An example of an AR(1) simulation (D3)

We'll do a "baby" simulation that illustrates functions and for-loop.

Our first version will have some bad features (e.g. "embedded constants")

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Suppose we want an AR(1) with model parameters rho=.4 and sigma=.2

Lets generate 100 of these

First set up the vector to hold the values

y<-rep(0,100)

Now generate the first value according to the stationary distribution

s<-sqrt(.04/.84)

y[1]<-rnorm(1,sd=s)

Now a for-loop for the rest

for (i in 2:100){
y[i]<-0.4*y[i-1]+rnorm(1, sd=.2)
}

Look at y using plot and qqnorm.

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Wrap this in a "hard wired" function

SimAR<-function(n){
y<-rep(0,n)
s=sqrt(.04/.84)
y[1]<-rnorm(1,sd=s)
for (i in 2:n){
y[i]<-0.4*y[i-1]+rnorm(1, sd=.2)}
return(y)
}

Test this with n=10, n=100, etc. look at some of the results via plots.

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How can you make the function better?

Suppose you pass more than one argument to the function f --- that is, don't hard wire the constants in the way we did.

This would make your function much more useful.

Note: When developing functions you usually want to keep the function you are designing in a text file and then just cut and past
the versions of your function into the command window of S-Plus.