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On White Noises Driven by Hidden Markov Chains
Author(s) -
Francq Christian,
Roussignol Michel
Publication year - 1997
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00068
Subject(s) - mathematics , markov chain , estimator , series (stratigraphy) , variance (accounting) , identification (biology) , gaussian , variable order markov model , hidden markov model , statistics , maximum likelihood , white noise , econometrics , markov model , artificial intelligence , computer science , paleontology , botany , physics , accounting , quantum mechanics , business , biology
We consider a time series model where the variance of the underlying process depends on the state of a non‐observed Markov chain. Maximum likelihood estimates are shown to be consistent. Estimators with asymptotic Gaussian distribution are proposed. Prediction and identification are also mentioned. This is illustrated by means of real and simulated data sets