Three-Toed Sloth

"Generalization Error Bounds for Time Series"

On Friday, my student Daniel McDonald, who I have been lucky enough to jointly advise with Mark Schervish, defeated the snake — that is, defended his thesis:

Generalization Error Bounds for Time Series

In this thesis, I derive generalization error bounds — bounds on the expected inaccuracy of the predictions — for time series forecasting models. These bounds allow forecasters to select among competing models, and to declare that, with high probability, their chosen model will perform well — without making strong assumptions about the data generating process or appealing to asymptotic theory. Expanding upon results from statistical learning theory, I demonstrate how these techniques can help time series forecasters to choose models which behave well under uncertainty. I also show how to estimate the beta-mixing coefficients for dependent data so that my results can be used empirically. I use the bound explicitly to evaluate different predictive models for the volatility of IBM stock and for a standard set of macroeconomic variables. Taken together my results show how to control the generalization error of time series models with fixed or growing memory.

PDF [2 Mb]

I hope to have a follow-up post very soon about the substance of Daniel's work, which is part of our INET grant, but in the meanwhile: congratulations, Dr. McDonald!

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