FITTING ARMA TIME-SERIES BY STRUCTURAL EQUATION MODELS

This paper outlines how the stationary ARMA (p, q) model can be specif ied as a structural equations model. Maximum likelihood estimates for the parameters in the ARMA model can be obtained by software for fitti ng structural equation models. For pure AR and mixed ARMA models, thes e estimates are approximately unbiased, while the efficiency is as goo d as those of specialized recursive estimators. The reported standard errors are generally found to be valid. Depending on sample size, esti mates for pure MA models are biased 5-10% and considerably less effici ent. Some assets of the method are that ARMA model parameters can be e stimated when only autocovariances are known, that model constraints c an be incorporated, and that the fit between observed and modelled cov ariances can be tested by statistical methods. The method is applied t o problems that involve the evaluation of pregnancy as a function of p erceived bodily changes, the effect of policy interventions in crime p revention, and the influence of weather conditions on absence from wor k.