Learning about models and their fit to data

The paper asks what is the most informative way of assessing the fit of a model to data. often an answer comes from the context. In particular, from a consideration of how the model is to be used. Such information often leads one to seek transformations of the data that deliver the requisite information. Even in those instances in which we are sure of the best way of looking at fit, e.g. by the mean of the sample scores of an alternative model, it is often useful to augment the information provided by these tests through a decomposition of them. In time series such decolpositions have often involved recursive analyses. In this paper we propose that he moments underlying tests be re-written as an integrated conditional moment, where the conditioning variable is chosen to elicit useful information. The idea is potentially useful in assessing non-linear models. To implement the approach non-parametric methods generally need to be applied to simulated data in order to perform the decomposition. A range of applications of the idea, drawn from published articles, is used to illustrate the advantages of the method. [C10].