ESTIMATION OF THE MOVING‐AVERAGE REPRESENTATION OF A STATIONARY PROCESS BY AUTOREGRESSIVE MODEL FITTING

R. J. Bhansali

Journal of Time Series Analysis, 1989, vol. 10, issue 3, 215-232

Abstract: Abstract. The Hannan‐Rissanen procedure for recursive order determination of an autoregressive moving‐average process provides ‘non‐parametric’ estimators of the coefficients b(u), say, of the moving‐average representation of a stationary process by auto‐regressive model fitting, and also that of the cross‐covariances, c(u), between the process and its linear innovations. An alternative ‘autoregressive’ estimator of the b(u) is obtained by inverting the autoregressive transfer function. Some uses of these estimators are discussed, and their asymptotic distributions are derived by requiring that the order k of the fitted autoregression approaches infinity simultaneously with the length T of the observed time series. The question of bias in estimating the parameters is also examined.

Date: 1989
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