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

Fuente: arXiv
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Main Author: Krabbe, Frederik
Format: Preprint
Published: 2024
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author Krabbe, Frederik
author_facet Krabbe, Frederik
contents 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 $(Y_τ)_{τ\leq t-1}$ and $(S_τ)_{τ\leq t}$ depends on $(Y_τ)_{τ\leq t-1}$ 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.
format Preprint
id arxiv_https___arxiv_org_abs_2412_19555
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Asymptotic Properties of the Maximum Likelihood Estimator for Markov-switching Observation-driven Models
Krabbe, Frederik
Econometrics
Statistics Theory
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 $(Y_τ)_{τ\leq t-1}$ and $(S_τ)_{τ\leq t}$ depends on $(Y_τ)_{τ\leq t-1}$ 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.
title Asymptotic Properties of the Maximum Likelihood Estimator for Markov-switching Observation-driven Models
topic Econometrics
Statistics Theory
url https://arxiv.org/abs/2412.19555