# Let's simulate an AR series and then produce our descriptive plots
# We want to do this a few times with different model specifications,
#    so let's create a function.
#

karsim<-function(alpha,n) {
	x<-arima.sim(n,model=list(ar=alpha,))
	kdescrip(x,"Simulated AR Series")
	return(x)
	}

x<-karsim(c(0,.8),200)

#EXAMPLE OF PARTIAL AUTOCORRELATIONS for n=200

par(mfrow=c(2,2))

# PROGRAM 3
# K. ENSOR, (ensor@rice.edu)
# Rice University

#first partial
plot(x[1:199],x[2:200],main="First PACF") # Scatterplot of obs. 1 lag apart
comppacf<-c(cor(x[1:199],x[2:200])) # Correlation of those observations

#second partial - lag separation is 2
X1<-matrix(0,nrow=198,ncol=1)       #Set up design matrix for input
X1[ ,1]<-x[2:199]                   # Data is center block
rf1<-lsfit(X1,x[3:200],intercept=F) # x is regressed on its past
rf1<-rf1$residuals                  # extract residuals
rb1<-lsfit(X1,x[1:198],intercept=F) # x is regressed on its future
rb1<-rb1$residuals                  # extract residuals
plot(rf1,rb1,main="Second PACF")    # Scatterplot of residuals from 2 regs.
comppacf<- c(comppacf,cor(rf1,rb1)) # Compute the correlation and store.

#third partial - lag separation is 3
X2<-matrix(0,nrow=197,ncol=2)
X2[ ,1]<-c(x[2:198])
X2[ ,2]<-c(x[3:199])
yf2<-c(x[4:200])
rf2<-lsfit(X2,yf2,intercept=F)  	   # regression on the past
rf2<-rf2$residuals
yb2<-c(x[1:197])
rb2<-lsfit(X2,yb2,intercept=F)      # regression on the future
rb2<-rb2$residuals
plot(rf2,rb2,main="Third PACF")
comppacf<- c(comppacf,cor(rf2,rb2))

#fourth partial
X3<-matrix(0,nrow=196,ncol=3)
X3[ ,1]<-x[2:197]
X3[ ,2]<-x[3:198]
X3[ ,3]<-x[4:199]
rf3<-lsfit(X3,x[5:200],intercept=F)  # regression on the past
rf3<-rf3$residuals
rb3<-lsfit(X3,x[1:196],intercept=F)  # regression on the future
rb3<-rb3$residuals
plot(rf3,rb3,main="Fourth PACF")

comppacf<-c(comppacf,cor(rf3,rb3))  # Compare to values computed from Splus
spluspacf<-acf(x,type="partial",plot=F) # Set up vector to extract values