#Experimentation with set.seed and arima.sim

#set.seed sets the PRN seed.
set.seed(101)
rnorm(1)
rnorm(1)
set.seed(101)
rnorm(1)

#This experiment shows how set.seed starts the "cycle" all over again.

#Two of the optional parameters of arima.sim are innov and start.innov. 
#They have default value NULL but they are very useful, in particualar
#the parameter innov gives us a way to control the "sigma" parameter of
#an ARIMA model

set.seed(101)
my.innov<-rnorm(500, sd=0.25)
set.seed(101)
my.start<-rnorm(500, sd=0.25)

#Here we took our "burn-in" sequence to have the same innovations and same
#number of innovations as our production sequence. This is uncommon, even
#a little weird, but it is not against the law.

#Now, lets simulate an ARIMA(2,0,3) of length 500
#First Specifiy the model; lets pick one with 5 parameters.
#Recall we have already handled sigma with innov

mymodel<-list( ar=c(0.1,0.1), ma=c(0.1, 0.1, 0.2) )

#There are several ways to specify the model. 

mysimulation<-arima.sim(model=mymodel, innov=my.innov, start.innov=my.start, n=500)

#Note: n=500 was actually redundant here. 
#By the way, if you apply arima.mle to this simulated data, you are quite likely to
#find a failure of convergence!

#This is an irritation, which we will not belabor right now, but it is worth 
#keeping our eye on.

arima.mle(mysimulation, model=list(order=c(2,0,3)))