ANALYSIS OF THE LIKELIHOOD FUNCTION FOR MARKOV‐SWITCHING VAR(CH) MODELS

Maddalena Cavicchioli

27 citations0/0 files storedJournal of Time Series Analysis

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Financial Risk and Volatility Modeling Monetary Policy and Economic Impact Statistical and numerical algorithms

Abstract

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.

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References

1995Multivariate Simultaneous Generalized ARCH 1994Chapter 49 Arch models 1997Markov-Switching Vector Autoregressions 1986Asymptotic Theory for ARCH Models: Estimation and Testing 2001On a Mixture Autoregressive Conditional Heteroscedastic Model

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2017Inference on Filtered and Smoothed Probabilities in Markov-Switching Autoregressive Models 2023Impulse response function analysis for Markov switching var models

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