Maximum Likelihood Estimator for Hidden Markov Models in Continuous Time
نویسنده
چکیده
The paper studies large sample asymptotic properties of the Maximum Likelihood Estimator (MLE) for the parameter of a continuous time Markov chain, observed in white noise. Using the method of weak convergence of likelihoods due to I.Ibragimov and R.Khasminskii [14], consistency, asymptotic normality and convergence of moments are established for MLE under certain strong ergodicity conditions on the chain.
منابع مشابه
On Bahadur Efficiency of the Maximum Likelihood Estimator in Hidden Markov Models
In this paper, we study large deviations of maximum likelihood and related estimators for hidden Markov models. A hidden Markov model consists of parameterized Markov chains in a Markovian random environment, with the underlying environmental Markov chain viewed as missing data. A difficulty with parameter estimation in this model is the non-additivity of the log-likelihood function. Based on a...
متن کاملAsymptotic Properties of the Maximum Likelihood Estimator in Autoregressive Models with Markov Regime by Randal Douc,1
An autoregressive process with Markov regime is an autoregressive process for which the regression function at each time point is given by a nonobservable Markov chain. In this paper we consider 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. Consistency and asy...
متن کاملExact likelihood inference for autoregressive gamma stochastic volatility models
Affine stochastic volatility models are widely applicable and appear regularly in empirical finance and macroeconomics. The likelihood function for this class of models is in the form of a high-dimensional integral that does not have a closed-form solution and is difficult to compute accurately. This paper develops a method to compute the likelihood function for discrete-time models that is acc...
متن کاملFinite Sample Properties of the Maximum Likelihood Estimator and of Likelihood Ratio Tests in Hidden Markov Models
Hidden Markov models were successfully applied in various fields of time series analysis, especially for analyzing ion channel recordings. The maximum likelihood estimator (MLE) has recently been proven to be asymptotically normally distributed. Here, we investigate finite sample properties of the MLE and of different types of likelihood ratio tests (LRTs) by means of simulation studies. The ML...
متن کاملEfficient maximum likelihood parameterization of continuous-time Markov processes.
Continuous-time Markov processes over finite state-spaces are widely used to model dynamical processes in many fields of natural and social science. Here, we introduce a maximum likelihood estimator for constructing such models from data observed at a finite time interval. This estimator is dramatically more efficient than prior approaches, enables the calculation of deterministic confidence in...
متن کامل