Model Selection: ARIMA(1,4),1,0)
Estimate the model after indentifying the right one.
Our model is:
our final forecasting model which we are going to forecast is:
but first we are going to have to test the if indeed the error term is a white noise process, graphing the error term and conducting test of the error terms stationary process give the following results (see c below)
Make a diagnostic test to check if you have identified the model correctly.
The white noise process seems to be verified by the graph therefore the variables seem to be cointegrated.
The Philip-Peron and the Augmented Dickey Fuller Test also provide strong evidence that the models error term is a white noise process
 
We can be fairly confident that the ARIMA(1,4),1,0) model would give unbiased forecast with very small errors.
Forecast the IP for the fourth quarter of 2009.
where t is 2009 Q3
Final Forecast: I predict that the U.S. Industrial Production Index will increase from 90.967 to 92.77, a quarterly percentage increase of 1.94%
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