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ESTIMATION OF THE MOVING‐AVERAGE REPRESENTATION OF A STATIONARY PROCESS BY AUTOREGRESSIVE MODEL FITTING
Author(s) -
Bhansali R. J.
Publication year - 1989
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1989.tb00025.x
Subject(s) - autoregressive model , mathematics , estimator , star model , moving average model , setar , series (stratigraphy) , autoregressive–moving average model , autoregressive integrated moving average , stationary process , moving average , representation (politics) , parametric model , statistics , nonlinear autoregressive exogenous model , parametric statistics , time series , paleontology , politics , political science , law , biology
. 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.