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A Small-Sample Correction for Testing for gth-Order Serial Correlation with Artificial Regressions

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  • David A. Belsley

    (Boston College)

Abstract

Monte Carlo experiments establish that the usual "t-statistic" used for testing for first-order serial correlation with artificial regressions is far from being distributed as a Student's t in small samples. Rather, it is badly biased in both mean and variance and results in grossly misleading tests of hypotheses when treated as a Student's t. Simply computed corrections for the mean and variance are derived, however, which are shown to lead to a transformed statistic producing acceptable tests. The test procedure is detailed and exemplar code provided.

Suggested Citation

  • David A. Belsley, 1996. "A Small-Sample Correction for Testing for gth-Order Serial Correlation with Artificial Regressions," Boston College Working Papers in Economics 331., Boston College Department of Economics.
    • Handle: RePEc:boc:bocoec:331
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    File URL: http://fmwww.bc.edu/EC-P/wp331.pdf
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    References listed on IDEAS

    as
    1. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    2. MacKinnon, James G, 1992. "Model Specification Tests and Artificial Regressions," Journal of Economic Literature, American Economic Association, vol. 30(1), pages 102-146, March.
    3. Breusch, T S, 1978. "Testing for Autocorrelation in Dynamic Linear Models," Australian Economic Papers, Wiley Blackwell, vol. 17(31), pages 334-355, December.
    4. Godfrey, Leslie G, 1978. "Testing for Higher Order Serial Correlation in Regression Equations When the Regressors Include Lagged Dependent Variables," Econometrica, Econometric Society, vol. 46(6), pages 1303-1310, November.
    5. Durbin, J, 1970. "Testing for Serial Correlation in Least-Squares Regression When Some of the Regressors are Lagged Dependent Variables," Econometrica, Econometric Society, vol. 38(3), pages 410-421, May.
    6. Godfrey, Leslie G, 1978. "Testing against General Autoregressive and Moving Average Error Models When the Regressors Include Lagged Dependent Variables," Econometrica, Econometric Society, vol. 46(6), pages 1293-1301, November.
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    Citations

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    Cited by:

    1. Godfrey, L.G. & Tremayne, A.R., 2005. "The wild bootstrap and heteroskedasticity-robust tests for serial correlation in dynamic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 377-395, April.
    2. Mohd. FAYAZ & Kaur Bhatia SANDEEP, 2016. "Trends , Patterns and Determinants of Indian Current Account Deficit," Applied Econometrics and International Development, Euro-American Association of Economic Development, vol. 16(1).
    3. Belsley, David A., 2002. "An investigation of an unbiased correction for heteroskedasticity and the effects of misspecifying the skedastic function," Journal of Economic Dynamics and Control, Elsevier, vol. 26(9-10), pages 1379-1396, August.

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    More about this item

    Keywords

    Serial correlation; hypothesis testing; size correction;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other
    • C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Other

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