Skip to main content


  • David Preinerstorfer (a1) and Benedikt M. Pötscher (a1)

The behavior of the power function of autocorrelation tests such as the Durbin–Watson test in time series regressions or the Cliff-Ord test in spatial regression models has been intensively studied in the literature. When the correlation becomes strong, Krämer (1985, Journal of Econometrics 28, 363–370.) (for the Durbin–Watson test) and Krämer (2005, Journal of Statistical Planning and Inference, 128, 489–496) (for the Cliff-Ord test) have shown that power can be very low, in fact can converge to zero, under certain circumstances. Motivated by these results, Martellosio (2010, Econometric Theory, 26, 152–186) set out to build a general theory that would explain these findings. Unfortunately, Martellosio (2010) does not achieve this goal, as a substantial portion of his results and proofs suffer from nontrivial flaws. The present paper now builds a theory as envisioned in Martellosio (2010) in an even more general framework, covering general invariant tests of a hypothesis on the disturbance covariance matrix in a linear regression model. The general results are then specialized to testing for spatial correlation and to autocorrelation testing in time series regression models. We also characterize the situation where the null and the alternative hypothesis are indistinguishable by invariant tests.

Corresponding author
*Address correspondence to David Preinerstorfer, Department of Statistics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090 Vienna, Austria. e-mail:
Hide All
Anselin, L. (2001) Spatial econometrics. In A companion to theoretical econometrics. Blackwell Companions Contemporary Economics, 310330.
Arnold, S.F. (1979) Linear models with exchangeably distributed errors. Journal of the American Statistical Association, 74, 194199.
Bartels, R. (1992) On the power function of the Durbin-Watson test. Journal of Econometrics, 51, 101112.
Bauer, H. (2001) Measure and integration theory, de Gruyter Studies in Mathematics, vol. 26. Walter de Gruyter.
Cambanis, S., Huang, S., & Simons, G. (1981) On the theory of elliptically contoured distributions. Journal of Multivariate Analysis, 11, 368385.
Gantmacher, F.R. (1959) The theory of matrices, vol. 2. AMS Chelsea Publishing.
Horn, R.A. & Johnson, C.R. (1985) Matrix analysis. Cambridge University Press.
Kadiyala, K.R. (1970) Testing for the independence of regression disturbances. Econometrica, 38, 97117.
Kariya, T. (1980) Note on a condition for equality of sample variances in a linear model. Journal of the American Statistical Association, 75, 701703.
King, M.L. (1985) A point optimal test for autoregressive disturbances. Journal of Econometrics, 27, 2137.
King, M.L. (1987) Testing for autocorrelation in linear regression models: A survey. In Specification analysis in the linear model. International Library of Economics, Routledge & Kegan Paul, 1973.
King, M.L. & Hillier, G.H. (1985) Locally best invariant tests of the error covariance matrix of the linear regression model. Journal of the Royal Statistical Society. Series B (Methodological), 47, 98102.
Kleiber, C. & Krämer, W. (2005) Finite-sample power of the Durbin-Watson test against fractionally integrated disturbances. Econometrics Journal, 8, 406417.
Krämer, W. (1985) The power of the Durbin-Watson test for regressions without an intercept. Journal of Econometrics, 28, 363370.
Krämer, W. (2005) Finite sample power of Cliff-Ord-type tests for spatial disturbance correlation in linear regression. Journal of Statistical Planning and Inference, 128, 489496.
Krämer, W. & Zeisel, H. (1990) Finite sample power of linear regression autocorrelation tests. Journal of Econometrics, 43, 363372.
Lehmann, E.L. & Romano, J.P. (2005) Testing statistical hypotheses, 3rd ed. Springer Texts in Statistics.
Löbus, J.U. & Ritter, L. (2000) The limiting power of the Durbin-Watson test. Communications in Statistics-Theory and Methods, 29, 26652676.
Martellosio, F. (2010) Power properties of invariant tests for spatial autocorrelation in linear regression. Econometric Theory, 26, 152186.
Martellosio, F. (2011a) Efficiency of the OLS estimator in the vicinity of a spatial unit root. Statistics & Probability Letters, 81, 12851291.
Martellosio, F. (2011b) Nontestability of equal weights spatial dependence. Econometric Theory, 27, 13691375.
Martellosio, F. (2012) Testing for spatial autocorrelation: The regressors that make the power disappear. Econometric Reviews, 31, 215240.
Mynbaev, K. (2012) Distributions escaping to infinity and the limiting power of the Cliff-Ord test for autocorrelation. ISRN Probability and Statistics.
Preinerstorfer, D. (2014) How to avoid the zero-power trap in testing for correlation. Working paper, in preparation.
Preinerstorfer, D. & Pötscher, B.M. (2013) On size and power of heteroskedasticity and autocorrelation robust tests. Econometric Theory, forthcoming.
Small, J.P. (1993) The limiting power of point optimal autocorrelation tests. Communications in Statistics–Theory and Methods, 22, 39073916.
Stroock, D.W. (1999) A concise introduction to the theory of integration, 3rd ed. Birkhäuser Boston.
Tillman, J. (1975) The power of the Durbin-Watson test. Econometrica, 43, 959974.
Tyler, D.E. (1981) Asymptotic inference for eigenvectors. Annals of Statistics, 9, 725736.
Zeisel, H. (1989) On the power of the Durbin-Watson test under high autocorrelation. Communications in Statistics-Theory and Methods, 18, 39073916.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
  • URL: /core/journals/econometric-theory
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
Type Description Title
Supplementary materials

Preinerstorfer supplementary material
Preinerstorfer supplementary material 1

 PDF (145 KB)
145 KB


Full text views

Total number of HTML views: 2
Total number of PDF views: 168 *
Loading metrics...

Abstract views

Total abstract views: 693 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 24th March 2018. This data will be updated every 24 hours.