A dynamic model of the financial–real interaction as a model selection criterion for nonparametric stock market prediction

Inspired by findings of low–dimensional nonlinearities and the Theorem of Takens (1983) forecasting models of financial time series are often built upon nonparametric, i.e. universal nonlinear, univariate relationships. Empirical investigations, however, are seriously contaminated by the problem of overfitting. Since statistical model selection theory in the nonlinear case is still in its infancy we would like to suggest the application of economic model selection criteria. It is a method of combining the flexibility of nonparametric regressions and important structural information in dynamic economic models. Therefore, conditions of economic models are imposed on the embedded nonlinear dynamical system to be estimated nonparametrically. In our empirical investigations we apply an univariate nonparametric forecasting model of stock returns, implemented via the Local Linear Maps of Ritter (1991), by an economic model selection criterion based on a discretized form of a continuous–time dynamic model on the interaction of real activity and asset markets. The dynamic economic model is estimated based on the Maximum Entropy inference since unobservable variables are involved. Results for monthly U.S. data show that nonparametric model selection is improved by this economic model selection criterion. On the other hand this result may be interpreted as support for the economic model.