Nonparametric Modeling of Stock Returns Constrained by a Model of the Financial-Real Interaction

Inspired by findings of nonlinearities and the Theorem of Takens (1981), forecasting models of financial time series are often built upon nonlinear univariate relationships. Empirical investigations, however, are seriously contaminated by the problem of overfitting, in particular in the presence of short and noisy time series, resulting in a gap between the degree of approximation and out-of-sample performance. Since the theory of statistical model selection is not well understood in the nonlinear case, this paper takes an alternative approach by putting economic constraints on the nonlinear dynamical system to be estimated. To be concrete, we restrict a univariate nonparametric forecasting model of stock returns, implemented via the Local Linear Maps of Ritter, Martinetz and Schulten (1990), to a discretized form of a continuous-time generalized Blanchard (1981) model of the financial-real interaction by Semmler, Chiarella and Mittnik (1998). This is performed by the method of penalty terms -- in the case of several constraints, algorithms developed by Abu-Mostafa (1990) may be appropriate. Empirical results for monthly U.S. data show that the wedge between the approximation and the out-of-sample performance is reduced.