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Testing the Constancy of Regression Relationships Over Time Using Least Squares Residuals

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  • B. P. M. McCabe
  • M. J. Harrison

Abstract

A test of the stability over time of the coefficients of a linear regression model is developed using the cumulative sum (cusum) of squares of the ordinary least squares residuals. An example of the application of the test is given. The power of the test under two systems of coefficient variation is examined using Monte Carlo simulation and compared with the power of the original Brown–Durbin–Evans variant of the test based on recursive residuals.

Suggested Citation

  • B. P. M. McCabe & M. J. Harrison, 1980. "Testing the Constancy of Regression Relationships Over Time Using Least Squares Residuals," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(2), pages 142-148, June.
    • Handle: RePEc:bla:jorssc:v:29:y:1980:i:2:p:142-148
    DOI: 10.2307/2986299
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    Cited by:

    1. Olmo, Jose & Pilbeam, Keith & Pouliot, William, 2011. "Detecting the presence of insider trading via structural break tests," Journal of Banking & Finance, Elsevier, vol. 35(11), pages 2820-2828, November.
    2. Watson, G. S., 1995. "Detecting a change in the intercept in multiple regression," Statistics & Probability Letters, Elsevier, vol. 23(1), pages 69-72, April.
    3. repec:cty:dpaper:09/10 is not listed on IDEAS
    4. Deng, Ai & Perron, Pierre, 2008. "The Limit Distribution Of The Cusum Of Squares Test Under General Mixing Conditions," Econometric Theory, Cambridge University Press, vol. 24(3), pages 809-822, June.
    5. Anders Westlund, 1984. "Sequential moving sums of squares of OLS residuals in parameter stability testing," Quality & Quantity: International Journal of Methodology, Springer, vol. 18(3), pages 261-273, May.
    6. Nielsen, Bent & Sohkanen, Jouni S., 2011. "Asymptotic Behavior Of The Cusum Of Squares Test Under Stochastic And Deterministic Time Trends," Econometric Theory, Cambridge University Press, vol. 27(4), pages 913-927, August.
    7. Deng, Ai & Perron, Pierre, 2008. "A non-local perspective on the power properties of the CUSUM and CUSUM of squares tests for structural change," Journal of Econometrics, Elsevier, vol. 142(1), pages 212-240, January.
    8. Saima Siddiqui & Sameena Zehra & Sadia Majeed & Muhammad Sabihuddin Butt, 2008. "Export-Led Growth Hypothesis in Pakistan: A Reinvestigation Using the Bounds Test," Lahore Journal of Economics, Department of Economics, The Lahore School of Economics, vol. 13(2), pages 59-80, Jul-Dec.
    9. Perron, Pierre & Yabu, Tomoyoshi, 2009. "Estimating deterministic trends with an integrated or stationary noise component," Journal of Econometrics, Elsevier, vol. 151(1), pages 56-69, July.
    10. Banerjee, Anindya & Lumsdaine, Robin L & Stock, James H, 1992. "Recursive and Sequential Tests of the Unit-Root and Trend-Break Hypotheses: Theory and International Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 271-287, July.
    11. Lee, B.M.S. & Bui-Lan, Anh, 1982. "Use Of Errors Of Prediction In Improving Forecast Accuracy: An Application To Wool In Australia," Australian Journal of Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 26(1), pages 1-14, April.
    12. Rao, Yao & McCabe, Brendan, 2017. "Is MORE LESS? The role of data augmentation in testing for structural breaks," Economics Letters, Elsevier, vol. 155(C), pages 131-134.
    13. Olmo, J. & Pilbeam, K. & Pouliot, W., 2009. "Detecting the Presence of Informed Price Trading Via Structural Break Tests," Working Papers 10.1016/j.jbankfin.2011.0, Department of Economics, City University London.
    14. Yao Rao & Brendan McCabe, 2020. "Structural Change and the Problem of Phantom Break Locations," Manchester School, University of Manchester, vol. 88(1), pages 211-228, January.
    15. Nielsen, Bent & Sohkanen, Jouni S., 2011. "Asymptotic Behavior Of The Cusum Of Squares Test Under Stochastic And Deterministic Time Trends," Econometric Theory, Cambridge University Press, vol. 27(04), pages 913-927, August.

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