Consider again the growth rate series of the US monthly producer price index of the prior problem. Let xt be the growth rate series. Use the fGarch package to fit the model:

require(fGarch)

m1

arma(3,2)+garch(1,1),data=x_t,trace=F, cond.dist="std")

rt

m1,standardize=T)

The rt denotes the standardized residuals. Apply the McLeod–Li test to detect any nonlinearity in the rt series and apply the BDS test to check whether the rt series consists of iid random variables.