dwtest - Durbin-Watson test

Syntax

[P,DW] = dwtest(R,X) [...] = dwtest(R,X,method) [...] = dwtest(R,X,method,tail)

Description

[P,DW] = dwtest(R,X) performs a Durbin-Watson test on the vector R of residuals from a linear regression, where X is the design matrix from that linear regression. P is the computed p-value for the test, and DW is the Durbin-Watson statistic. The Durbin-Watson test is used to test if the residuals are uncorrelated, against the alternative that there is autocorrelation among them.

[...] = dwtest(R,X,method) specifies the method to be used in computing the p-value. method can be either of the following:

'exact' — Calculates an exact p-value using the PAN algorithm (the default if the sample size is less than 400).
'approximate' — Calculates the p-value using a normal approximation (the default if the sample size is 400 or larger).

[...] = dwtest(R,X,method,tail) performs the test against one of the following alternative hypotheses, specified by tail:

Tail	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).

Examples

Fit a straight line to the census data and note the autocorrelation in the residuals:

load census
n = length(cdate);
X = [ones(n,1),cdate];
[b,bint,r1] = regress(pop,X);
p1 = dwtest(r1,X)
plot(cdate,r1,'b-',cdate,zeros(n,1),'k:')

Adding a squared term reduces the autocorrelation but it is still significantly different from zero:

X = [ones(n,1),cdate,cdate.^2];
[b,bint,r2] = regress(pop,X);
p2 = dwtest(r2,X)
line(cdate,r2,'color','r')

dwtest - Durbin-Watson test

Syntax

Description

Examples

See Also

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