Estimation of STAR–GARCH Models with Iteratively Weighted Least Squares

Abstract

This study applies the Iteratively Weighted Least Squares (IWLS) algorithm to a Smooth Transition Autoregressive (STAR) model with conditional variance. Monte Carlo simulations are performed to measure the performance of the algorithm, to compare its performance to the established methods in the literature, and to see the effect of the initial value selection method. The simulation results show that lower bias and mean squared error values are received for the slope parameter estimator from the IWLS algorithm in comparison to the other methods when the real value of the slope parameter is low. In an empirical illustration, the STAR–GARCH model is used to forecast daily US Dollar/Australian Dollar and the FTSE Small Cap index returns. 1-day ahead out-of-sample forecast results show that the forecast performance of the STAR–GARCH model improves with the IWLS algorithm and the model performs better than the benchmark model.