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Fitting Arma Time Series by Structural Equation Models

Published online by Cambridge University Press:  01 January 2025

Stef van Buuren
Stef van Buuren*
Affiliation:
Department of Statistics, TNO Prevention and Health, Leiden
*
Requests for reprints should be sent to Stef van Buuren, Dept. of Statistics, TNO Prevention and Health, P.O. Box 2215, 2301 CE Leiden, THE NETHERLANDS. Email: [email protected]
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Abstract

This paper outlines how the stationary ARMA (p, q) model can be specified as a structural equations model. Maximum likelihood estimates for the parameters in the ARMA model can be obtained by software for fitting structural equation models. For pure AR and mixed ARMA models, these estimates are approximately unbiased, while the efficiency is as good as those of specialized recursive estimators. The reported standard errors are generally found to be valid. Depending on sample size, estimates for pure MA models are biased 5–10% and considerably less efficient. Some assets of the method are that ARMA model parameters can be estimated when only autocovariances are known, that model constraints can be incorporated, and that the fit between observed and modelled covariances can be tested by statistical methods. The method is applied to problems that involve the evaluation of pregnancy as a function of perceived bodily changes, the effect of policy interventions in crime prevention, and the influence of weather conditions on absence from work.

Keywords

lagged variablesBox-Jenkins modelcovariance structuresPROC CALISintervention analysisautocorrelation
Type
Original Paper
Information
Psychometrika , Volume 62 , Issue 2 , June 1997 , pp. 215 - 236
Copyright
Copyright © 1997 The Psychometric Society

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Footnotes

This work is dedicated to the memory of my father, Gerrit van Buuren. I thank Erik Meijer for his comments on an earlier version of this paper, and Peter Smulders who contributed data and background knowledge in the weather example. I am grateful to the editor, the associate editor and several anonymous reviewers for their insightful suggestions and thorough review of the manuscript.

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