Uncertainty Principle for Time Series

Uncertainty Principle for Time Series is devoted to a "model-free" approach that bypasses most of the existing shortcomings; the proof of the existence of a "trend" is a key ingredient. Although time series is a classic object of study in many branches of applied sciences (econometrics, financial engineering, weather forecast, neurosciences, etc.), most of the existing settings are assuming the knowledge of a model and of the probabilistic nature of the uncertainties. Those...
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Uncertainty Principle for Time Series is devoted to a "model-free" approach that bypasses most of the existing shortcomings; the proof of the existence of a "trend" is a key ingredient. Although time series is a classic object of study in many branches of applied sciences (econometrics, financial engineering, weather forecast, neurosciences, etc.), most of the existing settings are assuming the knowledge of a model and of the probabilistic nature of the uncertainties. Those assumptions are almost always impossible to fulfill. Moreover a complete and elegant mathematical treatment exists only in the case of stationary processes, which almost never occur in practice. All those points explain the difficulty of applying the existing approaches in concrete situations.