Mixture transition distribution (MTD) modeling of heteroscedastic time series

Time series presenting non-Gaussian features such as heteroscedasticity or sudden bursts of activity play a central role in many fields including finance, insurance, and seismology. The heteroscedastic mixture transition distribution (HMTD) model, which generalizes several specifications previously proposed in the statistical literature, is a new model especially designed to handle series of this kind. By allowing the standard deviation of each component to be a function of the past of the observed process, a better modeling of the conditional probability distribution function of future observations is obtained. A numerical example shows that the HMTD can perform better than standard models such as ARMA and GARCH. Different issues related to the numerical estimation of mixture models are also discussed. (C) 2002 Elsevier Science B.V. All rights reserved.