Automated Kernel Smoothing of Dependent Data by Using Time Series Cross-Validation

Abstract

SUMMARY The problem of selecting the bandwidth of a kernel regression estimator when the observed data are serially correlated is considered. The bandwidth 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 optimal bandwidth and, given a time series model for the errors, the autocorrelation function of the data. In addition, different time series models having the same number of parameters can be compared by using TSCV. Boundary kernels play a key role in the proposed methodology since one-step-ahead prediction entails extrapolating past the available data. Boundary kernels are used at the bandwidth selection stage, but ‘proper’ kernels are used to estimate the regression function. It is shown that smooth (i.e. at least continuous) boundary kernels have some robustness to misspecification of the error model. This means that a simple correlation model, such as the first-order autoregressive process, will often suffice for selecting a bandwidth. A simulation study and real data examples indicate the usefulness of TSCV for smoothing time series data.