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Invariance principles for tempered fractionally integrated processes

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  • Sabzikar, Farzad
  • Surgailis, Donatas

Abstract

We discuss invariance principles for autoregressive tempered fractionally integrated moving averages in α-stable (1<α≤2) i.i.d. innovations and related tempered linear processes with vanishing tempering parameter limN→∞λ∕N=λ∗. We show that the limit of the partial sums process takes a different form in the weakly tempered (λ∗=0), strongly tempered (λ∗=∞), and moderately tempered (0<λ∗<∞) cases. These results are used to derive the limit distribution of the ordinary least squares estimate of AR(1) unit root with weakly, strongly, and moderately tempered moving average errors.

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  • Sabzikar, Farzad & Surgailis, Donatas, 2018. "Invariance principles for tempered fractionally integrated processes," Stochastic Processes and their Applications, Elsevier, vol. 128(10), pages 3419-3438.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:10:p:3419-3438
    DOI: 10.1016/j.spa.2017.11.004
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    Cited by:

    1. Farzad Sabzikar & Piotr Kokoszka, 2023. "Tempered functional time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(3), pages 280-293, May.
    2. Kris Brabanter & Farzad Sabzikar, 2021. "Asymptotic theory for regression models with fractional local to unity root errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(7), pages 997-1024, October.
    3. Sabzikar, Farzad & Wang, Qiying & Phillips, Peter C.B., 2020. "Asymptotic theory for near integrated processes driven by tempered linear processes," Journal of Econometrics, Elsevier, vol. 216(1), pages 192-202.
    4. Sepideh Mosaferi & Mark S. Kaiser, 2021. "Nonparametric Cointegrating Regression Functions with Endogeneity and Semi-Long Memory," Papers 2111.00972, arXiv.org, revised Jan 2025.
    5. dos Santos, Maike A.F., 2019. "Analytic approaches of the anomalous diffusion: A review," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 86-96.
    6. Beran, Jan & Sabzikar, Farzad & Surgailis, Donatas & Telkmann, Klaus, 2020. "On the empirical process of tempered moving averages," Statistics & Probability Letters, Elsevier, vol. 167(C).

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