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Partial autocorrelation functions of the fractional ARIMA processes with negative degree of differencing

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  • Inoue, Akihiko
  • Kasahara, Yukio

Abstract

Let {Xn : n[set membership, variant]Z} be a fractional ARIMA(p,d,q) process with partial autocorrelation function [alpha](·). In this paper, we prove that if d[set membership, variant](-1/2,0) then [alpha](n)~d/n as n-->[infinity]. This extends the previous result for the case 0

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  • Inoue, Akihiko & Kasahara, Yukio, 2004. "Partial autocorrelation functions of the fractional ARIMA processes with negative degree of differencing," Journal of Multivariate Analysis, Elsevier, vol. 89(1), pages 135-147, April.
    • Handle: RePEc:eee:jmvana:v:89:y:2004:i:1:p:135-147
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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. Chong, Terence Tai-Leung, 2000. "Estimating the differencing parameter via the partial autocorrelation function," Journal of Econometrics, Elsevier, vol. 97(2), pages 365-381, August.
    3. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
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    Cited by:

    1. D.S. Poskitt & Gael M. Martin & Simone D. Grose, 2012. "Bias Reduction of Long Memory Parameter Estimators via the Pre-filtered Sieve Bootstrap," Monash Econometrics and Business Statistics Working Papers 8/12, Monash University, Department of Econometrics and Business Statistics.
    2. Bingham, N.H. & Inoue, Akihiko & Kasahara, Yukio, 2012. "An explicit representation of Verblunsky coefficients," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 403-410.

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