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

No 359: Moments and the Autocorrelation Structure of the Exponential GARCH(p,q) Process

Changli He ()
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Changli He: 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 the autocorrelation structure of the Exponential GARCH(p,q) process of Nelson (1991) is considered. Conditions for the existence of any arbitrary unconditional moment are given. Furthermore, the expressions for the kurtosis and the autocorrelations of squared observations are derived. The properties of the autocorrelation structure are discussed and compared to those of the standard GARCH(p,q) process. In particular, it is seen that, the EGARCH(p,q) model has a richer autocorrelation structure than the standard GARCH(p,q) one. The statistical theory is further illustrated by a few special cases such as the symmetric and the asymmetric EGARCH(2,2) models under the assumption of normal errors or non-normal errors. The autocorrelations computed from an estimated EGARCH(2,1) model of Nelson (1991) are highlighted.

Keywords: autocorrelation function of squared observations; conditional variance model; GARCH; time series; volatility

JEL-codes: C22

40 pages, February 4, 2000

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