# ARIMA estimate validation through arima.sim

This is out of my curiosity trying to compare time series input to an ARMA model and reconstructed series after an ARMA estimate is obtained. These are the steps I am thinking:

1. Construct simulation time series

arma.sim <- arima.sim(model=list(ar=c(0.9),ma=c(0.2)),n = 100)


estimate the model from arma.sim, assuming we know it is a (1,0,1) model

arma.est1 <- arima(arma.sim, order=c(1,0,1))

2. also say we get arma.est1 in this form, which is close to the original (0.9,0,0.2):

Coefficients:
ar1     ma1  intercept
0.9115  0.0104    -0.4486
s.e.  0.0456  0.1270     1.1396

sigma^2 estimated as 1.15:  log likelihood = -149.79,  aic = 307.57

3. If I try to reconstruct another time series from arma.est1, how do I incorporate intercept or s.e. in arima.sim? Something like this doesn't seem to work well because arma.sim and arma.rec are far off:

arma.rec <- arima.sim(n=100, list(ar=c(0.9115),ma=c(0.0104)))


Normally we use predict() to check the estimate. But is this a legit way to look at the estimate?

• A simple solution is to manually add a constant after simulating arima using arima.sim. Arima in forecast function has the option to let you specify constant term. – forecaster Dec 24 '14 at 1:53