Model estimation Model estimation means finding the values of the model coefficients which provide the best fit to the data. At the identification state one or more models are tentatively chosen that seen to provide statistically adequate representations of the available data. At this stage we get precise estimates of the coefficients of the model chosen at the identification stage. That is we fit the chosen model to our time series data to get estimates of the coefficients. This stage provides some warning signals about the adequacy of our model. In particular, if the estimated coefficients do not satisfy certain mathematical inequality conditions, that model is rejected. . There are sophisticated computational algorithms designed to do this. Model checking (Diagnosis)
This involves testing the assumptions of the model to identify any areas where the model is inadequate. If the model is found to be inadequate, it is necessary to go back to Step 2 and try to identify a better model. Ideally, a model should extract all systematic information from the data. The