library(TSA)
# generate the random walk
# generate the noise (innovations)
set.seed(12791)
mu=0.1
sd=1
n=5000
e=rnorm(n=n,mean=mu,sd=sd)
# time plot of the innovations
plot(e,type='b')
plot(e,type='o')
abline(h=0,col='blue')
y=cumsum(e)
plot(y,type='o');abline(h=0,col='blue')

# moving average process of order 1
# MA(1) process

set.seed(12791)
mu=0
sd=1
n=500
theta=0.5
e=rnorm(n=n+1,mean=mu,sd=sd)
y=rep(NA,n)
for (t in 1:n) y[t]=e[t+1]-theta*e[t]
plot(y,type='o');abline(h=0,col='blue')
plot(y=y,x=zlag(y))