Scandinavian Working Papers in Economics

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

No 168: Fourth Moment Structure of the GARCH (p, q) Process

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

Abstract: In this paper, a necessary and sufficient condition for the existence of the unconditional fourth moment of the GARCH (p, q) process is given as well as an expression for the moment itself. Furthermore, the autocorrelation function of the centred and squared observations of this process is derivedl The statistical theory is further illustrated by a few special cases such as the GARCH (2,2) process and the ARCH (q) process.

Keywords: Autoregressive conditional heteroskedasticity; conditional variance; fattailed error distribution; time series; volatility

JEL-codes: C22

36 pages, April 1997

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Published as
Changli He and Timo Teräsvirta, (1999), 'Fourth Moment Structure of the GARCH (p, q) Process', Econometric Theory, vol 15, pages 824-846

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