Durbin-Watson Test

Definition

Test used to detect the presence of autocorrelation at lag $1$ in the residual

Assume $e_i$ is the residual structure of $e_t=\rho e_{t-1}+{\nu }_t$ $DW=\frac{{\sum }_{t=2}^T(e_t-e_{t-1}{)}^2}{{\sum }_{t=1}^T{e}_t^2}\simeq 2(1-\hat{\rho })$ where $T$ is the number of observations and $\hat{\rho }=\frac{\sum _{t=2}^T{e}_t{e}_{t-1}}{\sum _{t=2}^T{e}_{t-1}^2}$

$DW=2$ indicates no autocorrelation