rm(list = ls(all=TRUE))
library(stats)

par(bty = 'n') 
par(cex.lab=1.5)
par(cex.axis=1.5)
par(mar=c(4.5, 4.5, 2, 2)+0.1)
par(bg = "azure")


set.seed(1)
T <- 100

png(filename="512a.png", width=600, height=400, pointsize=14,  type="cairo", bg="azure")
y <- cumsum(rnorm(T))
y <- ts(y)
plot(y, xlim=c(0,T), ylim=c(-20,20), xaxs="i",yaxs="i", main="random walk", type="n")
grid(lwd=2)
axis(1, at=seq(0,T,T/10), label=F, tick=T); axis(2); 
lines(y, col=2, lwd=4)
dev.off()


png(filename="512b.png", width=600, height=400, pointsize=14,  type="cairo", bg="azure")
plot(y, xlim=c(0,T), ylim=c(-20,20), xaxs="i",yaxs="i", main="random walk", type="n")
grid(lwd=2)
axis(1, at=seq(0,T,T/10), label=F, tick=T); axis(2); 
lines(y, col=2, lwd=4)
N <- 10
for (t in 1:N)
{
  y1 <- cumsum(rnorm(T))
  lines(y1, col=t+2, lwd=2, lty=2)
}
dev.off()


png(filename="512c.png", width=600, height=400, pointsize=14,  type="cairo", bg="azure")
N <- 1000
x <- rep(0, N)
plot(y, xlim=c(0,T), ylim=c(-30,30), xaxs="i",yaxs="i", main="random walk", type="n")
grid(lwd=2)
axis(1, at=seq(0,T,T/10), label=F, tick=T); axis(2); 
lines(y, col=2, lwd=4)
for (t in 1:N)
{
  y1 <- cumsum(rnorm(T))
  lines(y1, col=t+2, lwd=2, lty=2)
  x[t] <- y1[T]
}
hist(x)
dev.off()


png(filename="512d.png", width=600, height=400, pointsize=14,  type="cairo", bg="azure")
library(corrplot)
d <- data.frame(cbind(y[1:25], y[26:50], y[51:75], y[76:100]))
cor <- cor(d)
corrplot(cor, method="shade")
dev.off()