Scandinavian Working Papers in Economics

SSE/EFI Working Paper Series in Economics and Finance,
Stockholm School of Economics

No 315: Higher-order dependence in the general Power ARCH process and a special case

Changli He () and Timo Teräsvirta ()
Additional contact information
Changli He: Dept. of Economic Statistics, Stockholm School of Economics, Postal: Stockholm School of Economics, P.O. Box 6501, S-113 83 Stockholm, Sweden
Timo Teräsvirta: Dept. of Economic Statistics, Stockholm School of Economics, Postal: Stockholm School of Economics, P.O. Box 6501, S-113 83 Stockholm, Sweden

Abstract: In this paper we consider a general first-order power ARCH process and, in particular, a special case in which the power parameter approaches zero. These considerations give us the autocorrelation function of the logarithms of the squared observations for first-order exponential and logarithmic GARCH processes. These autocorrelations decay exponentially with the lag and may be used for checking how well an estimated exponential or logarithmic GARCH model characterizes the corresponding autocorrelation structure of the observations. The results of the paper are also useful in illustrating differences in the autocorrelation structures of the classical first-order GARCH and the exponential or logarithmic GARCH models.

Keywords: Box-Cox transformation; conditional heteroskedasticity; exponential GARCH; logarithmic GARCH; higher-order dependence

JEL-codes: C22

16 pages, April 21, 1999

Note: The forthcoming version of the paper is C. He, H. Malmsten and T. Teräsvirta: Higher-order dependence in the general Power ARCH process and the role of the power parameter

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