# [R] Testing autocorrelation & heteroskedasticity of residuals in ts

Achim Zeileis Achim.Zeileis at wu-wien.ac.at
Wed Jul 21 11:32:58 CEST 2004

```On Wed, 21 Jul 2004 10:28:41 +0200 Pfaff, Bernhard wrote:

> >
> > Hi,
> >
> > I'm dealing with time series. I usually use stl() to
> > estimate trend, stagionality and residuals. I test for
> > normality of residuals using shapiro.test(), but I
> > can't test for autocorrelation and heteroskedasticity.
> > Is there a way to perform Durbin-Watson test and
> > Breusch-Pagan test (or other simalar tests) for time
> > series?
> > I find dwtest() and bptest() in the package lmtest,
>
> Hello Vito,
>
>
> library(lmtest)
> data(nottem)
> test <- summary(stl(nottem, s.win=4))
> bptest(formula(nottem ~ -1 + test\$time.series[,1] +
> test\$time.series[,2])) dwtest(formula(nottem ~ -1 +
> test\$time.series[,1] + test\$time.series[,2]))
>
> i.e. you define the residuals by providing the residuals as formula.
> Note:
> testres <- nottem-test\$time.series[,1]-test\$time.series[,2]
> cbind(testres, test\$time.series[,3])

Further note that testres are not the residuals that you supply to
dwtest() above because the coefficients are

R> coef(lm(formula(nottem ~ -1 + test\$time.series[,1] +
test\$time.series[,2])))
test\$time.series[, 1] test\$time.series[, 2]
0.9988047             1.0002117

but they are close to 1.

Anyway: for dwtest() I would probably just supply the residuals and
regress them on a constant.

R> dwtest(test\$time.series[,3] ~ 1)

which is very close to Bernhard's suggestion but a bit simpler.

For bptest() you could do something like

bptest(test\$time.series[,3] ~ 1 ,
varformula = ~ -1 + test\$time.series[,1] + test\$time.series[,2])

if that is the model you would like to test. At least it makes more
explicit what is tested.

> Anyway, are these tests applicable to stl as far as the underlying
> assumptions for the error term is concerned?

difficult to find a set of assumptions where a nonparametric estimate of
trend and season via STL yields a stationary, independent and
homoskedastic sequence of the residuals. (whether these apply to Vito's
data is of course a different question :))

Best,
Achim

> Bernhard
>
>
> > but it requieres an lm object, while I've a ts object.
> > Any help will be appreciated.
> > Best
> > Vito
> >
> > =====
> > Diventare costruttori di soluzioni
> >
> > Visitate il portale http://www.modugno.it/
> > e in particolare la sezione su Palese
> http://www.modugno.it/archivio/cat_palese.shtml
>
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