Abstract
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.
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Voss, H.U., Kurths, J. (2002). Analysis of Economic Delayed-Feedback Dynamics. In: Soofi, A.S., Cao, L. (eds) Modelling and Forecasting Financial Data. Studies in Computational Finance, vol 2. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0931-8_16
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DOI: https://doi.org/10.1007/978-1-4615-0931-8_16
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