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Higher order expansions for error variance matrix estimates in the Gaussian AR(1) linear regression model

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  • Karavias, Yiannis
  • Symeonides, Spyridon D.
  • Tzavalis, Elias

Abstract

We derive a stochastic expansion of the error variance–covariance matrix estimator for the linear regression model under Gaussian AR(1) errors. The higher order accuracy terms of the refined formula are not directly derived from formal Edgeworth-type expansions but instead, the paper adopts Magadalinos’ (1992) stochastic order of ω which is a convenient device to obtain the equivalent relation between the stochastic expansion and the asymptotic approximation of corresponding distribution functions. A Monte Carlo experiment compares tests based on the new estimator with others in the literature and shows that the new tests perform well.

Suggested Citation

  • Karavias, Yiannis & Symeonides, Spyridon D. & Tzavalis, Elias, 2018. "Higher order expansions for error variance matrix estimates in the Gaussian AR(1) linear regression model," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 54-59.
    • Handle: RePEc:eee:stapro:v:135:y:2018:i:c:p:54-59
    DOI: 10.1016/j.spl.2017.11.016
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    1. Velasco, Carlos & Robinson, Peter M., 2001. "Edgeworth Expansions For Spectral Density Estimates And Studentized Sample Mean," Econometric Theory, Cambridge University Press, vol. 17(3), pages 497-539, June.
    2. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(4), pages 631-653.
    3. P. C. B. Phillips, 1980. "Finite Sample Theory and the Distributions of Alternative Estimators of the Marginal Propensity to Consume," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(1), pages 183-224.
    4. Breusch, Trevor S., 1980. "Useful invariance results for generalized regression models," Journal of Econometrics, Elsevier, vol. 13(3), pages 327-340, August.
    5. Rothenberg, Thomas J, 1984. "Approximate Normality of Generalized Least Squares Estimates," Econometrica, Econometric Society, vol. 52(4), pages 811-825, July.
    6. Nicholas M. Kiefer & Timothy J. Vogelsang & Helle Bunzel, 2000. "Simple Robust Testing of Regression Hypotheses," Econometrica, Econometric Society, vol. 68(3), pages 695-714, May.
    7. Giraitis, Liudas & Phillips, Peter C.B., 2012. "Mean and autocovariance function estimation near the boundary of stationarity," Journal of Econometrics, Elsevier, vol. 169(2), pages 166-178.
    8. Beach, Charles M & MacKinnon, James G, 1978. "A Maximum Likelihood Procedure for Regression with Autocorrelated Errors," Econometrica, Econometric Society, vol. 46(1), pages 51-58, January.
    9. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    10. Gonçalves, Sílvia & Vogelsang, Timothy J., 2011. "Block Bootstrap Hac Robust Tests: The Sophistication Of The Naive Bootstrap," Econometric Theory, Cambridge University Press, vol. 27(4), pages 745-791, August.
    11. Magdalinos, Michael A. & Symeonides, Spyridon D., 1995. "Alternative size corrections for some GLS test statistics the case of the AR(1) model," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 35-59.
    12. Magdalinos, Michael A., 1992. "Stochastic Expansions and Asymptotic Approximations," Econometric Theory, Cambridge University Press, vol. 8(3), pages 343-367, September.
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