Sample ACF of Multivariate Stochastic Recurrence Equations

We study the weak limit behaviour of the sample autocorrelation function (ACF) of non-linear stationary sequences with regularly varying nite-dimensional distributions. In particular, we consider the sample ACF of solutions to multivariate stochastic recurrence equations (SRE's). The latter includes the important class of the squares of GARCH processes. Point process convergence is exploited to derive weak limits of the sample ACF. The limits are functionals of innnite variance stable random vectors. It turns out that the closer the distribution of the process is to having an innnite second moment the slower the rate of convergence of the sample ACF. In the case of an innnite second moment, the sample ACF converges to a non-degenerate limit law.