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Rank based tests for testing the constancy of the regression coefficients against random walk alternatives

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  • Manohar B. Rajarshi
  • Thekke V. Ramanathan
  • Chanchala A. Ghadge

Abstract

A class of approximately locally most powerful type tests based on ranks of residuals is suggest- ed for testing the hypothesis that the regression coefficient is constant in a standard regression model against the alternatives that a random walk process generates the successive regression coefficients. We derive the asymptotic null distribution of such a rank test. This distribution can be described as a generalization of the asymptotic distribution of the Cramer-von Mises test statistic. However, this distribution is quite complex and involves eigen values and eigen functions of a known positive definite kernel, as well as the unknown density function of the error term. It is then natural to apply bootstrap procedures. Extending a result due to Shorack in [25], we have shown that the weighted empirical process of residuals can be bootstrapped, which solves the problem of finding the null dis- tribution of a rank test statistic. A simulation study is reported in order to judge performance of the suggested test statistic and the bootstrap procedure.

Suggested Citation

  • Manohar B. Rajarshi & Thekke V. Ramanathan & Chanchala A. Ghadge, 2011. "Rank based tests for testing the constancy of the regression coefficients against random walk alternatives," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 21(3-4), pages 35-55.
    • Handle: RePEc:wut:journl:v:3-4:y:2011:p:35-55:id:1015
    DOI: 10.5277/ord1203-0403
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    References listed on IDEAS

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    1. Jandhyala, V.K. & MacNeill, I.B., 1992. "On Testing for the Constancy of Regression Coefficients under Random Walk and Change-Point Alternatives," Econometric Theory, Cambridge University Press, vol. 8(4), pages 501-517, December.
    2. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 38(2), pages 112-134.
    3. T. Ramanathan & M. Rajarshi, 1992. "Rank tests for testing randomness of a regression coefficient in a linear regression model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 39(1), pages 113-124, December.
    4. Thomas S. Shively, 1988. "An Exact Test For A Stochastic Coefficient In A Time Series Regression Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 9(1), pages 81-88, January.
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