ASYMPTOTICS FOR GARCH SQUARED RESIDUAL CORRELATIONS

Istv n Berkes, Lajos Horv th and Piotr Kokoszka

Econometric Theory, 2003, vol. 19, issue 04, pages 515-540

Abstract: We develop an asymptotic theory for quadratic forms of the autocorrelations of squared residuals from a GARCH(p,q) model. Denoting by , k 1, these autocorrelations computed from a realization of length n, we show that the statistic is a matrix computed from the data, converges to the chi-square distribution with K degrees of freedom for any 1 i1 iK. Our results are valid under weak assumptions on the innovations and model coefficients that admit that arbitrary low-order moments of the observations can be infinite. The matrix and its asymptotic limit D depend on the distribution of the innovations. A small simulation study illustrates the theory and shows, in particular, that using the matrix D computed under the assumption of normal innovations may lead to incorrect conclusions if the innovations have a different distribution.We thank the two referees for their comments and Professor Bruce E. Hansen, the co-editor in charge, for his sound advice on how to improve the paper. The work of Istv n Berkes was supported by the Hungarian National Foundation for Scientific Research, grant T 29621. The work of Lajos Horv th and Piotr Kokoszka was supported by NATO grant PST.CLG.977607.

Date: 2003
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