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Exact geometry of explosive 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 statistical curvature and related geometric quantities in the first order autoregressive models with stable and unit roots, as well as explosive roots larger than unity. We develop a method for deriving exact moments of arbitrary order in general autoregressive models. The covariance of the minimal sufficient statistic is an application of this method. Of particular interest is the Efron curvature which is continuous and bounded in finite samples, but increases rapidly when the autoregressive parameter changes from stable to explosive values, which has important inferential consequences. The initial value effect is also quantified exactly. We also include results for the Efron curvature in the pure stationary case with stochastic initial value for comparison, extending and correcting results from a previous discussion paper.

Suggested Citation

  • van GARDEREN, Kees Jan, 1997. "Exact geometry of explosive autoregressive models," LIDAM Discussion Papers CORE 1997068, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:1997068
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    Cited by:

    1. Forchini, G., 2000. "The density of the sufficient statistics for a Gaussian AR(1) model in terms of generalized functions," Statistics & Probability Letters, Elsevier, vol. 50(3), pages 237-243, 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.

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