Techniques which identify parametric models for a time series are considered in this chapter. When the model structure is unknown, the key issue becomes one of regularizing the inference, namely, discovering a model which explains the data well, but avoids excessive complexity. Strict model selection criteria-such as Akaike's, Rissanen's and the evidence approach-are contrasted with full Bayesian solutions which allow parameters to be estimated in tandem. In the latter paradigm, marginalization is the key operator allowing model complexity to be assessed and penalized naturally via integration over parameter subspaces. As usch, it is an important alternative (or adjunct) to `subjective' penalization via the choice of prior. These various strategies are considered in the context of model order determination for both harmonic and autoregressive signals, and it is emphasized that effective and numerically efficient identification algorithms result even in the case of uniform priors, if judicious integration of parameters is undertaken.
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