It is now possible to fit a complete model to a set of data. The steps are as follows:

- Fit a saturated model, for the signal, to the data.
- Use the residuals from this model to select an AR(
*m*) model and values ; the order,*m*, is determined by AIC or hypothesis testing. - Form a set of candidate models to fit the signal.
- Fit all of the models using a filter based on from the saturated model.
- Use model selection, on the filtered scale, to select the best model.
- Assess the quality of the model using data splitting,
*R*^{2},*R*^{2}_{pred}, and/or sensitivity analysis. - Use the resulting model to perform whatever analysis is required—hypothesis tests, confidence intervals, prediction, etc.

The fundamental assumption for this modeling approach is that the true noise is very complex, perhaps more complex than even the most general ARMA(*m*,*l*) model. Nevertheless, for any finite sample, some AR(*m*) model fits the noise reasonably well. Because there is no actual belief that an AR(*m*) model is correct, AIC rather than BIC will be used to select the best model. The main motivations for this are that : (i) it is easy to develop an AR(*m*) filter, but it is difficult to develop a similar ...

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