Abstract
In the paper, we consider the partial-sum process \( {\sum}_{k=1}^{\left[ nt\right]}{X}_k^{(n)}, \) where \( \left\{{X}_n^{(n)},k\in \mathbb{Z}\right\},n\ge 1, \) is a series of linear processes with innovations having heavy-tailed tapered distributions with tapering parameter bn depending on n. We show that, depending on the properties of a filter of a linear process under consideration and on the parameter bn defining if the tapering is hard or soft, the limit process for such partial-sum process can be a fractional Brownian motion or linear fractional stable motion.
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19 April 2020
Investigating the same problems for linear random fields with tapered innovations, I realized that the Hurst index of the limit FBM process and conditions on tapering parameter �� in Theorem 1 were incorrectly calculated.
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Paulauskas, V. A note on linear processes with tapered innovations. Lith Math J 60, 64–79 (2020). https://doi.org/10.1007/s10986-019-09445-w
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DOI: https://doi.org/10.1007/s10986-019-09445-w