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On highly skewed fractional log‐stable noise sequences and their application

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  • Harry Pavlopoulos
  • George Chronis

Abstract

Considering log‐LFSN (log‐linear fractional stable noise) sequences {Yn=eδ·Xn+ε}n∈ℤ, driven by non‐Gaussian one‐sided LFSN {Xn}n∈ℤ with constant skewness intensity β0∈[−1,1], for any δ∈ℝ−{0} and ε∈ℝ, we show that the auto‐covariance function (ACVF) {γY(h)}h∈ℤ exists if and only if {Xn}n∈ℤ is persistent, with stability index α∈(1,2), Hurst exponent H∈(1/α,1) and extreme skewness β0=−1 (if δ>0) or β0=1 (if δ

Suggested Citation

  • Harry Pavlopoulos & George Chronis, 2023. "On highly skewed fractional log‐stable noise sequences and their application," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(4), pages 337-358, July.
    • Handle: RePEc:bla:jtsera:v:44:y:2023:i:4:p:337-358
    DOI: 10.1111/jtsa.12671
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    References listed on IDEAS

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    1. Kokoszka, Piotr S. & Taqqu, Murad S., 1995. "Fractional ARIMA with stable innovations," Stochastic Processes and their Applications, Elsevier, vol. 60(1), pages 19-47, November.
    2. Rafal Weron, 1996. "Correction to: "On the Chambers-Mallows-Stuck Method for Simulating Skewed Stable Random Variables"," HSC Research Reports HSC/96/01, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    3. Weron, Rafal, 1996. "On the Chambers-Mallows-Stuck method for simulating skewed stable random variables," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 165-171, June.
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