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A Goodness-of-Fit Test for Time Series with Long Range Dependence

Jan Beran
Journal of the Royal Statistical Society. Series B (Methodological)
Vol. 54, No. 3 (1992), pp. 749-760
Published by: Wiley for the Royal Statistical Society
Stable URL: http://www.jstor.org/stable/2345855
Page Count: 12
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A Goodness-of-Fit Test for Time Series with Long Range Dependence
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Abstract

We propose a test statistic for goodness of fit in time series with slowly decaying serial correlations. The asymptotic distribution of the test statistic, originally proposed by Milhoj for time series with smooth spectra, turns out to be the same, under the null hypothesis, even if the spectrum has a pole at 0. In particular, the test is suitable to detect lack of independence in the observations, or estimated residuals, if the first few correlations are small but the decay of the correlations is slow.

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