in NN's in the 1990's. The celebrated Hal White et al. proof of NN non-parametric consistency as NN width (number of neurons) gets large at an appropriate rate was ultimately underwhelming, insofar as it merely established for NN's what had been known for decades for various other non-parametric estimators (kernel, series, nearest-neighbor, trees, spline, etc.). That is, it seemed that there was nothing special about NN's, so why bother? 

But the non-parametric consistency focus was all on NN width; no one thought or cared much about NN depth. Then, more recently, people noticed that adding NN depth (more hidden layers) could be seriously helpful, and the "deep learning" boom took off. 

Here are some questions/observations on the new "deep learning":

1.  Adding NN depth often seems helpful, insofar as deep learning often seems to "work" in various engineering applications, but where/what are the theorems? What can be said rigorously about depth?

2. Taddy emphasizes what might be called two-step deep learning. In the first step, "pre-trained" hidden layer nodes are obtained based on unsupervised learning (e.g., principle components (PC)) from various sets of variables. And then the second step proceeds as usual. That's very similar to the age-old idea of PC regression. Or, in multivariate dynamic environments and econometrics language, "factor-augmented vector autoregression" (FAVAR), as in Bernanke et al. (2005). So, are modern implementations of deep NN's effectively just nonlinear FAVAR's? If so, doesn't that also seem underwhelming, in the sense of -- dare I say it -- there being nothing really new about deep NN's?

3. Moreover, PC regressions and FAVAR's have issues of their own relative to one-step procedures like ridge or LASSO.  See this and this

Tuesday, February 13, 2018

Neural Nets, ML and AI

"The Technological Elements of Artificial Intelligence", by Matt Taddy, is packed with insight on the development of neural nets and ML as related to the broader development of AI. I have lots to say, but it will have to wait until next week. For now I just want you to have the paper. Ungated version at http://www.nber.org/chapters/c14021.pdf.

Abstract:

We have seen in the past decade a sharp increase in the extent that companies use data to optimize their businesses.  Variously called the `Big Data' or `Data Science' revolution, this has been characterized by massive amounts of data, including unstructured and nontraditional data like text and images, and the use of fast and flexible Machine Learning (ML) algorithms in analysis.  With recent improvements in Deep Neural Networks (DNNs) and related methods, application of high-performance ML algorithms has become more automatic and robust to different data scenarios.  That has led to the rapid rise of an Artificial Intelligence (AI) that works by combining many ML algorithms together - each targeting a straightforward prediction task - to solve complex problems.  

We will define a framework for thinking about the ingredients of this new ML-driven AI.  Having an understanding of the pieces that make up these systems and how they fit together is important for those who will be building businesses around this technology. Those studying the economics of AI can use these definitions to remove ambiguity from the conversation on AI's projected productivity impacts and data requirements.  Finally, this framework should help clarify the role for AI in the practice of modern business analytics and economic measurement.

Monday, February 12, 2018

ML, Forecasting, and Market Design

Nice stuff from Milgrom and Tadelis. Improved forecasting via improved machine learning in turn helps improve our ability to design effective markets -- better anticipating consumer/producer demand/supply movements, more finely segmenting and targeting consumers/producers, more accurately setting auction reserve prices, etc. Presumably full density forecasts, not just the point forecasts on which ML tends to focus, should soon move to center stage.
http://www.nber.org/chapters/c14008.pdf

Monday, February 5, 2018

Big Data, Machine Learning, and Economic Statistics

Greetings from a very happy Philadelphia celebrating the Eagles' victory!

The following is adapted from the "background" and "purpose" statements for a planned 2019 NBER/CRIW conference, "Big Data for 21st Century Economic Statistics". Prescient and fascinating reading. (The full call for papers is here.)

Background: The coming decades will witness significant changes in the production of the social and economic statistics on which government officials, business decision makers, and private citizens rely. The statistical information currently produced by the federal statistical agencies rests primarily on “designed data” -- that is, data collected through household and business surveys. The increasing cost of fielding these surveys, the difficulty of obtaining survey responses, and questions about the reliability of some of the information collected, have raised questions about the sustainability of that model. At the same time, the potential for using “big data” -- very large data sets built to meet governments’ and businesses’ administrative and operational needs rather than for statistical purposes -- in the production of official statistics has grown.

These naturally-occurring data include not only administrative data maintained by government agencies but also scanner data, data scraped from the Web, credit card company records, data maintained by payroll providers, medical records, insurance company records, sensor data, and the Internet of Things. If the challenges associated with their use can be satisfactorily resolved, these emerging sorts of data could allow the statistical agencies not only to supplement or replace the survey data on which they currently depend, but also to introduce new statistics that are more granular, more up-to-date, and of higher quality than those currently being produced.

Purpose: The purpose of this conference is to provide a forum where economists, data providers, and data analysts can meet to present research on the use of big data in the production of federal social and economic statistics. Among other things, this involves discussing (1) Methods for combining multiple data sources, whether they be carefully designed surveys or experiments, large government administrative datasets, or private sector big data, to produce economic and social statistics; (2) Case studies illustrating how big data can be used to improve or replace existing statistical data series or create new statistical data series; (3) Best practices for characterizing the quality of big data sources and blended estimates constructed using data from multiple sources.

Monday, January 29, 2018

Structural VAR Analysis

Kilian and Lutkepohl's Structural Vector Autoregressive Analysis is now out. The back-cover blurbs below are not hyperbole. Indeed Harald Uhlig's is an understatement in certain respects -- to his list of important modern topics covered I would certainly add the "external instrument" approach. For more on that, beyond K&L, which went to press some time ago, see Stock and Watson's masterful 2018 external-instrument survey and extension, just now released as an NBER working paper. (Ungated K&L draft here; ungated S&W draft here.)




Sunday, January 21, 2018

Averaging for Prediction in Econometrics and ML

Random thought. At the risk of belaboring the obvious, it's interesting to heighten collective awareness by thinking about the many appearances of averaging in forecasting, particularly in forecast combination. Some averages are weighted, and some are not. Most are linear, some are not.
  • The "equal weights puzzle" in forecast combination 
  • Random forests, and ensemble averaging algorithms more generally
  • Bootstrap aggregation ("bagging") 
  • Boosting 
  • Best subset averaging
  • Survey averages
  • k-nearest-neighbor forecasts
  • Amisano-Geweke equally-weighted prediction pools
  • "1/N" portfolios
  • Bayesian model averaging
  • Bates-Granger-Ramanathan frequentist model averaging
  • Any forecasts extracted from markets (the ultimate information aggregator), ranging from "standard" markets (e.g., volatility forecasts extracted from options prices, interest rate forecasts extracted from the current yield curve, etc.), to explicit so-called "prediction markets" (e.g., sports betting markets).

Sunday, January 14, 2018

Comparing Interval Forecasts

Here's a new one, "On the Comparison of Interval Forecasts".  

You'd think that interval forecast evaluation would be easy.  After all, point forecast evaluation is (more or less) well understood and easy, and density forecast evaluation is (more or less) well understood and easy, and interval forecasts seem  somewhere in between, so by some sort of continuity argument you'd think that their evaluation would also be well understood and easy.  But no.  In fact it's quite difficult, maybe impossible...

Monday, January 8, 2018

Yield-Curve Modeling


Happy New Year to all!

Riccardo Rebonato's Bond Pricing and Yield-Curve Modeling: A Structural Approach will soon appear from Cambridge University Press. It's very well done -- a fine blend of  theory, empirics, market sense, and good prose.  And not least, endearing humility, well-captured by a memorable sentence from the acknowledgements: "My eight-year-old son has forgiven me, I hope, for not playing with him as much as I would have otherwise; perhaps he has been so understanding because he has had a chance to build a few thousand paper planes with the earlier drafts of this book."

TOC below.  Pre-order here

Contents

Acknowledgements page ix
Symbols and Abbreviations xi

Part I The Foundations
1 What This Book Is About 3
2 Definitions, Notation and a Few Mathematical Results 24
3 Links among Models, Monetary Policy and the Macroeconomy 49
4 Bonds: Their Risks and Their Compensations 63
5 The Risk Factors in Action 81
6 Principal Components: Theory 98
7 Principal Components: Empirical Results 108

Part II The Building Blocks: A First Look
8 Expectations 137
9 Convexity: A First Look 147
10 A Preview: A First Look at the Vasicek Model 160

Part III The Conditions of No-Arbitrage
11 No-Arbitrage in Discrete Time 185
12 No-Arbitrage in Continuous Time 196
13 No-Arbitrage with State Price Deflators 206
14 No-Arbitrage Conditions for Real Bonds 224
15 The Links with an Economics-Based Description of Rates 241

Part IV Solving the Models
16 Solving Affine Models: The Vasicek Case 263
17 First Extensions 285
18 A General Pricing Framework 299
19 The Shadow Rate: Dealing with a Near-Zero Lower Bound 329

Part V The Value of Convexity
20 The Value of Convexity 351
21 A Model-Independent Approach to Valuing Convexity 371
22 Convexity: Empirical Results 391

Part VI Excess Returns
23 Excess Returns: Setting the Scene 415
24 Risk Premia, the Market Price of Risk and Expected Excess Returns 431
25 Excess Returns: Empirical Results 449
26 Excess Returns: The Recent Literature – I 473
27 Excess Returns: The Recent Literature – II 497
28 Why Is the Slope a Good Predictor? 527
29 The Spanning Problem Revisited 547

Part VII What the Models Tell Us
30 The Doubly Mean-Reverting Vasicek Model 559
31 Real Yields, Nominal Yields and Inflation: The D’Amico–Kim–Wei Model 575
32 From Snapshots to Structural Models: The Diebold–Rudebusch Approach 602
33 Principal Components as State Variables of Affine Models: The PCA Affine Approach 618
34 Generalizations: The Adrian–Crump–Moench Model 663
35 An Affine, Stochastic-Market-Price-of-Risk Model 688

36 Conclusions 714

Bibliography 725

index 000