A note on linear processes with tapered innovations

2019/05/06 by Paulauskas, Vygantas
#60F17 #FOS: Mathematics #Primary 60G99 #Probability (math.PR) #secondary 60G22

paper · doi:10.48550/arxiv.1905.01891

Abstract

In the paper we consider the partial sum process ∑_k=1^[nt]X_k⁽ⁿ⁾, where \X_k⁽ⁿ⁾, k∈ Z\, n≥ 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.

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