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The Student's t Approximation in a Stationary First Order Autoregressive Model


  • Nankervis, J C
  • Savin, N E


The exact distribution of the regression t statistic for testing the value of the AR parameter in a Gaussian first ord er autoregressive model is investigated by Monte Carlo methods. The S tudent's t distribution is not a satisfactory approximation for sampl es typical in economic applications. The main problem is the location of the distribution of the t statistic rather than the shape. Once t he t statistic is adjusted so that it has the same mean and standard deviation as Student's t, the distribution of the adjusted t statisti c is accurately approximated by Student's t. Techniques are presented for mak-ing these adjustments in practice. Copyright 1988 by The Econometric Society.

Suggested Citation

  • Nankervis, J C & Savin, N E, 1988. "The Student's t Approximation in a Stationary First Order Autoregressive Model," Econometrica, Econometric Society, vol. 56(1), pages 119-145, January.
  • Handle: RePEc:ecm:emetrp:v:56:y:1988:i:1:p:119-45

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    Cited by:

    1. Davidson, Russell & MacKinnon, James G., 1992. "Regression-based methods for using control variates in Monte Carlo experiments," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 203-222.
    2. Neil Kellard & Denise Osborn & Jerry Coakley & Nathan E. (Gene) Savin, 2015. "Papers with John," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(5), pages 663-671, September.
    3. Atsushi Inoue & Lutz Kilian, 2019. "The uniform validity of impulse response inference in autoregressions," Vanderbilt University Department of Economics Working Papers 19-00001, Vanderbilt University Department of Economics.
    4. van Giersbergen, Noud P. A. & Kiviet, Jan F., 2002. "How to implement the bootstrap in static or stable dynamic regression models: test statistic versus confidence region approach," Journal of Econometrics, Elsevier, vol. 108(1), pages 133-156, May.
    5. Brunner, Allan D. & Hess, Gregory D., 1995. "Potential problems in estimating bilinear time-series models," Journal of Economic Dynamics and Control, Elsevier, vol. 19(4), pages 663-681, May.

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