Estimating Moving Average Parameters: Classical Pileups and Bayesian Posteriors.

The authors analyze posterior distributions of the moving average parameter in the first-order case and sampling distributions of the corresponding maximum likelihood estimator. Sampling distributions 'pile up' at unity when the true parameter is near unity; hence, if one were to difference such a process, estimates of the moving average component of the resulting series would spuriously tend to indicate that the process was overdifferenced. Flat-prior posterior distributions do not pile up, however, regardless of the parameter's proximity to unity; hence, caution should be taken in dismissing evidence that a series has been overdifferenced.