Data-Driven Bandwidth Selection for Nonparametric Nonstationary Regressions

47 Pages Posted: 29 Jun 2011 Last revised: 4 Jul 2011

See all articles by Federico M. Bandi

Federico M. Bandi

Johns Hopkins University - Carey Business School

Valentina Corradi

University of Warwick - Department of Economics

Daniel Wilhelm

University College London

Date Written: June 8, 2011

Abstract

We provide a solution to the open problem of bandwidth selection for the nonparametric estimation of potentially non-stationary regressions, a setting in which the popular method of cross-validation has not been justified theoretically. Our procedure is based on minimizing moment conditions involving nonparametric residuals and applies to β-recurrent Markov chains, stationary processes being a special case, as well as nonlinear functions of integrated processes. Local and uniform versions of the criterion are proposed. The selected bandwidths are rate-optimal up to a logarithmic factor, a typical cost of adaptation in other contexts. We further show that the bias induced by (near-) minimax optimality can be removed by virtue of a simple randomized procedure. In a Monte Carlo exercise, we find that our proposed bandwidth selection method, and its subsequent bias correction, fare favorably relative to cross-validation, even in stationary environments.

Keywords: data-driven bandwidth selection, non-stationary autoregression, nonparametric cointegration, recurrence

JEL Classification: C13, C14, C22

Suggested Citation

Bandi, Federico Maria and Corradi, Valentina and Wilhelm, Daniel, Data-Driven Bandwidth Selection for Nonparametric Nonstationary Regressions (June 8, 2011). Available at SSRN: https://ssrn.com/abstract=1874509 or http://dx.doi.org/10.2139/ssrn.1874509

Federico Maria Bandi (Contact Author)

Johns Hopkins University - Carey Business School ( email )

100 International Drive
Baltimore, MD 21202
United States

Valentina Corradi

University of Warwick - Department of Economics ( email )

Coventry CV4 7AL
United Kingdom

Daniel Wilhelm

University College London ( email )

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

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