1. Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran;2. School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran
Abstract:
We propose data generating structures which can be represented as a mixture of autoregressive-autoregressive conditionally heteroscedastic models. The switching between the states is governed by a hidden Markov chain. We investigate semi-parametric estimators for estimating the functions based on the quasi-maximum likelihood approach and provide sufficient conditions for geometric ergodicity of the process. We also present an expectation–maximization algorithm for calculating the estimates numerically.