Possibly Nonstationary Cross-Validation

61 Pages Posted: 16 Mar 2016 Last revised: 24 Apr 2017

See all articles by Federico M. Bandi

Federico M. Bandi

Johns Hopkins University - Carey Business School

Valentina Corradi

University of Surrey - School of Economics

Daniel Wilhelm

University College London

Date Written: April 23, 2017

Abstract

Cross-validation is the most common data-driven procedure for choosing smoothing parameters in nonparametric regression. For the case of kernel estimators with iid or strong mixing data, it is well-known that the bandwidth chosen by cross-validation is optimal with respect to the average squared error and other performance measures. In this paper, we show that the cross-validated bandwidth continues to be optimal with respect to the average squared error even when the data-generating process is a beta-recurrent Markov chain. This general class of processes covers stationary as well as nonstationary Markov chains. Hence, the proposed procedure adapts to the degree of recurrence, thereby freeing the researcher from the need to assume stationary (or nonstationary) before inference begins. We study finite sample performance in a Monte Carlo study. We conclude by demonstrating the practical usefulness of cross-validation in a highly-persistent environment, namely that of nonlinear predictive systems for market returns.

Suggested Citation

Bandi, Federico Maria and Corradi, Valentina and Wilhelm, Daniel, Possibly Nonstationary Cross-Validation (April 23, 2017). Johns Hopkins Carey Business School Research Paper No. 17-01. Available at SSRN: https://ssrn.com/abstract=2748510 or http://dx.doi.org/10.2139/ssrn.2748510

Federico Maria Bandi

Johns Hopkins University - Carey Business School ( email )

100 International Drive
Baltimore, MD 21202
United States

Valentina Corradi

University of Surrey - School of Economics ( email )

Guildford
Guildford, Surrey GU2 5XH
United Kingdom

Daniel Wilhelm (Contact Author)

University College London ( email )

UCL Economics
30 Gordon Street
London, WC1H 0AX
United Kingdom

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