Geometry of Change: An Objective Analysis of Dynamic Systems

Abstract

Financial markets, economic and industrial systems share one property: a complex dynamic that is hard to predict with linear models and classical indicators. This work develops an approach that describes complex change through a system of extrema — key points fixing the extreme states of a system — and their spatial arrangement. Grounded in a strict mathematical idea, the geometric analysis captures the current structure of a process and enables forecasting of its likely development while minimizing subjective interpretation, yielding a formalized, reproducible and objective method applicable wherever timely identification of trend changes is critical.

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