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

Article type: Research Article

Authors: Cheng, J.

Affiliations: Department of Mathematical Sciences, Xi'an Jiaotong-Liverpool University, Suzhou, China. Tel.: +86 512 8816 1522; Fax: +86 512 8816 1899; E-mail: Jie.cheng@xjtlu.edu.cn

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.

Keywords: Markov switching autoregressive models, autocovariance structure, spectral density function, frequency domain analysis

DOI: 10.3233/MAS-160373

Journal: Model Assisted Statistics and Applications, vol. 11, no. 4, pp. 277-291, 2016