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Asymptotic properties of the periodogram of a discrete stationary process

Published online by Cambridge University Press:  14 July 2016

Richard A. Olshen
Richard A. Olshen*
Affiliation:
Yale University
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Extract

Suppose x1,…, xN are indefinitely many observations on a stochastic process which is weakly stationary with spectral density f(λ), – π ≦ λ ≦ π. An asymptotically unbiased, and to that extent plausible, estimate of 4rf(λ)is the periodogram Yet the periodograms of processes which possess spectral densities are notoriously subject to erratic behavior.

Type
Research Papers
Information
Journal of Applied Probability , Volume 4 , Issue 3 , November 1967 , pp. 508 - 528
Copyright
Copyright © Applied Probability Trust 

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