Premium
A LINEAR ESTIMATION PROCEDURE FOR THE PARAMETERS OF AUTOREGRESSIVE MOVING‐AVERAGE PROCESSES
Author(s) -
Chiu SheanTsong
Publication year - 1991
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.1467-9892.1991.tb00086.x
Subject(s) - mathematics , autoregressive model , least squares function approximation , gaussian , mathematical optimization , asymptotically optimal algorithm , autoregressive–moving average model , set (abstract data type) , generalized least squares , linear model , moving average , statistics , computer science , physics , quantum mechanics , estimator , programming language
. A linear estimation procedure for the parameters of autoregressive moving‐average processes is proposed. The basic idea is to write the spectrum for the moving‐average part as a linear function of a properly selected set of parameters and to use Chiu's weighted least‐squares procedure to reduce the problem to a weighted linear least‐squares problem. The proposed procedure finds estimates by solving systems of linear equations and does not need optimization programs. An one‐step estimate is also suggested. It is shown that the estimates are asymptotically equal to the commonly used ‘approximate’ maximum likelihood estimate described in the paper. For Gaussian processes, the estimates obtained by the proposed procedures are asymptotically efficient.