Scandinavian Working Papers in Economics

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

No 169: Properties of the Autocorrelation Function of Squared Observations for Second Order GARCH Processes under Two Sets of Parameter Constraints

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: Nonnegativety constraints on the parameters of the GARCH (p, Q) model may be relaxed without giving up the requirement of the conditional variance remaining non- negative with probability one. This paper looks into the consequences of adopting these less severe constraints in the GARCH (2,2) case and its two second-order special cases, GARCH (2,1) and GARCH (1,2). This is done by comparing the autocorrelation function of squared observations under these two sets of constraints. The less severe constraints allow more flexibility in the shape of the autocorrelation function than the constraints restricting the parameters to be nonnegative. The theory is illustrated by an empirical example.

Keywords: Autoregressive conditional heteroskedasticity; conditional variance; fourth moment condition; time series; volatility

JEL-codes: C22

18 pages, April 1997

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