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Asymptotics for moving average processes with dependent innovations


  • Wang, Qiying
  • Lin, Yan-Xia
  • Gulati, Chandra M.


Let Xt be a moving average process defined by Xt=[summation operator]k=0[infinity][psi]k[var epsilon]t-k, t=1,2,... , where the innovation {[var epsilon]k} is a centered sequence of random variables and {[psi]k} is a sequence of real numbers. Under conditions on {[psi]k} which entail that {Xt} is either a long memory process or a linear process, we study asymptotics of the partial sum process [summation operator]t=0[ns]Xt. For a long memory process with innovations forming a martingale difference sequence, the functional limit theorems of [summation operator]t=0[ns]Xt (properly normalized) are derived. For a linear process, we give sufficient conditions so that [summation operator]t=1[ns]Xt (properly normalized) converges weakly to a standard Brownian motion if the corresponding [summation operator]k=1[ns][var epsilon]k is true. The applications to fractional processes and other mixing innovations are also discussed.

Suggested Citation

  • Wang, Qiying & Lin, Yan-Xia & Gulati, Chandra M., 2001. "Asymptotics for moving average processes with dependent innovations," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 347-356, October.
  • Handle: RePEc:eee:stapro:v:54:y:2001:i:4:p:347-356

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    References listed on IDEAS

    1. Yokoyama, Ryozo, 1995. "On the central limit theorem and law of the iterated logarithm for stationary processes with applications to linear processes," Stochastic Processes and their Applications, Elsevier, vol. 59(2), pages 343-351, October.
    2. Hannan, E. J., 1979. "The central limit theorem for time series regression," Stochastic Processes and their Applications, Elsevier, vol. 9(3), pages 281-289, December.
    3. Sowell, Fallaw, 1990. "The Fractional Unit Root Distribution," Econometrica, Econometric Society, vol. 58(2), pages 495-505, March.
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    Cited by:

    1. Kulik, Rafal, 2006. "Limit theorems for self-normalized linear processes," Statistics & Probability Letters, Elsevier, vol. 76(18), pages 1947-1953, December.
    2. Moon, H.J., 2008. "The functional CLT for linear processes generated by mixing random variables with infinite variance," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2095-2101, October.


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