Durbin-Watson test

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The Durbin-Watson test is a statistical test with which one tries to check whether a first-order autocorrelation is present, i.e. That is, whether the correlation between two consecutive residuals in a regression analysis is non-zero. The test was developed by the British statistician James Durbin and the Australian Geoffrey Watson.



In the case of first-order autocorrelation, the interference terms are modeled as follows . In the Durbin-Watson test, a null hypothesis is set up that states that there is no autocorrelation ( ) and its counter-hypothesis that states that there is autocorrelation ( ).

Test statistics

The test statistic is:

Here each denotes the residuals of the regression in the -th period. If the difference between the residual quantities is very small or very large, then there is positive or negative autocorrelation. This means that the Durbin-Watson value tends towards zero or four.

Test decision

Test statistic value correlation meaning
no autocorrelation
perfect positive autocorrelation
perfect negative autocorrelation

The acceptance and rejection areas can be determined in a table. For there is positive autocorrelation, for negative autocorrelation, between and there is no autocorrelation. In the intervals and there are fuzzy areas in which no statements can be made.

Durbin h statistics

In autoregressive models , this test statistic is skewed towards the value two, so that the autocorrelation is underestimated. However, the Durbin h statistic, which is standard normal distributed and undistorted for large samples, can easily be derived from the above statistic :


where the estimated variance of the regression coefficient of the time-lagged endogenous variable is and must be.

Durbin-Watson test for panel data

For panel data , the above test statistic can be generalized as follows:

, with = residuals of the Within regression

These test statistics are then compared with the acceptance and rejection ranges tabulated as a function of T (length of the balanced panel data set ), K (number of regressors) and N (number of observed individuals) [see, for example, Bhargava et al. (1982), p. 537]. A variant of this statistic for unbalanced panel data was developed by Baltagi and Wu (1999).


  • Gujarati, Damodar N. (1995): Basic Econometrics, 3 ed., New York et al .: McGraw-Hill, 1995, pp. 605f.
  • Eckey, Hans-Friedrich / Kosfeld, Reinhold / Dreger, Christian (2004): Ökonometrie, 3rd, revised. and exp. Ed., Wiesbaden: Gabler, 2004, page 114ff.
  • Verbeek, Marno (2004): A Guide to Modern Econometrics, 2nd ed., Chichester: John Wiley & Sons, 2004, pp. 102f.
  • Bhargava, A./Franzini, L./Narendranathan, W. (1982): Serial Correlation and the Fixed Effects Models, in: Review of Economic Studies, Vol. 49 Iss. 158, 1982, pp. 533-549.

Individual evidence

  1. Compare to this paragraph: Eckey, Hans-Friedrich / Kosfeld, Reinhold / Dreger, Christian (2004): Ökonometrie, 3., revised. and exp. Ed., Wiesbaden: Gabler, 2004.
  2. d1 in Formula 16 in Baltagi / Wu (1999), Unequally spaced panel data regressions with AR (1) disturbances. Econometric Theory, 15 (6), pp. 814-823.

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