MA(1) Model

set.seed(123);
# Simulate 250 observations from the described MA(1) model
ma1_sim <- arima.sim(model=list(ma=0.5), n=250, mean=0, sd=0.1) + 0.05;
# Generate the theoretical ACF with upto lag 10
acf_ma1_model <- ARMAacf(ar=0, ma=0.5, lag.max=10)

# Split plotting window in three rows
par(mfrow=c(3,1))

# First plot: The simulated observations
plot(ma1_sim, type="l",main="MA(1) Process: mu=0.05, theta=0.5",xlab="time",ylab="y(t)")
abline(h=0)

# Second plot: Theoretical ACF
plot(1:10, acf_ma1_model[2:11], type="h", col="blue",  ylab="ACF", main="theoretical ACF")

# Third plot: Sample ACF
# Assign to tmp the Sample ACF
tmp <- acf(ma1_sim, lag.max=10)
plot(acf_ma1_model, main="Sample ACF")

# Reset graphical window to only one graph
par(mfrow=c(1,1))