Asymptotic normality of the maximum likelihood estimator in state space models
TLDR
This paper generalizes the results of Bickel, Ritov and Ryden to state space models, where the latent process is a continuous state Markov chain satisfying regularity conditions, which are fulfilled if the latentprocess takes values in a compact space.Abstract:
State space models is a very general class of time series models capable of modelling dependent observations in a natural and interpretable way. Inference in such models has been studied by Bickel, Ritov and Ryden, who consider hidden Markov models, which are special kinds of state space models, and prove that the maximum likelihood estimator is asymptotically normal under mild regularity conditions. In this paper we generalize the results of Bickel, Ritov and Ryden to state space models, where the latent process is a continuous state Markov chain satisfying regularity conditions, which are fulfilled if the latent process takes values in a compact space.read more
Citations
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Journal ArticleDOI
Hidden Markov processes
Yariv Ephraim,Neri Merhav +1 more
TL;DR: An overview of statistical and information-theoretic aspects of hidden Markov processes (HMPs) is presented and consistency and asymptotic normality of the maximum-likelihood parameter estimator were proved under some mild conditions.
Journal ArticleDOI
Inference for nonlinear dynamical systems
TL;DR: This work presents a new method that makes maximum likelihood estimation feasible for partially-observed nonlinear stochastic dynamical systems (also known as state-space models) where this was not previously the case.
Journal ArticleDOI
Fitting population models incorporating process noise and observation error
Perry de Valpine,Alan Hastings +1 more
TL;DR: The numerically integrated state-space (NISS) method as mentioned in this paper was proposed to fit models to time series of population abun- dances that incorporate both process noise and observation error in a likelihood framework.
MonographDOI
Modelling nonlinear economic time series
TL;DR: In this article, the authors propose a non-parametric approach for estimating parametric models from state space models and nonlinear and non-stationary models, based on nonparametric models and parametric linearity tests.
Journal ArticleDOI
Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime
TL;DR: In this paper, the asymptotic properties of the maximum likelihood estimator in a possibly nonstationary process of this kind for which the hidden state space is compact but not necessarily finite are investigated.
References
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Bayesian Forecasting and Dynamic Models
Mike West,Jeff Harrison +1 more
TL;DR: In this article, the authors propose a model called the Dynamic Regression Model (DRM) which is an extension of the First-Order Polynomial Model (FOPM) and the Dynamic Linear Model (DLM).
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Smoothness priors analysis of time series
Genshiro Kitagawa,Will Gersch +1 more
TL;DR: In this article, the Akaike AIC is used to evaluate Parametric Models and to estimate the probability of a smooth trend in a time series, and the AIC can be used for time series analysis.
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Maximum-likelihood estimation for hidden Markov models
TL;DR: In this paper, the consistency of a sequence of maximum likelihood estimators is proved and the conclusion of the Shannon-McMillan-Breiman theorem on entropy convergence is established for hidden Markov models.
Journal ArticleDOI
Asymptotic normality of the maximum-likelihood estimator for general hidden Markov models
TL;DR: It is shown that under mild conditions the MLE is also asymptotically normal and proved that the observed information matrix is a consistent estimator of the Fisher information.