Testing for independence in heavy-tailed time series using the codifference function

Abstract: In this paper, we consider a Portmanteau-type test of randomness for symmetric stable random variables with exponent , using a test statistic that differs from, but has the same general form as Box–Pierce Q-statistic, which is defined using the codifference function. We obtain that unlike a similar test proposed in [Runde, R., 1997. The asymptotic null distribution of the Box–Pierce Q-statistic for random variables with infinite variance—with an application to German stock returns. Journal of Econometrics 78, 205–216], the asymptotic distribution of the proposed statistic is similar to the classical case, that is asymptotically distributed, both in finite and infinite variance cases. Simulation studies are performed to obtain the small sample performance of the proposed statistic. We found that the proposed statistic works fairly well, in the sense that in the infinite variance case, under suitable choice of the design parameter, its empirical levels are closer to the theoretical ones than Runde’s statistic. In the finite variance case, its empirical level is approximately the same as that of Ljung–Box’s statistic [Ljung, G.M. and Box, G.E.P., 1978. On a measure of lack of fit in time series models. Biometrika 65, 297–303]. Furthermore, the statistic also has good power against the AR(1) alternative. We provide an empirical example using some stocks chosen from the LQ45 index listed in the Indonesia Stock Exchange (IDX). [Copyright &y& Elsevier]