Nonparametric Lag Selection for Time Series

Abstract

A nonparametric version of the Final Prediction Error (FPE) is proposed for lag selection in nonlinear autoregressive time series. We derive its consistency for both local constant and local linear estimators using a derived optimal bandwidth. Further asymptotic analysis suggests a greater probability of overfitting (too many lags) than underfitting (missing important lags). Thus a correction factor is proposed to increase correct fitting by reducing overfitting. Our Monte-Carlo study also corroborates that the correction factor generally improves the probability of correct lag selection for both linear and nonlinear processes. The proposed methods are successfully applied to the Canadian lynx data and daily returns of DM/US-Dollar exchange rates.