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Asymptotics for moving average processes with dependent innovations

Author

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

Abstract

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

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    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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