The Durbin-Watson clue in a spurious regression

Question

You regress two independent random walks in levels. The residuals from this regression are themselves nearly a random walk, so their consecutive values are almost perfectly positively correlated.

Roughly what value does the Durbin-Watson statistic approach, and what does that tell you?

Accepted Answer

The Durbin-Watson statistic is related to the lag-1 residual autocorrelation r1 by the approximation DW \approx 2\,(1 - r1). In a spurious regression the residuals inherit the nonstationarity of the random walks, so consecutive residuals are almost identical, giving r1 \approx 1. Plugging in: DW \approx 2\,(1 - 1) = 0. So the Durbin-Watson statistic drifts toward 0. A DW near 0 signals extreme positive autocorrelation in the residuals, which violates the regression assumptions and is a classic warning that the fit is spurious. The practical rule of thumb: if R^2 is larger than the Durbin-Wats…

The Durbin-Watson clue in a spurious regression

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