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ANALYSIS OF THE LIKELIHOOD FUNCTION FOR MARKOV‐SWITCHING VAR(CH) MODELS
Author(s) -
Cavicchioli Maddalena
Publication year - 2014
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/jtsa.12085
Subject(s) - mathematics , heteroscedasticity , autoregressive model , estimator , likelihood function , consistency (knowledge bases) , context (archaeology) , strong consistency , markov chain , conditional variance , statistics , delta method , restricted maximum likelihood , econometrics , maximum likelihood , autoregressive conditional heteroskedasticity , paleontology , volatility (finance) , geometry , biology
In this work, we give simple matrix formulae for maximum likelihood estimates of parameters in a broad class of vector autoregressions subject to Markovian changes in regime. This allows us to determine explicitly the asymptotic variance–covariance matrix of the estimators, giving a concrete possibility for the use of the classical testing procedures. In the context of multivariate autoregressive conditional heteroskedastic models with changes in regime, we provide formulae for the analytic derivatives of the log likelihood. Then we prove the consistency of some maximum likelihood estimators and give some formulae for the asymptotic variance of the different estimators.