Adam Smith Business School

'Empirical Risk Minimisation for Time Series, Nonparametric Performance Bounds for Prediction'

Friday 11 March, 4.00-5.00pm
Zoom 

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Biography

Christian Brownlees is an Associate Professor in the Department of Economics and Business at the Universitat Pompeu Fabra since 2017. He received his B.S. degree in Economics and Quantitative Methods in 2003 and Ph.D. degree in Statistics in 2007 from Università di Firenze. He was a Post-Doc Research Fellow at NYU Stern until 2011. Over the years he has studied, visited and researched at the University of Reading, Monash University, UCSD and EUI.

Abstract

Empirical risk minimisation is a standard principle for choosing algorithms in learning theory. In this paper, we study the properties of empirical risk minimisation 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 minimisation achieves asymptotically the optimal predictive performance that is attainable within the class of algorithms.

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First published: 4 March 2022