Transformations for an Exact Goodness-of-Fit Test of Structural Change in the Linear Regression Model

  • Maxwell L. King
  • Phillip M. Edwards
Conference paper
Part of the Studies in Empirical Economics book series (STUDEMP)


This paper considers testing for structural change of unknown form in the linear regression model as a problem of testing for goodness-of-fit. Transformations of recursive (or other LUS) residuals that reduce the problem to one of testing independently distributed uniform variables are presented. Exact empirical distribution function tests can then be applied without having to estimate unknown parameters. The tests are illustrated by their application to a money demand model.


Linear Regression Model American Statistical Association Empirical Distribution Function Classical Linear Regression Recursive Residual 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Brown RL, Durbin J, Evans JM (1975) Techniques for testing the constancy of regression relationships over time. Journal of the Royal Statistical Society B 37:149–163Google Scholar
  2. Csörgö M, Seshadri V, Yalovsky M (1973) Some exact tests for normality in the presence of unknown parameters. Journal of the Royal Statistical Society B 35:507–522Google Scholar
  3. Durbin J (1969) Tests for serial correlation in regression analysis based on the periodogram of least squares residuals. Biometrika 56:1–15CrossRefGoogle Scholar
  4. Farebrother RW (1976a) Algorithm AS104: BLUS residuals. Applied Statistics 25:317–322CrossRefGoogle Scholar
  5. Farebrother RW (1976b) Recursive residuals — a remark on Algorithm AS75: Basic procedures for large, sparse or weighted linear least squares problems. Applied Statistics 25:323–324CrossRefGoogle Scholar
  6. Goldman J (1976) Detection in the presence of spherically symmetric random vectors. IEEE Transactions on Information Theory IT-22:52–59CrossRefGoogle Scholar
  7. King ML (1980) Robust tests for spherical symmetry and their application to least squares regression. The Annals of Statistics 8:1265–1271CrossRefGoogle Scholar
  8. King ML (1987) Testing for autocorrelation in linear regression models: a survey. In: King ML, Giles DEA (eds) Specification analysis in the linear model. Routledge and Kegan Paul, LondonGoogle Scholar
  9. Klein B (1977) The demand for quality-adjusted cash balances: Price uncertainty in the US demand for money function. Journal of Political Economy 85:691–715CrossRefGoogle Scholar
  10. Krämer W, Sonnberger H (1986) The linear regression model under test. Physica-Verlag, HeidelbergCrossRefGoogle Scholar
  11. Lucas RE (1976) Econometric policy evaluation: a critique. Carnegie-Rochester Conferences in Public Policy 1:19–46CrossRefGoogle Scholar
  12. Mardia KV (1980) Tests for univariate and multivariate normality. In: Krishnaiah PR (ed) Handbook of statistics 1: Analysis of variance. North-Holland, AmsterdamGoogle Scholar
  13. Pearson ES, Hartley HO (1972) Biometrika tables for statisticians 2. Cambridge University Press, CambridgeGoogle Scholar
  14. Phillips GDA, Harvey AC (1974) A simple test for serial correlation in regression analysis. Journal of the American Statistical Association 69:935–939CrossRefGoogle Scholar
  15. Stephens MA (1974) EDF statistics for goodness of fit and some comparisons. Journal of the American Statistical Association 69:730–737CrossRefGoogle Scholar
  16. Theil H (1965) The analysis of disturbances in regression analysis. Journal of the American Statistical Association 60:1067–1079CrossRefGoogle Scholar
  17. Theil H (1968) A simplification of the BLUS procedure for analyzing regression disturbances. Journal of the American Statistical Association 63:242–251CrossRefGoogle Scholar

Copyright information

© Physica-Verlag Heidelberg 1989

Authors and Affiliations

  • Maxwell L. King
    • 1
  • Phillip M. Edwards
    • 1
  1. 1.Monash UniversityClaytonAustralia

Personalised recommendations