AUTOMATED KERNEL SMOOTHING OF DEPENDENT DATA BY USING TIME-SERIES CROSS-VALIDATION

The problem of selecting the bandwidth of a kernel regression estimato r when the observed data are serially correlated is considered. The ba ndwidth is selected by using a version of cross-validation that seeks a good one-step-ahead predictor of the data. This method, referred to as time series cross-validation (TSCV), simultaneously estimates an op timal bandwidth and, given a time series model for the errors, the aut ocorrelation function of the data. In addition, different time series models having the same number of parameters can be compared by using T SCV. Boundary kernels play a key role in the proposed methodology sinc e one-step-ahead prediction entails extrapolating past the available d ata. Boundary kernels are used at the bandwidth selection stage, but ' proper' kernels are used to estimate the regression function. It is sh own that smooth (i.e. at least continuous) boundary kernels have some robustness to misspecification of the error model. This means that a s imple correlation model, such as the first-order autoregressive proces s, will often suffice for selecting a bandwidth. A simulation study an d real data examples indicate the usefulness of TSCV for smoothing tim e series data.