Finish example 10.14

ch10.r

@@ -79,3 +79,52 @@ t = seq(-1, 1, len=1000)
 R = (1/3)*outer(cos(2*pi*t), cos(2*pi*t))
 image(t, t, R, col=topo.colors(255), xlab="t_1", ylab="t_2")
 
+## Example 10.12
+
+# R code for Example 10.11: Plot the time function
+t = seq(-2, 2, len = 1000)
+x = matrix(0, 1000, 20)
+
+for (i in 1:20) {
+    x[,i] = cos((2*pi*t) + (2*pi*runif(1)))
+}
+
+matplot(t, x, lwd=2, col="gray", type="l", lty="solid", xaxp=c(-2,2, 8))
+grid()
+lines(t, 0*cos(2*pi*t), lwd=5, col="darkred")
+points(numeric(20), x[501,], lwd=2, col="darkorange")
+points(numeric(20) + 0.5, x[626,], lwd=2, col="blue", pch=4)
+
+# R code for Example 10.12: Plot the autocorrelation function
+t = seq(-1, 1, len=1000)
+R = toeplitz(0.5*(cos(2*pi*t)))
+image(t, t, R, col=topo.colors(255), ylim=c(1,-1), xlab="t_1", ylab="t_2")
+
+#############
+# Chapter 10.3 Wide sense stationary processes
+
+## Example 10.14
+
+# R code to demonstrate autocorrelation
+
+# Figure 1
+Xa = rnorm(1000)
+Xa2 = rnorm(1000)
+
+plot(Xa, type="l", lwd=2, col="blue")
+grid()
+lines(Xa2, lwd=2)
+
+# Figure 2
+N = 1000
+T = 1000
+X = matrix(rnorm(N*T), N, T)
+xc = matrix(0, N, 2*T-1)
+
+for (i in 1:N) {
+    xc[i,] = ccf(X[i,], X[i,], lag.max=2*T-1)$acf/T
+}
+
+plot(xc[1,], type="l", lwd=2, col="darkblue")
+lines(xc[2,], lwd=2)
+