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Robustness of the CUSUM and CUSUM-of-Squares Tests to Serial Correlation, Endogeneity and Lack of Structural Invariance. Some Monte Carlo Evidence

Author

Listed:
  • Caporale, Guglielmo Maria

    (London South Bank University)

  • Pittis, Nikitas

    (University of Piraeus)

Abstract

This paper investigates by means of Monte Carlo techniques the robustness of the CUSUM and CUSUM-of-squares tests (Brown et al., 1975) to serial correlation, endogeneity and lack of structural invariance. Our findings suggest that these tests perform better in the context of a dynamic model of the ADL type, which is not affected by serial correlation or nonpredetermined regressors even if over-specified. In this case, the empirical sizes of both tests are close to the nominal ones, whether a stationary or a cointegration environment is considered. The CUSUM-of-squares test is to be preferred, as it is very powerful to detect changes in the conditional model parameters, whether or not the variance of the regression error is included in the set of parameters shifting, especially towards the end of the sample.

Suggested Citation

  • Caporale, Guglielmo Maria & Pittis, Nikitas, 2004. "Robustness of the CUSUM and CUSUM-of-Squares Tests to Serial Correlation, Endogeneity and Lack of Structural Invariance. Some Monte Carlo Evidence," Economics Series 157, Institute for Advanced Studies.
  • Handle: RePEc:ihs:ihsesp:157
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    File URL: http://www.ihs.ac.at/publications/eco/es-157.pdf
    File Function: First version, 2004
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    References listed on IDEAS

    as
    1. Ploberger, Werner & Krämer;, Walter, 1990. "The Local Power of the CUSUM and CUSUM of Squares Tests," Econometric Theory, Cambridge University Press, vol. 6(03), pages 335-347, September.
    2. Peter C. B. Phillips & Bruce E. Hansen, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Oxford University Press, vol. 57(1), pages 99-125.
    3. Park, Joon Y. & Phillips, Peter C.B., 1989. "Statistical Inference in Regressions with Integrated Processes: Part 2," Econometric Theory, Cambridge University Press, vol. 5(01), pages 95-131, April.
    4. King, Maxwell L., 1985. "A point optimal test for autoregressive disturbances," Journal of Econometrics, Elsevier, vol. 27(1), pages 21-37, January.
    5. Phillips, P C B, 1988. "Reflections on Econometric Methodology," The Economic Record, The Economic Society of Australia, vol. 64(187), pages 344-359, December.
    6. Hansen, Bruce E, 2002. "Tests for Parameter Instability in Regressions with I(1) Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 45-59, January.
    7. repec:cup:etheor:v:6:y:1990:i:3:p:335-47 is not listed on IDEAS
    8. Xiao, Zhijie & Phillips, Peter C. B., 2002. "A CUSUM test for cointegration using regression residuals," Journal of Econometrics, Elsevier, vol. 108(1), pages 43-61, May.
    9. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    10. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    11. Kramer, Walter & Ploberger, Werner & Alt, Raimund, 1988. "Testing for Structural Change in Dynamic Models," Econometrica, Econometric Society, vol. 56(6), pages 1355-1369, November.
    12. Ploberger, Werner & Kramer, Walter, 1992. "The CUSUM Test with OLS Residuals," Econometrica, Econometric Society, vol. 60(2), pages 271-285, March.
    13. Martin MORYSON, 1994. "Testing for Random Walk Coefficients in a Simple State Space Model," SFB 373 Discussion Papers 1994,21, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    CUSUM and CUSUM-of-squares tests; Parameter instability; Structural invariance; Marginal and conditional processes; ADL model;

    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
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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