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Gordin's theorem and the periodogram

Published online by Cambridge University Press:  14 July 2016

Holger Rootzén
Holger Rootzén*
Affiliation:
Tekniska Högskolan i Lund, Sweden
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Abstract

In 1968 M. I. Gordin proved a very strong central limit theorem for stationary, ergodic sequences by means of approximation with martingales. In the present paper Gordin's theorem is generalized to cover also the periodogram of a stationary sequence, and the restriction of ergodicity is removed. It is noted that known central limit theorems for stationary processes can often be generalized to the periodogram by means of this result.

Keywords

PERIODOGRAMCENTRAL LIMIT THEOREMTIME SERIES ANALYSIS
Type
Short Communications
Information
Journal of Applied Probability , Volume 13 , Issue 2 , June 1976 , pp. 365 - 370
Copyright
Copyright © Applied Probability Trust 1976 

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References

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