Ergodicity of Autoregressive Processes with Markov-Switching and Consistency of the Maximum-Likelihood Estimator

1 January 1998

journal article
research article
Published by Taylor & Francis in Statistics

Vol. 32 (2) , 151-173
https://doi.org/10.1080/02331889808802659

Abstract

An autoregressive model with Markov-switching assumes a sequence of random vectors to be a non linear autoregressive model given a sequence of non observed state variables which forms a Markov chain. A particular case of this model is the hidden Markov model. In this paper conditions for the existence of an ergodic stationary solution are given and consistency of the maximum likelihood estimator is proved.

Keywords

This publication has 9 references indexed in Scilit:

Time Series Analysis
Published by Walter de Gruyter GmbH ,1994
Maximum-likelihood estimation for hidden Markov models
Stochastic Processes and their Applications, 1992
A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle
Econometrica, 1989
Products of Random Matrices with Applications to Schrödinger Operators
Published by Springer Nature ,1985
Subadditive Ergodic Theory
The Annals of Probability, 1973
Statistical Inference for Probabilistic Functions of Finite State Markov Chains
The Annals of Mathematical Statistics, 1966
Identifiability of Finite Mixtures
The Annals of Mathematical Statistics, 1963
Products of Random Matrices
The Annals of Mathematical Statistics, 1960
Note on the Consistency of the Maximum Likelihood Estimate
The Annals of Mathematical Statistics, 1949