Empirical Risk Minimization for Time Series: Nonparametric Performance Bounds for Prediction

45 Pages Posted: 13 Aug 2021

See all articles by Christian T. Brownlees

Christian T. Brownlees

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences; Barcelona School of Economics

Jordi Llorens-Terrazas

Universitat Pompeu Fabra; Barcelona Graduate School of Economics (Barcelona GSE)

Date Written: August 6, 2021

Abstract

Empirical risk minimization is a standard principle for choosing algorithms in learning theory. In this paper we study the properties of empirical risk minimization for time series. The analysis is carried out in a general framework that covers different types of forecasting applications encountered in the literature. We are concerned with 1-step-ahead prediction of a univariate time series generated by a parameter-driven process. A class of recursive algorithms is available to forecast the time series. The algorithms are recursive in the sense that the forecast produced in a given period is a function of the lagged values of the forecast and of the time series. The relationship between the generating mechanism of the time series and the class of algorithms is unspecified. Our main result establishes that the algorithm chosen by empirical risk minimization achieves asymptotically the optimal predictive performance that is attainable within the class of algorithms.

Keywords: Empirical risk minimization, oracle inequality, time series, fore- casting, Markov chain

JEL Classification: C14, C22, C53, C58

Suggested Citation

Brownlees, Christian T. and Llorens-Terrazas, Jordi, Empirical Risk Minimization for Time Series: Nonparametric Performance Bounds for Prediction (August 6, 2021). Available at SSRN: https://ssrn.com/abstract=3900432 or http://dx.doi.org/10.2139/ssrn.3900432

Christian T. Brownlees (Contact Author)

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences ( email )

Ramon Trias Fargas 25-27
Barcelona, 08005
Spain

HOME PAGE: http://econ.upf.edu/~cbrownlees/

Barcelona School of Economics ( email )

Carrer de Ramon Trias Fargas, 25-27
Barcelona, 08005
Spain

Jordi Llorens-Terrazas

Universitat Pompeu Fabra ( email )

Barcelona
Spain

Barcelona Graduate School of Economics (Barcelona GSE) ( email )

Ramon Trias Fargas, 25-27
Barcelona, Barcelona 08005
Spain

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