Durbin-Watson test — what does it test?

hard

Answer

$\mathrm{DW}\; = \;{\Sigma}(e_{t}\; - \;e_{t - 1})^{2}\; / \;{\Sigma}e_{t}^{2}$
$Range ~ [0, 4].$
$DW \approx 2: no autocorr.$
$DW < 1.5: positive autocorr (common in time series).$
$DW > 2.5: negative autocorr.$
$Only detects lag-1 correlation — use Breusch-Godfrey for higher orders.$
$When positive: fix with Cochrane-Orcutt, Prais-Winsten, GLS with AR(1) errors, or explicit ARIMA modeling.$

Check yourself — multiple choice

Tests normality
Tests lag-1 autocorrelation in regression residuals; DW≈2 = no autocorr; < 1.5 = positive; > 2.5 = negative → fix via Cochrane-Orcutt or GLS(AR1)
Same as heteroscedasticity
Not real

Durbin-Watson: lag-1 autocorr in residuals; DW ≈ 2 is clean.

#regression#assumptions

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