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Modelling Long‐memory Time Series with Finite or Infinite Variance: a General Approach

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  • Remigijus Leipus
  • Marie‐Claude Viano

Abstract

We present a class of generalized fractional filters which is stable with respect to series and parallel connection. This class extends the so‐called fractional ARUMA and fractional ARMA filters previously introduced by e.g. Goncalves (1987) and Robinson (1994) and recently studied by Giraitis and Leipus (1995) and Viano et al. (1995). Conditions for the existence of the induced stationary SαS and L2 processes are given. We describe the asymptotic dependence structure of these processes via the codifference and the covariance sequences respectively. In the L2 case, we prove the weak convergence of the normalized partial sums.

Suggested Citation

  • Remigijus Leipus & Marie‐Claude Viano, 2000. "Modelling Long‐memory Time Series with Finite or Infinite Variance: a General Approach," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(1), pages 61-74, January.
    • Handle: RePEc:bla:jtsera:v:21:y:2000:i:1:p:61-74
    DOI: 10.1111/1467-9892.00173
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    Cited by:

    1. Reisen, Valdério A. & Zamprogno, Bartolomeu & Palma, Wilfredo & Arteche, Josu, 2014. "A semiparametric approach to estimate two seasonal fractional parameters in the SARFIMA model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 98(C), pages 1-17.
    2. Dissanayake, G.S. & Peiris, M.S. & Proietti, T., 2016. "State space modeling of Gegenbauer processes with long memory," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 115-130.
    3. Wilfredo Palma & Ngai Hang Chan, 2005. "Efficient Estimation of Seasonal Long‐Range‐Dependent Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(6), pages 863-892, November.
    4. 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.
    5. 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.
    6. D. Marinucci, 2005. "The Empirical Process for Bivariate Sequences with Long Memory," Statistical Inference for Stochastic Processes, Springer, vol. 8(2), pages 205-223, September.

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