On approximate system modeling, complexity and macro-econometrics

Macro-econometric modeling provides a paradigm for the most difficult problems in system identification: data blocks are often short, throwing doubt upon the relevance of asymptotic methods; Bayesian methods are not attractive because of the problem of the selection of priors; the detection of causal relations is a problem area in itself, and in particular all of the observed time series of a given macro-econometric system may well be endogenous; finally, common-sense and economic insight dictates that macroeconometric system dynamics are time-varying, and this invites the introduction of hierarchical models with an associated leap in complexity and difficulty of analysis. Over the last ten years, approximate system modeling via minimum prediction error (MPE) methods, has developed into both a concrete set of analytical results (principally in the work of L. Ljung, P.E. Caines et al.) and a philosophical viewpoint. The central idea is that the construction of models from data consists in the choice of a predictor for the data such that a combination of (a measure of) the prediction errors and a measure of the predictor complexity is a minimum. This idea has its philosophical roots in the work of Reichenbach, Goodman, Barker and Kemeny, and its system theoretic roots in the work of Akaike, Hannan, Rissanen, Willems, Ljung and Caines, amongst others. In this talk we shall discuss the relevance of MPE approximate system modeling to the problems of macro-econometrics sketched above.