Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime
Randal Douc, Eric Moulines, Tobias Ryden
Abstract
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 asymptotic normality are shown to follow from uniform exponential forgetting of the initial distribution for the hidden Markov chain conditional on the observations.
Create a lesson
Related papers
Repairing covariance functions on metric trees through a Hausdorff-type distance
Alfredo Alegría
Fisher Information and Differentiability for r-Largest Generalized Extreme-Value Models
Jihong Park, Yire Shin, Jeong-Soo Park
Multiscale Sequential Auditing of Quantile Regression with Point Masses
Asad Ullah
Adaptive Confidence Sets for Nonparametric Density Estimation under Local Differential Privacy
Aditya Khan, Thibault Randrianarisoa
Robust Nonparametric Methods for α-Mixing Sequences via Median-of-Means
Attila Lovas, Marcell Tukora
Separating Statistical Inference from Experimental Runtime: An Architecture for Sequential Scientific Analysis
Alexander Stepanov, Andrej Novikov