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Asymptotic properties of certain functionals of the periodogram

Published online by Cambridge University Press:  14 July 2016

Herbert T. Davis
Herbert T. Davis*
Affiliation:
The University of New Mexico
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Abstract

The asymptotic properties of the periodogram of a weakly stationary time series for the triangular array of fundamental frequencies is studied. For linear Gaussian processes, results are obtained relating the asymptotic distribution of certain Riemann sums of the periodogram of the process to those of the periodogram of the innovation process.

Keywords

PERIODOGRAMWEAKLY STATIONARY TIME SERIESGAUSSIANASYMPTOTIC DISTRIBUTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 3 , September 1974 , pp. 578 - 581
Copyright
Copyright © Applied Probability Trust 1974 

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References

[1] Fisher, R. A. (1929) Tests of significance in harmonic analysis. Proc. Roy. Soc. A 125, 54–59.Google Scholar
[2] Loève, M. (1960) Probability Theory. 2nd ed. Van Nostrand, Princeton, N. J. Google Scholar
[3] Walker, A. M. (1965) Some asymptotic results for the periodogram of a stationary time series. J. Austral. Math. Soc. 5, 107–129.Google Scholar