# LjungBoxTest: Ljung-Box Test for Randomness In FitAR: Subset AR Model Fitting

## Description

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

## Usage

 `1` ```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

## 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.

## 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.

## Note

This test may also be used to test a time series for randomness taking k = 0.

A.I. McLeod

## 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.

`Box.test`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```#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) ```