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Generalization Error Bounds for Time Series

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thesis
posted on 06.04.2012, 00:00 by Daniel J. McDonald

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 β-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.

History

Date

06/04/2012

Degree Type

Dissertation

Department

Statistics

Degree Name

Doctor of Philosophy (PhD)

Advisor(s)

Cosma Shalizi,Mark Schervish

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