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2008 Penalized estimate of the number of states in Gaussian linear AR with Markov regime
Ricardo Ríos, Luis-Angel Rodríguez
Electron. J. Statist. 2: 1111-1128 (2008). DOI: 10.1214/08-EJS272

Abstract

We deal with the estimation of the regime number in a linear Gaussian autoregressive process with a Markov regime (AR-MR). The problem of estimating the number of regimes in this type of series is that of determining the number of states in the hidden Markov chain controlling the process. We propose a method based on penalized maximum likelihood estimation and establish its strong consistency (almost sure) without assuming previous bounds on the number of states.

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Ricardo Ríos. Luis-Angel Rodríguez. "Penalized estimate of the number of states in Gaussian linear AR with Markov regime." Electron. J. Statist. 2 1111 - 1128, 2008. https://doi.org/10.1214/08-EJS272

Information

Published: 2008
First available in Project Euclid: 21 November 2008

zbMATH: 1320.62194
MathSciNet: MR2460859
Digital Object Identifier: 10.1214/08-EJS272

Subjects:
Primary: 62F05
Secondary: 62M05

Keywords: autoregressive processes , hidden Markov chains , penalized maximum likelihood

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society

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