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A note on linear processes with tapered innovations (1905.01891v1)
Published 6 May 2019 in math.PR
Abstract: In the paper we consider the partial sum process $\sum_{k=1}{[nt]}X_k{(n)}$, where ${X_k{(n)}, \ k\in Z},\ n\ge 1,$ is a series of linear processes with innovations having heavy-tailed tapered distributions with tapering parameter $b_n$ depending on $n$. It is shown that, depending on the properties of a filter of a linear process under consideration and on the parameter $b_n$ defining if the tapering is hard or soft, the limit process for such partial sum process can be fractional Brownian motion or linear fractional stable motion.