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Differential Geometry Of Arma Models

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  • Nalini Ravishanker
  • Edward L. Melnick
  • Chih‐Ling Tsai

Abstract

. A general approach for the development of a statistical inference on autoregressive moving‐average (ARMA) models is presented based on geometric arguments. ARMA models are characterized as members of the curved exponential family. Geometric properties of ARMA models are computed and used to suggest parameter transformations that satisfy predetermined properties. In particular, the effect on the asymptotic bias of the maximum likelihood estimator of model parameters is illustrated. Hypothesis testing of parameters is discussed through the application of a modified form of the likelihood ratio test statistic.

Suggested Citation

  • Nalini Ravishanker & Edward L. Melnick & Chih‐Ling Tsai, 1990. "Differential Geometry Of Arma Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 11(3), pages 259-274, May.
    • Handle: RePEc:bla:jtsera:v:11:y:1990:i:3:p:259-274
    DOI: 10.1111/j.1467-9892.1990.tb00057.x
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    Cited by:

    1. Bernardo M. Lagos & Pedro A. Morettin, 2004. "Improvement of the Likelihood Ratio Test Statistic in ARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(1), pages 83-101, January.
    2. Canepa Alessandra, 2022. "Small Sample Adjustment for Hypotheses Testing on Cointegrating Vectors," Journal of Time Series Econometrics, De Gruyter, vol. 14(1), pages 51-85, January.
    3. Patrick Marsh, "undated". "Saddlepoint Approximations in Non-Stationary Time Series," Discussion Papers 00/57, Department of Economics, University of York.
    4. Patrick Marsh, "undated". "Some Geometry for the Maximal Invariant in Linear Regression," Discussion Papers 04/07, Department of Economics, University of York.

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