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On a Mixture GARCH Time‐Series Model

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  • Zhiqiang Zhang
  • Wai Keung Li
  • Kam Chuen Yuen

Abstract

. Recently, there has been a lot of interest in modelling real data with a heavy‐tailed distribution. A popular candidate is the so‐called generalized autoregressive conditional heteroscedastic (GARCH) model. Unfortunately, the tails of GARCH models are not thick enough in some applications. In this paper, we propose a mixture generalized autoregressive conditional heteroscedastic (MGARCH) model. The stationarity conditions and the tail behaviour of the MGARCH model are studied. It is shown that MGARCH models have tails thicker than those of the associated GARCH models. Therefore, the MGARCH models are more capable of capturing the heavy‐tailed features in real data. Some real examples illustrate the results.

Suggested Citation

  • Zhiqiang Zhang & Wai Keung Li & Kam Chuen Yuen, 2006. "On a Mixture GARCH Time‐Series Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(4), pages 577-597, July.
    • Handle: RePEc:bla:jtsera:v:27:y:2006:i:4:p:577-597
    DOI: 10.1111/j.1467-9892.2006.00467.x
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    Cited by:

    1. Bentarzi, M. & Hamdi, F., 2008. "Mixture periodic autoregressive conditional heteroskedastic models," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 1-16, September.
    2. Frédérique Bec & Anders Rahbek & Neil Shephard, 2008. "The ACR Model: A Multivariate Dynamic Mixture Autoregression," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(5), pages 583-618, October.
    3. Wang, Hui & Pan, Jiazhu, 2014. "Normal mixture quasi maximum likelihood estimation for non-stationary TGARCH(1,1) models," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 117-123.

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