Tempered fractional stable motion adds an exponential tempering to the power-law kernel in a linear fractional stable motion, or a shift to the power-law filter in a harmonizable fractional stable motion. Increments from a stationary time series that can exhibit semi-long-range dependence. This paper develops the basic theory of tempered fractional stable processes, including dependence structu...

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...