Durbin-Watson Test

Purpose

The Durbin-Watson test assesses whether or not there is autocorrelation among the residuals of time series data.

Definition

The Durbin-Watson test statistic, DW, is

$$DW=\frac{{\displaystyle \sum _{i=1}^{n-1}{\left(r_{i+1}-r_i\right)}^2}}{{\displaystyle \sum _{i=1}^n{r}_i^2}},$$

where r_i is the ith raw residual, and n is the number of observations.

How To

After obtaining a fitted model, say, mdl, using fitlm or stepwiselm, you can perform the Durbin-Watson test using

dwtest(mdl)

For details, see the dwtest method of the LinearModel class.

Test for Autocorrelation Among Residuals

This example shows how to test for autocorrelation among the residuals of a linear regression model.

Load the sample data and fit a linear regression model.

load hald
mdl = fitlm(ingredients,heat);

Perform a two-sided Durbin-Watson test to determine if there is any autocorrelation among the residuals of the linear model, mdl.

[p,DW] = dwtest(mdl,'exact','both')

p = 
0.8421

DW = 
2.0526

The value of the Durbin-Watson test statistic is 2.0526. The $$p$$-value of 0.8421 suggests that the residuals are not autocorrelated.