Estimation of nonlinear time series with conditional heteroscedastic variances by iteratively weighted least squares

Abstract

In this paper we consider a unified approach for fitting conditionally nonlinear time series models with heteroscedastic variances. The model considered is completely general, requiring only that the forms of the mean and conditional variance functions be specified. Based on the recent results of Mak (1993) on general estimating equations, we derive a convenient expression for the conditional information matrix. Furthermore, it is shown that estimation in such models can be performed via an iteratively weighted least squares algorithm (IWLS), so that the computational problems involved can be conveniently handled by many popular statistical packages. Its implementation is numerically illustrated using the "threshold plus ARCH" model. The algorithm is also demonstrated using both simulated and real data to be superior to the popular BHHH algorithm, which requires a much longer computing time and fails to converge if initial values are not chosen properly.