A Novel and Effective Method for Quantifying the Performance of Time Series Volatility

This article presents a volatility quantification method based on the Wasserstein–Fourier (WF) distance to detect dynamic changes and identify abnormal behaviors of time series. Specifically, if one of the time series in WF distance is determined as having known statistical properties, then the focus of the research is naturally shifted to explore the properties of the other time series it contains. Theoretically, the proposed method named constrained WF (CWF) combines the natures of WF distance with the statistical characteristics of the fixed time series in a good way, and obtains some unique properties. In terms of application, experiments conducted on both simulated and real-world datasets demonstrate the effectiveness of this new proposed volatility quantification method. Furthermore, the comparison with other methods of the same type gives promising results, highlighting its advantages in applicability and recognition accuracy. Based on theoretical analysis, simulated research and experimental verifications, this work establishes CWF as a meaningful and practical model for quantifying the volatility of time series.