Nonparametric Lag Selection for Time Series

A nonparametric version of the Final Prediction Error (FPE) is analysed for lag selection in nonlinear autoregressive time series under very general conditions including heteroskedasticity. We prove consistency and derive probabilities of incorrect selections that have been previously unavailable. Since it is more likely to over®t (have too many lags) than to under®t (miss some lags), a correction factor is proposed to reduce over®tting and hence increase correct ®tting. For the FPE calculation, the local linear estimator is introduced in addition to the Nadaraya-Watson estimator in order to cover a very broad class of processes. To achieve faster computation, a plug-in bandwidth is suggested for the local linear estimator. Our Monte-Carlo study corroborates that the correction factor generally improves the probability of correct lag selection for both linear and nonlinear processes and that the plug-in bandwidth works at least as well as its commonly used competitor. The proposed methods are applied to the Canadian lynx data and daily returns of DM/US-Dollar exchange rates.