Estimating MS-BLGARCH Models Using Recursive Method

Abstract

In this paper a new class of models is proposed for modeling nonlinear and stationary time series. This new class of models is referred to as the Markov-switching bilinear GARCH (MS-BLGARCH) models. In these models, the parameters are allowed to depend on an unobservable time-homogeneous and stationary Markov chain with finite state space. The statistical inference for these models is rather difficult due to the dependence on the whole regime path. We propose a recursive algorithm for parameter estimation in MS − BLGARCH. The proposed method is useful for long time series as well as for data available in real time. The main idea is to use the maximum likelihood estimation (MLE) method and from this develop a recursive Expectation-Maximization (EM) algorithm.