Asymptotic properties of autoregressive regime-switching models

Asymptotic properties of autoregressive regime-switching models

The statistical properties of the likelihood ratio test statistic (LRTS) for autoregressive regime-switching models are addressed in this paper. This question is particularly important for estimating the number of regimes in the model. Our purpose is to extend the existing results for mixtures (Liu and Shao, 2003) and hidden Markov chains (Gassiat, 2002). First, we study the case of mixtures of...

Regime Switching Garch Models

We develop univariate regime-switching GARCH (RS-GARCH) models wherein the conditional variance switches in time from one GARCH process to another. The switching is governed by a time-varying probability, specified as a function of past information. We provide sufficient conditions for geometric ergodicity and existence of moments. Because of path dependence, maximum likelihood estimation is no...

Regime - Switching Models

Markov Regime-Switching Tests: Asymptotic Critical Values

Empirical research with Markov regime-switching models often requires the researcher not only to estimate the model but also to test for the presence of more than one regime. Despite the need for both estimation and testing, methods of estimation are better understood than are methods of testing. We bridge this gap by explaining, in detail, how to apply the newest results in the theory of regim...

Asymptotic Properties of the Maximum Likelihood Estimator in Autoregressive Models with Markov Regime by Randal Douc,1

An autoregressive process with Markov regime is an autoregressive process for which the regression function at each time point is given by a nonobservable Markov chain. In this paper we consider the asymptotic properties of the maximum likelihood estimator in a possibly nonstationary process of this kind for which the hidden state space is compact but not necessarily finite. Consistency and asy...