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

J. Cheng*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)277-291
Number of pages15
JournalModel Assisted Statistics and Applications
Issue number4
Publication statusPublished - 2016


  • Markov switching autoregressive models
  • autocovariance structure
  • frequency domain analysis
  • spectral density function


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