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On the estimation of a harmonic component in a time series with stationary dependent residuals

Published online by Cambridge University Press:  01 July 2016

A. M. Walker
A. M. Walker*
Affiliation:
University of Sheffield
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Abstract

Let observations (X1, X2, …, Xn) be obtained from a time series {Xt} such that where the ɛt are independently and identically distributed random variables each having mean zero and finite variance, and the gu(θ) are specified functions of a vector-valued parameter θ. This paper presents a rigorous derivation of the asymptotic distributions of the estimators of A, B, ω and θ obtained by an approximate least-squares method due to Whittle (1952). It is a sequel to a previous paper (Walker (1971)) in which a similar derivation was given for the special case of independent residuals where gu(θ) = 0 for u > 0, the parameter θ thus being absent.

Keywords

TIME SERIESHARMONIC COMPONENTSLINEAR RESIDUAL PROCESSLEAST SQUARES ESTIMATIONASYMPTOTIC DISTRIBUTION OF ESTIMATES
Type
Research Article
Information
Advances in Applied Probability , Volume 5 , Issue 2 , August 1973 , pp. 217 - 241
Copyright
Copyright © Applied Probability Trust 1973 

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References

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