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A central limit theorem for stationary linear processes generated by linearly positively quadrant-dependent process

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  • Kim, Tae-Sung
  • Baek, Jong-Il

Abstract

A central limit theorem is obtained for a stationary linear process of the form Xt=[summation operator]j=0[infinity]aj[var epsilon]t-j, where {[var epsilon]t} is a strictly stationary sequence of linearly positive quadrant dependent random variables with E[var epsilon]t=0, E[var epsilon]ts 2, and [summation operator]t=n+1[infinity]E[var epsilon]1[var epsilon]t=O(n-[rho]) for some [rho]>0 and [summation operator]j=0[infinity]aj

Suggested Citation

  • Kim, Tae-Sung & Baek, Jong-Il, 2001. "A central limit theorem for stationary linear processes generated by linearly positively quadrant-dependent process," Statistics & Probability Letters, Elsevier, vol. 51(3), pages 299-305, February.
    • Handle: RePEc:eee:stapro:v:51:y:2001:i:3:p:299-305
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    References listed on IDEAS

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    1. Fakhre-Zakeri, Issa & Farshidi, Jamshid, 1993. "A central limit theorem with random indices for stationary linear processes," Statistics & Probability Letters, Elsevier, vol. 17(2), pages 91-95, May.
    2. Fakhre-Zakeri, Issa & Lee, Sangyeol, 1997. "A random functional central limit theorem for stationary linear processes generated by martingales," Statistics & Probability Letters, Elsevier, vol. 35(4), pages 417-422, November.
    3. Birkel, T., 1993. "A Functional Central Limit Theorem for Positively Dependent Random Variables," Journal of Multivariate Analysis, Elsevier, vol. 44(2), pages 314-320, February.
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    Cited by:

    1. 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.
    2. Jong-Il Baek & Sung-Tae Park, 2010. "RETRACTED ARTICLE: Convergence of Weighted Sums for Arrays of Negatively Dependent Random Variables and Its Applications," Journal of Theoretical Probability, Springer, vol. 23(2), pages 362-377, June.

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