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Fractional ARIMA with stable innovations

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  • Kokoszka, Piotr S.
  • Taqqu, Murad S.

Abstract

We develop the theory of fractionally differenced ARIMA time series with stable infinite variance innovations establishing conditions for existence and invertibility. We analyze their asymptotic dependence structure by means of the codifference and the covariation, measures of dependence which are extensions of the covariance and are applicable to stochastic processes with infinite variance.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:60:y:1995:i:1:p:19-47
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    References listed on IDEAS

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    1. Klüppelberg, Claudia & Mikosch, Thomas, 1993. "Spectral estimates and stable processes," Stochastic Processes and their Applications, Elsevier, vol. 47(2), pages 323-344, September.
    2. Piotr S. Kokoszka & Murad S. Taqqu, 1994. "Infinite Variance Stable Arma Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(2), pages 203-220, March.
    3. Cline, Daren B. H. & Brockwell, Peter J., 1985. "Linear prediction of ARMA processes with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 19(2), pages 281-296, April.
    4. Davis, Richard & Resnick, Sidney, 1985. "More limit theory for the sample correlation function of moving averages," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 257-279, September.
    5. Bhansali, R. J., 1993. "Estimation of the Impulse-Response Coefficients of a Linear Process with Infinite Variance," Journal of Multivariate Analysis, Elsevier, vol. 45(2), pages 274-290, May.
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