Asymptotic Properties of the Maximum Likelihood Estimator for Markov-switching Observation-driven Models

Frederik Krabbe

Papers from arXiv.org

Abstract: A Markov-switching observation-driven model is a stochastic process $((S_t,Y_t))_{t \in \mathbb{Z}}$ where $(S_t)_{t \in \mathbb{Z}}$ is an unobserved Markov chain on a finite set and $(Y_t)_{t \in \mathbb{Z}}$ is an observed stochastic process such that the conditional distribution of $Y_t$ given $(Y_\tau)_{\tau \leq t-1}$ and $(S_\tau)_{\tau \leq t}$ depends on $(Y_\tau)_{\tau \leq t-1}$ and $S_t$. In this paper, we prove consistency and asymptotic normality of the maximum likelihood estimator for such model. As a special case, we also give conditions under which the maximum likelihood estimator for the widely applied Markov-switching generalised autoregressive conditional heteroscedasticity model introduced by Haas, Mittnik, and Paolella (2004b) is consistent and asymptotically normal.

Date: 2024-12, Revised 2025-12
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