🤖 AI Summary
Financial time series exhibit intertwined fast and slow dynamic components that are challenging to disentangle for effective risk modeling and strategy design. This work formalizes the multiscale decomposition problem as a generalized eigenvalue problem, integrating variance and tail stationarity criteria to achieve an interpretable separation of slowly varying and rapidly fluctuating components in asset returns. The proposed method successfully identifies economically meaningful multiscale structures across diverse datasets—including foreign exchange rates, equity ETFs, and government bond yields—thereby substantially enhancing the efficacy of parameter drift detection, mean-reversion modeling, and tail risk management.
📝 Abstract
Financial time series exhibit multiscale behavior, with interaction between multiple processes operating on different timescales. This paper introduces a method for separating these processes using variance and tail stationarity criteria, framed as generalized eigenvalue problems. The approach allows for the identification of slow and fast components in asset returns and prices, with applications to parameter drift, mean reversion, and tail risk management. Empirical examples using currencies, equity ETFs and treasury yields illustrate the practical utility of the method.