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A Linear Estimation Procedure For The Parameters Of Autoregressive Moving‐Average Processes

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  • Shean‐Tsong Chiu

Abstract

. 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.

Suggested Citation

  • Shean‐Tsong Chiu, 1991. "A Linear Estimation Procedure For The Parameters Of Autoregressive Moving‐Average Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 12(4), pages 315-327, July.
    • Handle: RePEc:bla:jtsera:v:12:y:1991:i:4:p:315-327
    DOI: 10.1111/j.1467-9892.1991.tb00086.x
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