Christian Brownlees, Universitat Pompeu Fabra

"Empirical Risk Minimization for Time Series"

Abstract

Empirical risk minimization is a standard principle for choosing algorithms in learning theory. In this paper we study empirical risk minimization for choosing a recursive prediction algorithm to forecast a univariate time series. The class of algorithms we consider includes 1-step-ahead prediction formulae of ARMA and GARCH models. The analysis is nonparametric in the sense that the relation be- tween the prediction algorithm and the time series is assumed to be unknown. We establish performance bounds for empirical risk minimization based on a companion Markov chain that embeds the time series and the prediction algorithm.

(Joint with Jordi Llorens–Terrazas)

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