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Exact Geometry of Autoregressive Models

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  • van GARDEREN , Kees Jan

    (Center for Operations Research and Econometrics (CORE), Université catholique de Louvain (UCL), Louvain la Neuve, Belgium)

Abstract

This paper derives exact expressions for the statistical curvature and related geometric quantities in the first order autoregressive models. We present a method that combines the algebra of differential and difference operators to simplify the problem, and to obtain results valid for all sample sizes. The exact covariance matrix for the sufficient statistic is also derived.

Suggested Citation

  • van GARDEREN , Kees Jan, 1996. "Exact Geometry of Autoregressive Models," LIDAM Discussion Papers CORE 1996048, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:1996048
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp1996.html
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    Cited by:

    1. J. Roderick McCrorie, 2021. "Moments in Pearson's Four-Step Uniform Random Walk Problem and Other Applications of Very Well-Poised Generalized Hypergeometric Series," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 244-281, November.
    2. van Garderen, Kees Jan & Peter Boswijk, H., 2014. "Bias correcting adjustment coefficients in a cointegrated VAR with known cointegrating vectors," Economics Letters, Elsevier, vol. 122(2), pages 224-228.
    3. 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.
    4. 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.

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