(This article was originally published at No Hesitations, and syndicated at StatsBlogs.)
Instead, people focus on kernel-HAC sans prewhitening, and obsess over truncation lag selection. Truncation lag selection is indeed very important when pre-whitening is forgotten, as too short a lag can lead to seriously distorted inference, as emphasized in the brilliant early work of Kiefer-Vogelsang and in important recent work by Lewis, Lazarus, Stock and Watson. But all of that becomes much less important when pre-whitening is successfully implemented.
[Of course spectra need not be rational, so ARMA is just an approximation to a more general Wold representation (and remember, GARCH(1,1) is just an ARMA(1,1) in squares). But is that really a problem? In econometrics don't we feel comfortable with ARMA approximations 99.9 percent of the time? The only econometrically-interesting process I can think of that doesn't admit a finite-ordered ARMA representation is long memory (fractional integration). But that too can be handled parametrically by introducing just one more parameter, moving from ARMA(p,q) to ARFIMA(p,d,q).]
My earlier post linked to the key early work of Den Haan and Levin, which remains unpublished. I am confident that their basic message remains intact. Indeed recent work revisits and amplifies it in important ways; see Kapetanios and Psaradakis (2016) and new work in progress by Richard Baillie to be presented at the September 2016 NBER/NSF time-series meeting at Columbia ("Is Robust Inference with OLS Sensible in Time Series Regressions?").
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