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Exact geometry of autoregressive models

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  • van GARDEREN, Kees Jan

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.
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  • van GARDEREN, Kees Jan, 1999. "Exact geometry of autoregressive models," LIDAM Reprints CORE 1385, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvrp:1385
    DOI: 10.1111/1467-9892.00122
    Note: In : Journal of Time Series Analysis, 20, 1-21, 1999
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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. 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.
    4. 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.

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