Article contents
Gordin's theorem and the periodogram
Published online by Cambridge University Press: 14 July 2016
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.
- Type
- Short Communications
- Information
- Copyright
- Copyright © Applied Probability Trust 1976
References
- 3
- Cited by