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Asymptotic Inference For Non‐Invertible Moving‐Average Time Series

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  • Ngai Hang Chan
  • Ruey S. Tsay

Abstract

. This paper is concerned with statistical inference of nonstationary and non‐invertible autoregressive moving‐average (ARMA) processes. It makes use of the fact that a derived process of an ARMA(p, q) model follows an AR(q) model with an autoregressive (AR) operator equivalent to the moving‐average (MA) part of the original ARMA model. Asymptotic distributions of least squares estimates of MA parameters based on a constructed derived process are obtained as corresponding analogs of a nonstationary AR process. Extensions to the nearly non‐invertible models are considered and the limiting distributions are obtained as functionals of stochastic integrals of Brownian motions and Ornstein‐Uhlenbeck processes. For application, a two‐stage procedure is proposed for testing unit roots in the MA polynomial. Examples are given to illustrate the application.

Suggested Citation

  • Ngai Hang Chan & Ruey S. Tsay, 1996. "Asymptotic Inference For Non‐Invertible Moving‐Average Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(1), pages 1-17, January.
    • Handle: RePEc:bla:jtsera:v:17:y:1996:i:1:p:1-17
    DOI: 10.1111/j.1467-9892.1996.tb00261.x
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    Cited by:

    1. Yang, Yaxing & Ling, Shiqing & Wang, Qiying, 2022. "Consistency of global LSE for MA(1) models," Statistics & Probability Letters, Elsevier, vol. 182(C).

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