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

โœ Scribed by Shuyuan He

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
332 KB
Volume
58
Category
Article
ISSN
0047-259X

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โœฆ Synopsis

We consider a stationary time series [X t ] given by X t = k= & k Z t&k , where [Z t ] is a strictly stationary martingale difference white noise. Under assumptions that the spectral density f (*) of [X t ] is squared integrable and m { |k| m 2 k ร„ 0 for some {>1ร‚2, the asymptotic normality of the sample autocorrelations is shown. For a stationary long memory ARIMA( p, d, q) sequence, the condition m { |k| m 2 k ร„ 0 for some {>1ร‚2 is equivalent to the squared integrability of f (*). This result extends Theorem 4.2 of Cavazos-Cadena [5], which were derived under the condition m |k| m 2 k ร„ 0.

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