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Yulia Gel, Department of Statistics and Actuarial Science, University of Waterloo

In this talk we discuss how modern regularization procedures can be employed for estimation and forecasting of the same-realization of time series, which can be viewed as a "large p-small n" problem in a time series framework. In particular, we show that banding enables us to employ an approximating model of a much higher order than typically suggested by AIC, while controlling how many parameters are to be estimated precisely and the level of accuracy.

We present results on asymptotic consistency of banded autocovariance matrices under the Frobenius norm and provide a theoretical justification on optimal band selection using V-fold crossvalidation, which can be viewed as an alternative model selection criterion for the same-realization prediction. Our numerical studies show that the banded prediction yields a substantially lower predictive root mean squared error than forecasting methods that are based on classical model selection criteria.  We also illustrate our procedure by application to forecasting sea surface temperature. This is a joint work with Peter Bickel, University of California, Berkeley.

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