Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime

DOI10.1214/009053604000000021zbMath1056.62028arXivmath/0503681OpenAlexW3102710946MaRDI QIDQ1766135

Randal Douc, Tobias Rydén, Eric Moulines

Publication date: 28 February 2005

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0503681

zbMATH Keywords

consistencyasymptotic normalityhidden Markov modelmaximum likelihoodidentifiabilitygeometric ergodicityautoregressive processswitching autoregression

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Non-Markovian processes: estimation (62M09) Markov processes: estimation; hidden Markov models (62M05)

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Cites Work

• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Markov chains and stochastic stability
• Analysis of time series subject to changes in regime
• Correlation functions of a function of a finite-state Markov process with application to channel kinetics
• Stochastic models for heterogeneous DNA sequences
• Maximum-likelihood estimation for hidden Markov models
• Markov-switching vector autoregressions. Modelling, statistical inference, and application to business cycle analysis
• Convergence of the Monte Carlo expectation maximization for curved exponential families.
• The stochastic EM algorithm: Estimation and asymptotic results
• Asymptotic normality of the maximum-likelihood estimator for general hidden Markov models
• Inference in hidden Markov models. I: Local asymptotic normality in the stationary case.
• Markov chain Monte Carlo methods for stochastic volatility models.
• Asymptotic normality of the maximum likelihood estimator in state space models
• Exponential forgetting and geometric ergodicity in hidden Markov models
• Recursive computation of smoothed functionals of hidden Markovian processes using a particle approximation
• Consistent Estimation of Linear and Non-linear Autoregressive Models with Markov Regime
• Adaptive estimation and identification for discrete systems with Markov jump parameters
• Hidden Markov Models for Speech Recognition
• A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle
• Ergodicity of Autoregressive Processes with Markov-Switching and Consistency of the Maximum-Likelihood Estimator
• Maximizing Generalized Linear Mixed Model Likelihoods With an Automated Monte Carlo EM Algorithm
• RECURSIVE ESTIMATION IN SWITCHING AUTOREGRESSIONS WITH A MARKOV REGIME
• Statistique de chaînes de Markov cachées à espace d'états fini. Le cas non stationnaire
• Particle approximations of Lyapunov exponents connected to Schrödinger operators and Feynman–Kac semigroups
• Stochastic sampling algorithms for state estimation of jump Markov linear systems
• On stability of nonlinear AR processes with Markov switching
• Monte Carlo EM Estimation for Time Series Models Involving Counts
• The simulation smoother for time series models
• A Bayesian approach to tracking multiple targets using sensor arrays and particle filters
• Statistical Inference for Probabilistic Functions of Finite State Markov Chains
• Note on the Consistency of the Maximum Likelihood Estimate
• On the Statistical Treatment of Linear Stochastic Difference Equations
• Probability
• Tools for statistical inference. Methods for the exploration of posterior distributions and likelihood functions.
• On the stability of interacting processes with applications to filtering and genetic algorithms
• Stationarity of multivariate Markov-switching ARMA models
• Asymptotics of the maximum likelihood estimator for general hidden Markov models