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Asymptotic properties of least-squares estimates of parameters of the spectrum of a stationary non-deterministic time-series

Published online by Cambridge University Press:  09 April 2009

A. M. Walker
A. M. Walker
Affiliation:
University of Cambridge and Institue of Advanced Studies, Australian National University.
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Let {xt} (t = 0, ±1, ±2 …) be a stationary non-deterministic time series with E(x2t) < ∞, E(xt) = 0, and let its spectrum be continuous (strictly absolutely continuous) so that the spectral distribution function is the spectral density function. It is well known that {xt} then has a unique one-sided movingaverage representation where .

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 4 , Issue 3 , August 1964 , pp. 363 - 384
Copyright
Copyright © Australian Mathematical Society 1964

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