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Fast Times, Slow Times: Timescale Separation in Financial Timeseries Data

Jan Rosenzweig

TL;DR

This paper tackles multiscale structure in financial time series by separating slow and fast processes. It builds a timescale-separation framework based on variance drift minimization and higher-moment tail stability, formulated as generalized eigenvalue problems; the variance case yields $ ext{E}[(doldsymbol{X}_t)^T oldsymbol{X}_t + oldsymbol{X}_t^T doldsymbol{X}_t] oldsymbol{w} = eta ext{E}[oldsymbol{X}_t^T oldsymbol{X}_t] oldsymbol{w}$ and its discretized form $ ext{C}(t,T) oldsymbol{w} = oldsymbol{ ext{λ}} ext{C}(t,0) oldsymbol{w}$ with $oldsymbol{ ext{λ}} = (1+eta)/(2T)$, while the tail-case uses $oldsymbol{ ext{λ}} = ext{E}[ (oldsymbol{X}_t oldsymbol{w}^T)^{2k-1}(oldsymbol{X}_{t+T} oldsymbol{w}^T) ]$ and nonlinear FastICA iterations. Empirically, linear ($k=1$) and nonlinear ($k=4$) tICA applied to G10 currencies, factor ETFs, and US Treasuries reveal slow components with robust out-of-sample persistence; tail-driven components differ from volatility-driven ones and show limited gains beyond $k=4$. The method is computationally tractable, broadly applicable, and provides actionable insights into parameter drift, mean reversion, and tail risk management across asset classes.

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.

Fast Times, Slow Times: Timescale Separation in Financial Timeseries Data

TL;DR

This paper tackles multiscale structure in financial time series by separating slow and fast processes. It builds a timescale-separation framework based on variance drift minimization and higher-moment tail stability, formulated as generalized eigenvalue problems; the variance case yields and its discretized form with , while the tail-case uses and nonlinear FastICA iterations. Empirically, linear () and nonlinear () tICA applied to G10 currencies, factor ETFs, and US Treasuries reveal slow components with robust out-of-sample persistence; tail-driven components differ from volatility-driven ones and show limited gains beyond . The method is computationally tractable, broadly applicable, and provides actionable insights into parameter drift, mean reversion, and tail risk management across asset classes.

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.
Paper Structure (6 sections, 23 equations, 3 figures)

This paper contains 6 sections, 23 equations, 3 figures.

Table of Contents

  1. Stationarity in Finance
  2. Types of Stationarity
  3. Variance Timescales
  4. Tail Timescales
  5. Empirical Examples
  6. Conclusion

Figures (3)

  • Figure 1: G10 currencies: Blind extraction of slowest components over 2006-2010 (green background), continuation over 2010-2025 (white background). Weights are rescaled to unit gross exposure.
  • Figure 2: Factor ETF: Blind extraction of slowest components over 2021-2022 (green background), continuation over 2022-2025 (white background). Weights are rescaled to unit gross exposure.
  • Figure 3: US Treasuries: Blind extraction of slowest components over 1994-1998 (green background), continuation over 1998-2025 (white background). Weights are rescaled to unit gross exposure.