dwtest

Durbin-Watson test with linear regression model object

Syntax

p = dwtest(mdl)

p = dwtest(mdl,method)

p = dwtest(mdl,method,tail)

[p,DW] = dwtest(___)

Description

p = dwtest(mdl) returns the p-value of the Durbin-Watson Test on the residuals of the linear regression model mdl. The null hypothesis is that the residuals are uncorrelated, and the alternative hypothesis is that the residuals are autocorrelated.

p = dwtest(mdl,method) specifies the algorithm for computing the p-value.

p = dwtest(mdl,method,tail) specifies the alternative hypothesis.

[p,DW] = dwtest(___) also returns the Durbin-Watson statistic using any of the input argument combinations in the previous syntaxes.

Examples

Test Residuals for Autocorrelation

Determine whether a fitted linear regression model has autocorrelated residuals.

Load the census data set and create a linear regression model.

load census
mdl = fitlm(cdate,pop);

Find the p-value of the Durbin-Watson autocorrelation test.

p = dwtest(mdl)

p = 
3.6190e-15

The small p-value indicates that the residuals are autocorrelated.

Input Arguments

mdl — Linear regression model

LinearModel object

Linear regression model, specified as a LinearModel object created using fitlm or stepwiselm.

method — Algorithm for computing p-value

'exact' | 'approximate'

Algorithm for computing the p-value, specified as one of these values:

• 'exact' — Calculate an exact p-value using Pan’s algorithm [2].

• 'approximate' — Calculate the p-value using a normal approximation [1].

The default is 'exact' when the sample size is less than 400, and 'approximate' otherwise.

tail — Type of alternative hypothesis

'both' (default) | 'right' | 'left'

Type of alternative hypothesis to test, specified as one of these values:

Value	Alternative Hypothesis
'both'	Serial correlation is not 0.
'right'	Serial correlation is greater than 0 (right-tailed test).
'left'	Serial correlation is less than 0 (left-tailed test).

dwtest tests whether mdl has no serial correlation, against the specified alternative hypothesis.

Output Arguments

p — p-value of test

numeric value

p-value of the test, returned as a numeric value. dwtest tests whether the residuals are uncorrelated, against the alternative that autocorrelation exists among the residuals. A small p-value indicates that the residuals are autocorrelated.

DW — Durbin-Watson statistic

nonnegative numeric value

Durbin-Watson statistic value, returned as a nonnegative numeric value.

More About

Durbin-Watson Test

The Durbin-Watson test tests the null hypothesis that linear regression residuals of time series data are uncorrelated, against the alternative hypothesis that autocorrelation exists.

The test statistic for the Durbin-Watson test 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.

The p-value of the Durbin-Watson test is the probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis. A significantly small p-value casts doubt on the validity of the null hypothesis and indicates autocorrelation among residuals.

References

[1] Durbin, J., and G. S. Watson. "Testing for Serial Correlation in Least Squares Regression I." Biometrika 37, pp. 409–428, 1950.

[2] Farebrother, R. W. Pan's "Procedure for the Tail Probabilities of the Durbin-Watson Statistic." Applied Statistics 29, pp. 224–227, 1980.

Extended Capabilities

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced in R2012a