thus we obtain by OLS regression the AR(8)model
where rt is the error term of the process estimated
we get exactly the same result , if we consider this AR model as a special case of an ARMA model estimated by iterative nonlinear least squares
viii. example: ARIMA(8,d,8) model for r that contains only coefficients significant at least on the one percent level.
now we try to improve the model by including a moving average term. in this case we must use the iterative nonlinear least squares method. now the aim is to obtain coefficients significant on the 1% level again after of a series of trials with varying ARMA(8,8) model we got finally the following results by omitting non significant coefficients