Analysis of Economic Delayed-Feedback Dynamics

Systems with a time-delayed feedback occur in various areas, for example in physics, climatology, physiology, and economy. In case of a nonlinear feedback, the systems can show complex behavior, like bifurcations, several types of oscillations, and chaotic solutions.We propose a new technique for the analysis of deterministic nonlinear delayed-feedback systems from a time series of economic data. It is based on the concepts of maximal correlation and nonparametric regression analysis, and allows for testing time series for delay-induced dynamics and for estimating the delay times.For high-quality data, the resulting models can be investigated themselves, which is a prerequisite for both an understanding of the feedback mechanism leading to the observed dynamics and model improvement. Since the method is nonparametric, it can be applied to a broad class of possible delay-induced dynamics.We demonstrate the efficiency of this technique on numerical simulations of a Nerlove-Arrow model with time delay and other models. As a real-world financial data application, the time series of the gross private domestic investment of the USA is analyzed.