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Bartlett correction in the stable second‐order autoregressive model with intercept and trend

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  • Noud P.A. van Giersbergen

Abstract

This paper derives the Bartlett factors that can be used to obtain higher‐order improvements for testing hypotheses about the autoregressive (AR) parameters in the stable AR(2) model with possible intercept and linear trend. The factors are obtained for testing hypotheses about individual parameters (φ1 and φ2) as well as their sum. Moreover, the effect of deterministic terms on the correction factors is found explicitly. All corrections are non‐decreasing in the AR parameters. Furthermore, the Bartlett corrections for φ1 and φ2 tend to infinity as φ2 approaches 1, whereas the correction for φ1 + φ2 tends to infinity as φ1 + φ2 is close to 1. The effectiveness of these Bartlett corrections in finite samples is evaluated by simulations.

Suggested Citation

  • Noud P.A. van Giersbergen, 2013. "Bartlett correction in the stable second‐order autoregressive model with intercept and trend," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(4), pages 482-498, November.
    • Handle: RePEc:bla:stanee:v:67:y:2013:i:4:p:482-498
    DOI: 10.1111/stan.12018
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    References listed on IDEAS

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    1. Willa W. Chen & Rohit S. Deo, 2012. "The restricted likelihood ratio test for autoregressive processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(2), pages 325-339, March.
    2. Andrews, Donald W K & Chen, Hong-Yuan, 1994. "Approximately Median-Unbiased Estimation of Autoregressive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 187-204, April.
    3. Taniguchi, Masanobu, 1988. "Asymptotic expansions of the distributions of some test statistics for Gaussian ARMA processes," Journal of Multivariate Analysis, Elsevier, vol. 27(2), pages 494-511, November.
    4. Rolf Larsson, 1998. "Bartlett Corrections for Unit Root Test Statistics," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(4), pages 425-438, July.
    5. Bent Nielsen, 2004. "On the Distribution of Likelihood Ratio Test Statistics for Cointegration Rank," Econometric Reviews, Taylor & Francis Journals, vol. 23(1), pages 1-23.
    6. Bravo, Francesco, 1999. "A Correction Factor For Unit Root Test Statistics," Econometric Theory, Cambridge University Press, vol. 15(2), pages 218-227, April.
    7. Jensen, J. L. & Wood, Andrew T. A., 1997. "On the non-existence of a Bartlett correction for unit root tests," Statistics & Probability Letters, Elsevier, vol. 35(2), pages 181-187, September.
    8. Chen, Willa W. & Deo, Rohit S., 2009. "Bias Reduction And Likelihood-Based Almost Exactly Sized Hypothesis Testing In Predictive Regressions Using The Restricted Likelihood," Econometric Theory, Cambridge University Press, vol. 25(5), pages 1143-1179, October.
    9. van Giersbergen, Noud P.A., 2009. "Bartlett Correction In The Stable Ar(1) Model With Intercept And Trend," Econometric Theory, Cambridge University Press, vol. 25(3), pages 857-872, June.
    10. Nabeya, Seiji & Perron, Pierre, 1994. "Local asymptotic distribution related to the AR(1) model with dependent errors," Journal of Econometrics, Elsevier, vol. 62(2), pages 229-264, June.
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