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The Asymptotic Distribution of Sample Autocorrelations for a Class of Linear Filters

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  • Cavazoscadena, R.

Abstract

We consider a stationary time series {Xt} given by Xt = [Sigma]k[psi]kZt - k, where the driving stream {Zt} consists of independent and identically distributed random variables with mean zero and finite variance. Under the assumption that the filtering weights [psi]k are squared summable and that the spectral density of {Xt} is squared integrable, it is shown that the asymptotic distribution of the sequence of sample autocorrelation functions is normal with covariance matrix determined by the well-known Bartlett formula. This result extends classical theorems by Bartlett (1964, J. Roy Statist. Soc. Supp.8 27-41, 85-97) and Anderson and Walker (1964, Ann. Math. Statist.35 1296-1303), which were derived under the assumption that the filtering sequence {[psi]k] is summable.

Suggested Citation

  • Cavazoscadena, R., 1994. "The Asymptotic Distribution of Sample Autocorrelations for a Class of Linear Filters," Journal of Multivariate Analysis, Elsevier, vol. 48(2), pages 249-274, February.
    • Handle: RePEc:eee:jmvana:v:48:y:1994:i:2:p:249-274
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