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Band-limited spectral estimation of autoregressive-moving-average processes

Published online by Cambridge University Press:  14 July 2016

P. J. Thomson
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Abstract

Consider an autoregressive-moving-average process of given order where it is known that a number of moving-average roots are of unit modulus. Such a situation might arise, for example, when a time series has been differenced to induce stationarity by removing a non-stationary polynomial or seasonal trend. A band-limited spectral estimation procedure is proposed for estimating the coefficients of such a process and the asymptotic properties of the estimators investigated. The asymptotic theory is illustrated with reference to simulated and real data. A preliminary investigation of the use of Akaike's AIC criterion and this procedure to determine the number of roots of unit modulus (in the case where this is unknown) is also carried out by means of simulation.

The proposed band-limited spectral estimation procedure can also be used to take account of other possible effects met in practice. These include, for example, the band-limited response of a recording device or trend-contaminated low-frequency components.

Keywords

ARMA MODELTIME SERIES INFERENCEFOURIER METHODSFILTERINGASYMPTOTIC RESULTS
Type
Part 2—Estimation for Time Series
Information
Journal of Applied Probability , Volume 23 , Issue A: Essays in Time Series and Allied Processes , 1986 , pp. 143 - 155
Copyright
Copyright © 1986 Applied Probability Trust 

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