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Exact Geometry of Autoregressive Models

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  • Kees Jan van Garderen

Abstract

Exact expressions for the statistical curvature and related geometric quantities in first‐order autoregressive models are derived. We present a method for calculating moments that is applicable in general autoregressive models. It 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 minimal sufficient statistic is also derived.

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  • Kees Jan van Garderen, 1999. "Exact Geometry of Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(1), pages 1-21, January.
    • Handle: RePEc:bla:jtsera:v:20:y:1999:i:1:p:1-21
    DOI: 10.1111/1467-9892.00122
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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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