non-stationary AR(10)

In the revision of Bayesian Core on which Jean-Michel Marin and I worked together most of last week, having missed our CIRM break last summer (!), we have now included an illustration of what happens to an AR(p) time series when the customary stationarity+causality condition on the roots of the associated polynomial is not satisfied.  More specifically, we generated several time-series with the same underlying white noise and random coefficients that have a fair chance of providing non-stationary series and then plotted the 260 next steps of the series by the R code

p=10
T=260
dat=seri=rnorm(T) #white noise

par(mfrow=c(2,2),mar=c(2,2,1,1))
for (i in 1:4){
  coef=runif(p,min=-.5,max=.5)
  for (t in ((p+1):T))
    seri[t]=sum(coef*seri[(t-p):(t-1)])+dat[t]
  plot(seri,ty="l",lwd=2,ylab="")
  }

leading to outputs like the following one