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

Yanlin Shi*, Kin-Yip Ho

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contribution

Abstract

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. Instead, this research incorporates the a-stable distribution in the GARCH-type model. The issue of the a-stable distribution is that its second moment does not exist. To solve this problem, the tempered stable distribution, which retains most characteristics of the a-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 modelling the financial volatility in general contexts with a MRS-GARCH-type specification.

Original languageEnglish
Title of host publicationMODSIM 2015
Subtitle of host publicationProceedings of the 21st International Congress on Modelling and Simulation
EditorsTony Weber, Malcolm McPhee, Robert Anderssen
Place of PublicationGold Coast
PublisherModelling and Simulation Society of Australia and New Zealand
Pages994-1000
Number of pages7
ISBN (Electronic)9780987214355
DOIs
Publication statusPublished - 2015
Externally publishedYes
Event21st International Congress on Modelling and Simulation: Partnering with Industry and the Community for Innovation and Impact through Modelling, MODSIM 2015 - Held jointly with the 23rd National Conference of the Australian Society for Operations Research and the DSTO led Defence Operations Research Symposium, DORS 2015 - Broadbeach, Australia
Duration: 29 Nov 20154 Dec 2015

Conference

Conference21st International Congress on Modelling and Simulation: Partnering with Industry and the Community for Innovation and Impact through Modelling, MODSIM 2015 - Held jointly with the 23rd National Conference of the Australian Society for Operations Research and the DSTO led Defence Operations Research Symposium, DORS 2015
CountryAustralia
CityBroadbeach
Period29/11/154/12/15

Keywords

  • Fat-tailed distribution
  • GARCH Model
  • Regime-switching
  • Tempered stable distribution

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