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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?

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  • $\begingroup$ 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. $\endgroup$ – forecaster Dec 24 '14 at 1:53

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