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THE FINITE-SAMPLE DENSITY OF THE SUFFICIENT STATISTIC AND RELATED TESTS IN A GAUSSIAN AUTOREGRESSION

Karim M. Abadir

Econometric Theory2026https://doi.org/10.1017/s0266466625100297article
AJG 4ABDC A*
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0.50

Abstract

A first-order Gaussian autoregressive model is considered. The exact finite-sample joint density of the minimal sufficient statistic is derived, for any value of the autoregressive parameter. This allows us to derive explicitly the exact density of the autocorrelation coefficient and its Studentized t-ratio, whose densities were available only in the asymptotic case and not for all values of the parameter and the statistic. This article also demonstrates how to solve a general problem in statistical distribution theory (well beyond the specific case of autoregressive models), that of inverting confluent characteristic functions in multiple variables.

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https://doi.org/https://doi.org/10.1017/s0266466625100297

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@article{karim2026,
  title        = {{THE FINITE-SAMPLE DENSITY OF THE SUFFICIENT STATISTIC AND RELATED TESTS IN A GAUSSIAN AUTOREGRESSION}},
  author       = {Karim M. Abadir},
  journal      = {Econometric Theory},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1017/s0266466625100297},
}

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F · citation impact0.50 × 0.4 = 0.20
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R · text relevance †0.50 × 0.4 = 0.20

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