Sunday, June 7, 2015

Econometric Seasonality Research is Back

Seasonality research is back! Well, at least a bit.

I recall heady earlier days, with classic work like Granger's typical spectral shape, mutiplicative seasonal Box-Jenkins and the airline model, Nerlove's unobserved-components models and Harvey's basic structural model, Barsky and Miron's work on seasonal cycles and business cycles, Engle, Granger and Hylleberg's work on seasonal integration and cointegration, and on and on. If you're interested and want systematic treatments, take a look at classic books like Nerlove, Grether and Carvalho (1979)Hylleberg (1986)Harvey (1991), Miron (1996), and Ghysels and Osborne (2001) (with an exceptionally-insightful foreword by Tom Sargent). And don't forget the legendary 1976 Conference on Seasonal Analysis of Economic Time Series (Zellner, ed., 1978).

Seasonality is clearly a large and important part of time-series econometrics; in the meticulous Nerlove et al. book index, for example, the seasonality entries alone occupy more than a page. [Historical note: Interestingly, the Nerlove et al. index was actually produced by Quang Vuong! Quang was Marc Nerlove's Ph.D. student just before me, and he moved with Marc from Northwestern to Penn in the early 1980's to finish his Northwestern Ph.D., just as I was starting my Penn Ph.D. with Marc. We overlapped at Penn for a little while. It was a great honor to join Quang, Isabel Perrigne and Ingmar Prucha in hosting Marc's 80th Birthday Conference in May 2014.]

Yet econometric seasonality research receded in the last fifteen years or so. No worries, pendulums swing, and the pendulum is swinging back. 

So then, what's going on now?

The classic issues in seasonal adjustment (e.g., overadjustment, underadjustment) are alive and well, and as relevant as ever. On underadjustment see Gilbert et al.'s 2015 Federal Reserve Board piece on the "residual seasonality" problem

There are also important issues of too-quickly-adapting adjustments (effectively a type of overadjustment). See Wright's very nice 2013 Brookings Papers piece on "unseasonal seasonals".

There are interesting and largely-unexplored issues of seasonality not only in conditional-mean dynamics, but also in conditional-variance dynamics, as in Campbell and Diebold's 2005 work on weather forecasting for weather derivatives.

Much remains to be explored regarding simultaneous adjustment of sets of series, which may for example share common seasonal components, as in McElroy (2015). (Of course this is not unrelated to the literature on seasonal cointegration.)

Related but distinct is the issue of "top down" vs. "bottom up" approaches to seasonal adjustment (e.g., is seasonally-adjusted GDP better-obtained by adjusting GDP directly or by adjusting its components separately and adding them?). See Rudebusch, Wilson and Mahedy's 2015 FRB San Francisco Economic Letter.

We're recognizing that in addition to "standard" seasonal adjustment, we may want to control for unusual weather conditions and specific weather events, as in 2015 work by Boldin and Wright.

In the U.S. there's the problem of likely-spurious Q1 GDP collapses, which is related to many of the above-mentioned issues. See the following 2015 pieces, many already mentioned above (and see Wolfers1 and  Wolfers2 for nice overviews/interpretations):
-- Federal Reserve Board piece on the "residual seasonality" problem 
-- Stark's FRB Phila Research Rap
-- Rudebusch, Wilson and Mahedy's FRB San Francisco Economic Letter

-- A recent No Hesitations post.