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Aproximate Distributions of the Periodogram and Related Statistics under Normality

Published online by Cambridge University Press:  18 October 2010

Seiji Nabeya  and
Katsuto Tanaka
Seiji Nabeya
Affiliation:
Hitotsubashi University, Kunitachi, Tokyo
Katsuto Tanaka
Affiliation:
Hitotsubashi University, Kunitachi, Tokyo
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Abstract

Under normality, we obtain higher-order approximations to the distributions of the periodogram and related statistics. Our approach is based on the theorem which decomposes the periodogram into the sum of two independent random variables. It is seen that this decomposition enables us to study fairly closely the higher-order properties of not only the periodogram, but also periodogram-based statistics such as the estimators of the spectrum and prediction error variance. Some of the approximation results are graphically presented together with the exact results based on simulations.

Type
Research Article
Information
Econometric Theory , Volume 2 , Issue 1 , April 1986 , pp. 33 - 65
Copyright
Copyright © Cambridge University Press 1986 

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References

1. Anderson, T. W. The Statistical Analysis of Time Series. New York: Wiley, 1971.Google Scholar
2. Bentkus, R. Yu., and Rudzkis, R. A.. On the distribution of some statistical estimates of spectral density. Theory of Probability and Its Applications 27 (1982): 795–814.Google Scholar
3. Davis, H. T. and Jones, R. H.. Estimation of the innovation variance of a stationary time series. Journal of the American Statistical Association 63 (1968): 141–149.Google Scholar
4. Grenander, U. and Rosenblatt, M.. Statistical Analysis of Stationary Time Series. New York: Wiley, 1957.Google Scholar
5. Hannan, E. J. and Nicholls, D. F.. The estimation of the prediction error variance. Journal of the American Statistical Association. 72 (1977): 834–840.Google Scholar
6. Johnson, N. L. and Kotz, S.. Distributions in Statistics: Continuous Univariate Distributions-2. New York Wiley, 1970.Google Scholar
7. Wittwer, G. Über die asymptotische Verteilung des Periodogramms stationärer Gaussscher zufälliger Folgen. Mathematische Operationsforschung und Statistik, Series Statistics. 9 (1978): 357–368.Google Scholar
8. Wittwer, G. Über die mehrdimensionalen asymptotischen Verteilungen des Periodogramms Gaussscher stationärer Folgen. Mathematische Operationsforschung und Statistik, Series Statistics. 12 (1981): 361–376.Google Scholar