Testing Coefficients of Autoregressive Conditional Heteroskedasticity Models by Graphical Approach

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Author(s)

Fengjing Cai 1,* Yuan Li 2

1. School of Mathematics & Information Science, Wenzhou University, Wenzhou, Zhejiang Province, China

2. School of Mathematics & Information Science, Guangzhou University, Guangzhou,Guangdong Province, China

* Corresponding author.

DOI: https://doi.org/10.5815/ijem.2012.02.11

Received: 19 Nov. 2011 / Revised: 10 Jan. 2012 / Accepted: 29 Feb. 2012 / Published: 6 Apr. 2012

Index Terms

Time Series Chain Graph, ARCH, GARCH

Abstract

The graphical approach is applied to the autoregressive conditional heteroskedasticity time series models. After transformation, it is shown that the coefficients of GARCH model are the conditional correlation coefficients conditioned on the other components of the time series, then a new method is proposed to test the significance of the coefficients of GARCH model.

Cite This Paper

Fengjing Cai , Yuan Li,"Testing Coefficients of Autoregressive Conditional Heteroskedasticity Models by Graphical Approach", IJEM, vol.2, no.2, pp.71-78, 2012. DOI: 10.5815/ijem.2012.02.11

Reference

[1] Engle  R. F. “Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation”, Econometrica, Vol  50,No. 4, pp. 987-1007, 1982. 

[2] Bollerslev T. “Generalized autoregressive conditional heteroskedasticity” Journal of Econometrics, Vol.  31, No. 3, pp. 307-327,1986. 

[3] Whittaker J. “Graphical models in applied multivariate statistics”, New York:Wiley, pp.1-120,1990. 

[4] Cox D.R., Wermuth N. “Linear dependencies represented by chain  graphs”, Statistical Science, Vol. 8,No. 3, pp.204-218,1993. 

[5] Edwards D. “Introduction to graphical modelling”, New York: Springer, pp.1-20,2001. 

[6] Lauritzen S.L. “Graphical models”, Oxford: Oxford University Press,  pp.1-33,1996. 

[7] Reale M. “A graphical modelling approach to time series”, Lancaster University, pp.1-143,1998. 

[8] Eichler M. “Graphical models in time series analysis”, University Heidelberg, pp.1-100, 1999. 

[9] Dahlhaus R. “Graphical interaction models for multivariate time series”, Metrika, Vol. 51, No. 2, pp. 157-172, 2000. 

[10] Gather U., Imhoff M., Fried R. “Graphical models for multivariate time series from intensive care monitoring”, Statistics in Medicine, Vol.  21,No. 18, pp. 2685-2701,2002.

[11] Eichler M. “Granger causality and path diagrams for multivariate time series”,Journal of Econometrics, Vol. 137, No. 2, pp.334-353, 2007.

[12] IP W.C., Wong H., Li Y., Luo X.H. “Testing coefficients of AR and bilinear time series models by a graphical approach”, Science in China Series A: Mathematics, Vol. 51, No. 12,pp. 2304-2314 , 2008.

[13] Shao J. “Mathematical statistics”,New York: Springer-Verlag, pp.1-530,1999.

[14] Liu J. “On stationarity and asymptotic inference of bilinear time series models”, Statist Sin,Vol. 2, pp.479-494,1992