On mixture memory Garch models

Muyi LI, Wai Keung LI, Guodong LI

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

We propose a new volatility model, which is called the mixture memory generalized autoregressive conditional heteroskedasticity (MM‐GARCH) model. The MM‐GARCH model has two mixture components, of which one is a short‐memory GARCH and the other is the long‐memory fractionally integrated GARCH. The new model, a special ARCH( ∞ ) process with random coefficients, possesses both the properties of long‐memory volatility and covariance stationarity. The existence of its stationary solution is discussed. A dynamic mixture of the proposed model is also introduced. Other issues, such as the expectation–maximization algorithm as a parameter estimation procedure, the observed information matrix, which is relevant in calculating the theoretical standard errors, and a model selection criterion, are also investigated. Monte Carlo experiments demonstrate our theoretical findings. Empirical application of the MM‐GARCH model to the daily S&P 500 index illustrates its capabilities. Copyright © 2013 Wiley Publishing Ltd.
Original languageEnglish
Pages (from-to)606-624
JournalJournal of Time Series Analysis
Volume34
Issue number6
Early online dateAug 2013
DOIs
Publication statusPublished - Nov 2013

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GARCH Model
Memory Model
Conditional Heteroskedasticity
Data storage equipment
Generalized Autoregressive Conditional Heteroscedasticity
Volatility
Model
Autoregressive Conditional Heteroscedasticity
Observed Information
Model Selection Criteria
Random Coefficients
Information Matrix
Monte Carlo Experiment
Expectation-maximization Algorithm
Stationarity
Standard error
Stationary Solutions
Parameter Estimation
GARCH model
Parameter estimation

Citation

Li, M., Li, W. K., & Li, G. (2013). On mixture memory Garch models. Journal of Time Series Analysis, 34(6), 606-624. doi: 10.1111/jtsa.12037

Keywords

  • Long memory in volatility
  • Covariance stationarity
  • Mixture ARCH(∞)
  • EM algorithm