FitAR (version 1.94)

LjungBoxTest: Ljung-Box Test for Randomness

Description

The Ljung-Box Portmanteau test for the goodness of fit of ARIMA models is implemented.

Usage

LjungBoxTest(res, k=0, lag.max=30, StartLag=1, SquaredQ=FALSE)

Arguments

res

residuals

k

number of ARMA parameters, default k = 0

lag.max

maximum lag, default MaxLag = 30

StartLag

test is done for lags m=StartLag:MaxLag, default StartLag = 1

SquaredQ

if TRUE, use squared residuals for ARCH test, default Squared = FALSE

Value

A matrix with columns labelled m, Qm, pvalue, where m is the lag and Qm is the Ljung-Box Portmanteau statistic and pvalue its p-value.

Details

This test is described in detail in Wei (2006, p.153, eqn. 7.5.1). The df are given by h-k, where h is the lag, running from StartLag to lag.max, when h-k < 1, it is reset to 1. This is ok, since the test is conservative in this case.

A powerful test for ARCH and other nonlinearities is obtained by using squared values of the series to be tested (McLeod & Li, 1983). Note that if Squared=TRUE is used the data "res" is centered by sample mean correction before squaring.

References

W.W.S. Wei (2006, 2nd Ed.), Time Series Analysis: Univariate and Multivariate Methods.

A.I. McLeod. & W.K. Li (1983), Diagnostic checking ARMA time series models using squared-residual autocorrelations, Journal of Time Series Analysis 4, 269--273.

See Also

Box.test

Examples

#test goodness-of-fit of AR(2) model fit to log(lynx)
data(lynx)
z<-log(lynx)
ans<-FitAR(z, 1:2)
#notice that the test is also available as a component of the output of FitAR 
ans$LjungBox
#a plot of the test is produced
plot(ans)
#doing the test manually
res<-resid(ans)
LjungBoxTest(res, k=2, lag.max=20, StartLag=5)

#test for subset case
z<-log(lynx)
pvec<-SelectModel(z, ARModel="ARz", Criterion="BIC", lag.max=10, Best=1)
ans<-FitAR(z, pvec)
plot(ans)
res<-resid(ans)
LjungBoxTest(res, k=length(pvec), lag.max=20, StartLag=11)
#test for ARCH effect,
LjungBoxTest(res,SquaredQ=TRUE)