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Can One Use the Durbin–Levinson Algorithm to Generate Infinite Variance Fractional ARIMA Time Series?

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  • Piotr S. Kokoszka
  • Murad S. Taqqu

Abstract

The Durbin–Levinson algorithm is used to generate Gaussian time series with a given covariance structure. This is the most efficient way, for example, to simulate a Gaussian fractional ARIMA (FARIMA) time series, a linear sequence with i.i.d. Gaussian innovations which exhibits long‐range dependence. The paper studies the applicability of the Durbin–Levinson algorithm to the simulation of infinite variance FARIMA sequences including an α‐stable FARIMA.

Suggested Citation

  • Piotr S. Kokoszka & Murad S. Taqqu, 2001. "Can One Use the Durbin–Levinson Algorithm to Generate Infinite Variance Fractional ARIMA Time Series?," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(3), pages 317-337, May.
    • Handle: RePEc:bla:jtsera:v:22:y:2001:i:3:p:317-337
    DOI: 10.1111/1467-9892.00226
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    Cited by:

    1. Jin, Hao & Tian, Zheng & Qin, Ruibing, 2009. "Bootstrap tests for structural change with infinite variance observations," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 1985-1995, October.
    2. Li, Yuanbo & Chan, Chu Kin & Yau, Chun Yip & Ng, Wai Leong & Lam, Henry, 2024. "Burn-in selection in simulating stationary time series," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
    3. Piotr Kokoszka & Michael Wolf, 2002. "Subsampling the mean of heavy-tailed dependent observations," Economics Working Papers 600, Department of Economics and Business, Universitat Pompeu Fabra.
    4. Jin, Hao & Zhang, Jinsuo & Zhang, Si & Yu, Cong, 2013. "The spurious regression of AR(p) infinite-variance sequence in the presence of structural breaks," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 25-40.
    5. Piotr Kokoszka & Michael Wolf, 2004. "Subsampling the mean of heavy‐tailed dependent observations," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(2), pages 217-234, March.

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