#> source("c:/Work07/ShortCourse07/Programs/ARwalk1thin.txt",print.eval=TRUE)#
#This a picture of a random walk#
#recurrent for b<1 and transient for b>1#
nsim<-2500;
par(mfrow=c(2,2),mar=c(4.5,4.5,1.5,1.5))
m<-250		#number of points to plot
step<-round(nsim/m)
#---------------------------------------------------------
b<-.4;std<-1/sqrt(1-b^2);
x<-0;y<-0;d<-20;
for(i in 1:nsim){x<-c(x,b*x[[i]]+rnorm(1))}
for(i in 1:nsim){y<-c(y,b*y[[i]]+rnorm(1))}
xplot<-x[1];yplot<-y[1];for(i in 1:m) {xplot<-c(xplot,x[i*step]);yplot<-c(yplot,y[i*step])}
plot(xplot,yplot,type="l",xlim=c(-3*std,3*std),ylim=c(-3*std,3*std),lwd=2,xlab="x",main=expression(theta==.4))
#---------------------------------------------------------
b<-.8;std<-1/sqrt(1-b^2)
x<-0;y<-0;d<-20;
for(i in 1:nsim){x<-c(x,b*x[[i]]+rnorm(1))}
for(i in 1:nsim){y<-c(y,b*y[[i]]+rnorm(1))}
xplot<-x[1];yplot<-y[1];for(i in 1:m) {xplot<-c(xplot,x[i*step]);yplot<-c(yplot,y[i*step])}
plot(xplot,yplot,type="l",xlim=c(-3*std,3*std),ylim=c(-3*std,3*std),lwd=2,xlab="x",main=expression(theta==.8))
#---------------------------------------------------------
b<-.99;std<-1/sqrt(1-b^2)
x<-0;y<-0;d<-20;
for(i in 1:nsim){x<-c(x,b*x[[i]]+rnorm(1))}
for(i in 1:nsim){y<-c(y,b*y[[i]]+rnorm(1))}
xplot<-x[1];yplot<-y[1];for(i in 1:m) {xplot<-c(xplot,x[i*step]);yplot<-c(yplot,y[i*step])}
plot(xplot,yplot,type="l",xlim=c(-3*std,3*std),ylim=c(-3*std,3*std),lwd=2,xlab="x",main=expression(theta==.95))
#---------------------------------------------------------
b<-1.1;x<-0;y<-0;d<-20;
for(i in 1:nsim){x<-c(x,b*x[[i]]+rnorm(1))}
for(i in 1:nsim){y<-c(y,b*y[[i]]+rnorm(1))}
xplot<-x[1];yplot<-y[1];for(i in 1:m) {xplot<-c(xplot,x[i*step]);yplot<-c(yplot,y[i*step])}
plot(xplot,yplot,type="l",xlim=c(-d,d),ylim=c(-d,d),lwd=2,xlab="x",main=expression(theta==1.001))
#---------------------------------------------------------