Estimating smooth transition autoregressive models with GARCH errors in the presence of extreme observations and outliers

This paper investigates several empirical issues regarding quasimaximum likelihood estimation of Smooth Transition Autoregressive (STAR) models with GARCH errors, specifically STAR-GARCH and STAR-STGARCH. Convergence, the choice of different algorithms for maximising the likelihood function, and the sensitivity of the estimates to outliers and extreme observations, are examined using daily data for S&P 500, Heng Seng and Nikkei 225 for the period January 1986 to April 2000. ∗The first author wishes to thank the C.A. Vargovic Memorial Award at the University of Western Australia for financial support. The second author acknowledges the financial support of the Australian Research Council and the Institute of Social and Economic Research at Osaka University.