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A Note on the Asymptotic Normality of Sample Autocorrelations for a Linear Stationary Sequence


  • He, Shuyuan


We consider a stationary time series {Xt} given byXt=[summation operator][infinity]k=-[infinity] [psi]kZt-k, where {Zt} is a strictly stationary martingale difference white noise. Under assumptions that the spectral densityf([lambda]) of {Xt} is squared integrable andm[tau] [summation operator]k[greater-or-equal, slanted]m [psi]2k-->0 for some[tau]>1/2, the asymptotic normality of the sample autocorrelations is shown. For a stationary long memoryARIMA(p, d, q) sequence, the conditionm[tau] [summation operator]k[greater-or-equal, slanted]m [psi]2k-->0 for some[tau]>1/2 is equivalent to the squared integrability off([lambda]). This result extends Theorem 4.2 of Cavazos-Cadena [5], which were derived under the conditionm [summation operator]k[greater-or-equal, slanted]m [psi]2k-->0.

Suggested Citation

  • He, Shuyuan, 1996. "A Note on the Asymptotic Normality of Sample Autocorrelations for a Linear Stationary Sequence," Journal of Multivariate Analysis, Elsevier, vol. 58(2), pages 182-188, August.
  • Handle: RePEc:eee:jmvana:v:58:y:1996:i:2:p:182-188

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    Cited by:

    1. Biao Wu, Wei & Min, Wanli, 2005. "On linear processes with dependent innovations," Stochastic Processes and their Applications, Elsevier, vol. 115(6), pages 939-958, June.


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