Asymptotic Properties of the Maximum Likelihood Estimator for Markov-switching Observation-driven Models
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914222411087872 |
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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 |
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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 |