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Hybrid model incorporating multiple scale dynamics for time series forecasting

Most of the real world physical systems have critical thresholds, also known as tipping points, at which the system abruptly shifts its state from one to another. From dynamical system's perspective, bifurcation is the phenomenon responsible for these critical transitions in the system. There are various directions which can be adopted to study this bifurcation problem in an attempt to predict this phenomenon. The focus of this paper is classical bifurcation theory based approach incorporating multiple scale dynamics which is able to give analysis of bifurcations responsible for critical transitions in electricity price time series system. Fitz-Hugh Nagumo (FHN), which is a classical example exhibiting slow-fast scale dynamics is studied and later on hybridized with nonlinear neural networks to model this time series in various markets. Encouraging results allow us to look into this approach in future.