On a GARCH Model with Normal Scale Mixture Innovations

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Feng Feng 1,*

1. School of Management, Fuzhou University, Fuzhou, Fujian Province, China

* Corresponding author.

DOI: https://doi.org/10.5815/ijem.2012.02.02

Received: 3 Jan. 2012 / Revised: 2 Feb. 2012 / Accepted: 29 Feb. 2012 / Published: 6 Apr. 2012

Index Terms

GARCH model, Normal scale mixture, EM algorithm, Tail behavior, Volatility Clustering


Recently, there has been a lot of interest in modeling real data with a heavy tailed distribution. A popular candidate is the so-called generalized autoregressive conditional heteroscedastic (GARCH) model. Unfortunately, the tails of normal GARCH models are not thick enough in some applications. In this paper, we propose a GARCH model with normal scale mixture innovations, the parameters estimation procedure using EM algorithm is also provided. It is shown that GARCH models with normal scale mixture innovations have tails thicker than those of normal GARCH models. Therefore, the GARCH models with normal scale mixture innovations are more capable of capturing the heavy-tailed features in real data. Shanghai Stock Market Index as a real example illustrates the results.

Cite This Paper

Feng Feng,"On a GARCH Model with Normal Scale Mixture Innovations", IJEM, vol.2, no.2, pp.8-14, 2012. DOI: 10.5815/ijem.2012.02.02 


[1] Bollerslev, “Generalised autoregressive conditional heteroscedasticity,” J. Econometrics, vol. 51, pp. 307–327, 1986. 

[2] Bollerslev, “A conditional heteroscedastic time series model for speculative prices and rates of return,” Rev. Econom Statist, Vol. 69, pp.542–547,1987.

[3] Chun Shan Wong and Wai Keung Li, “On a mixture autoregressive model,” Journal of Royal Statistical Society, vol. 62, pp.95–115,2000.

[4] Chun Shan Wong and Wai Keung Li, “On a mixture autoregressive conditional heteroscedastic model,” Journal of American Statistical Association, vol. 96, pp.982–995,2001.

[5] Engle, “Autoregressive conditional heteroscedasticity with estimates of the variance of the UK inflation,” Econometrica, vol. 50, pp.987–1008,1982.

[6] Mar´ıa Concepci´on Aus´ın Pedro Galeano, “Bayesian estimation of the gaussian mixture GARCH model,” Computional Statistics & Data, vol. 51, pp.2636–2652,2007.

[7] Pi Liu-yi, Liu Zhong and Mao Shi-song, “Probability Distribution Analysis on Market Value, Amount and Varities of Stocks,” Chinese Journal of Applied Probability and Statistics, vol. 14, pp.386–394,1998.

[8] Zhang Z., W.K. Li and K.C. Yuen, “On a mixture GARCH time series model,” Journal of Time Series Analysis, vol. 27, pp.577–597,2006