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Spectral density of Markov switching models: Derivation, simulation studies and application

Cheng, Jie

Authors



Abstract

This paper is concerned with frequency domain analysis of Markov mean-switching autoregressive (MMSAR) models, linear Markov switching autoregressive (LMSAR) model and transitional Markov switching autoregressive (TMSAR) model. We derive the general expressions of autocovariance functions and spectra for these three models. Simulation studies of theoretical spectral density functions of these three models are presented. The results show that Markov chain seems to be the most important determinants of the frequency distribution of the volatility. A time series is analysed and both smoothed periodogram and theoretical spectra (of LMSAR and TMSAR models) show similar pattern and give clear ideas of business cycle.

Journal Article Type Article
Acceptance Date Nov 7, 2016
Publication Date Nov 7, 2016
Journal Model Assisted Statistics and Applications
Print ISSN 1574-1699
Publisher IOS Press
Peer Reviewed Peer Reviewed
Volume 44
Issue 4
Pages 277-291
DOI https://doi.org/10.3233/MAS-160373
Keywords Markov switching autoregressive models; autocovariance structure; spectral density function; frequency domain analysis
Publisher URL https://content.iospress.com/articles/model-assisted-statistics-and-applications/mas373