The Durbin–Watson test is arguably, next to the method of least squares, the most widely applied procedure in all of statistics; it is routinely provided by most software packages and almost automatically applied in the analysis of economic time series when a researcher is fitting a linear regression model (see Linear Regression Models)
where y (T ×1) and X (T ×K, nonstochastic, rank K) denote the vector of observations of the dependent and the matrix of observations of K independent (regressor-) variables, respectively, β is a K ×1 vector of unknown regression coefficients to be estimated, and u (T ×1) is an unobservable vector of stochastic errors (disturbances, latent variables) with mean zero and equal variances. In the case of uncorrelated disturbances it is known from the Gauss-Markov-Theorem that the ordinary least squares estimator \(\hat{\beta }\) for β, where \(\hat{\beta } = {(X^{\prime}X)}^{-1}X^{\prime}y\) is best linear unbiased (BLUE) for β. In a...
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References and Further Reading
Anderson TW (1948) On the theory of testing serial correlation. Skand Aktuarietidskr 31:88–116
Breusch TS (1978) Testing for autocorrelation in dynamic linear models. Aust Econ Pap 17:334–355
Durbin J, Watson GS (1950) Testing for serial correlation in least sqares regression I. Biometrika 37:409–428
Durbin J, Watson GS (1951) Testing for serial correlation in least sqares regression II. Biometrika 38:159–178
Durbin J, Watson GS (1971) Testing for serial correlation in least sqares regression III. Biometrika 58:1–19
Godfrey LG (1978) Testing against general autoregressive and moving average error models when the regressors include lagged dependent variables. Econometrica 46:1303–1310
Imhof JP (1961) Computing the distribution of quadratic forms in normal variables. Biometrika 48:419–426
Krämer W (1985) The power of the Durbin-Watson test for regression without an intercept. J Econom 28:363–370
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Krämer, W. (2011). Durbin–Watson Test. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_219
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