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Long‐Range Dependence And Mixing For Discrete Time Fractional Processes

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  • M. C. Viano
  • Cl. Deniau
  • G. Oppenheim

Abstract

. A large class of discrete time stationary processes, an extension of the well‐known fractionally integrated autoregressive moving‐average models, is investigated. For a suitable choice of parameters, these processes are long‐range dependent. After a detailed study of the asymptotic behaviour of their correlations, we investigate their mixing properties and then give some simulated examples.

Suggested Citation

  • M. C. Viano & Cl. Deniau & G. Oppenheim, 1995. "Long‐Range Dependence And Mixing For Discrete Time Fractional Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(3), pages 323-338, May.
    • Handle: RePEc:bla:jtsera:v:16:y:1995:i:3:p:323-338
    DOI: 10.1111/j.1467-9892.1995.tb00237.x
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    References listed on IDEAS

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    1. Viano, M. C. & Deniau, C. & Oppenheim, G., 1994. "Continuous-time fractional ARMA processes," Statistics & Probability Letters, Elsevier, vol. 21(4), pages 323-336, November.
    2. Pham, Tuan D. & Tran, Lanh T., 1985. "Some mixing properties of time series models," Stochastic Processes and their Applications, Elsevier, vol. 19(2), pages 297-303, April.
    3. Uwe Hassler, 1993. "Regression Of Spectral Estimators With Fractionally Integrated Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(4), pages 369-380, July.
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    Cited by:

    1. G. Oppenheim & M. Haye & M.-C. Viano, 2000. "Long Memory with Seasonal Effects," Statistical Inference for Stochastic Processes, Springer, vol. 3(1), pages 53-68, January.
    2. Gao, Jiti & Anh, Vo & Heyde, Chris, 2002. "Statistical estimation of nonstationary Gaussian processes with long-range dependence and intermittency," Stochastic Processes and their Applications, Elsevier, vol. 99(2), pages 295-321, June.
    3. Ould Haye, Mohamedou & Philippe, Anne, 2011. "Marginal density estimation for linear processes with cyclical long memory," Statistics & Probability Letters, Elsevier, vol. 81(9), pages 1354-1364, September.

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