Semiparametric transition models

Abstract

A new semiparametric time series model is introduced–the semiparametric transition (SETR) model–that generalizes the threshold and smooth transition models by letting the transition function to be of an unknown form. Estimation is based on a combination of the (local) least squares estimations of the transition function and regression parameters. The asymptotic behavior for the regression coefficient estimator of the SETR model is established, including its oracle property. Monte Carlo simulations demonstrate that the proposed estimator is more robust to the form of the transition function than parametric threshold and smooth transition methods and more precise than varying coefficient estimators.