A discussion on the innovation distribution of the Markov regime-switching GARCH model

Yanlin Shi*, Lingbing Feng

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


The Markov Regime-Switching Generalized autoregressive conditional heteroskedastic (MRS-GARCH) model is a widely used approach to model the financial volatility with potential structural breaks. The original innovation of the MRS-GARCH model is assumed to follow the Normal distribution, which cannot accommodate fat-tailed properties commonly existing in financial time series. Many existing studies point out that this problem can lead to inconsistent estimates. To overcome it, the Student's t-distribution and General Error Distribution (GED) are the two most popular alternatives. However, a recent study points out that the Student's t-distribution lacks stability. Also, it incorporates the α-stable distribution in the GARCH-type model. The issue of the α-stable distribution is that its second moment does not exist. To solve this problem, the tempered stable distribution, which retains most characteristics of the α-stable distribution and has defined moments, is a natural candidate. In this paper, we conduct a series of simulation studies to demonstrate that MRS-GARCH model with tempered stable distribution consistently outperform that with Student's t-distribution and GED. Our empirical study on the S&P 500 daily return volatility also generates robust results. Therefore, we argue that the tempered stable distribution could be a widely useful tool for modeling the financial volatility in general contexts with a MRS-GARCH-type specification.

Original languageEnglish
Pages (from-to)278-288
Number of pages11
JournalEconomic Modelling
Publication statusPublished - 1 Feb 2016
Externally publishedYes


  • fat-tailed distribution
  • GARCH model
  • regime-switching
  • tempered stable distribution


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