Nonstationary Cross-Validation

Cross-validation is the most common data-driven procedure for choosing the bandwidth sequence in nonparametric regression. For the case of i.i.d or strong mixing data, it is well-known that the bandwidth chosen by cross-validation is optimal with respect to the mean integrated squared error. However, the properties of cross-validated bandwidths in the context of nonstationary regressions have not yet been established. This is the subject of the current paper. For the case of β-recurrent (stationary or nonstationary) Markov chains, we show that the bandwidth chosen via cross-validation is optimal with respect to the average squared error. The accuracy of estimators based on cross-validated bandwidths is analyzed via a Monte Carlo study. The practical usefulness of cross-validated bandwidths in a highly-persistent, possibly nonstationary environment is illustrated by virtue of an application to nonlinear predictive regressions.

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