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Memory Effects, Multiple Time Scales and Local Stability in Langevin Models of the S&P500 Market Correlation

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  • Tobias Wand
  • Martin He{ss}ler
  • Oliver Kamps

Abstract

The analysis of market correlations is crucial for optimal portfolio selection of correlated assets, but their memory effects have often been neglected. In this work, we analyse the mean market correlation of the S&P500 which corresponds to the main market mode in principle component analysis. We fit a generalised Langevin equation (GLE) to the data whose memory kernel implies that there is a significant memory effect in the market correlation ranging back at least three trading weeks. The memory kernel improves the forecasting accuracy of the GLE compared to models without memory and hence, such a memory effect has to be taken into account for optimal portfolio selection to minimise risk or for predicting future correlations. Moreover, a Bayesian resilience estimation provides further evidence for non-Markovianity in the data and suggests the existence of a hidden slow time scale that operates on much slower times than the observed daily market data. Assuming that such a slow time scale exists, our work supports previous research on the existence of locally stable market states.

Suggested Citation

  • Tobias Wand & Martin He{ss}ler & Oliver Kamps, 2023. "Memory Effects, Multiple Time Scales and Local Stability in Langevin Models of the S&P500 Market Correlation," Papers 2307.12744, arXiv.org.
    • Handle: RePEc:arx:papers:2307.12744
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    References listed on IDEAS

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    1. Martin He{ss}ler & Tobias Wand & Oliver Kamps, 2023. "Efficient Multi-Change Point Analysis to decode Economic Crisis Information from the S&P500 Mean Market Correlation," Papers 2308.00087, arXiv.org.
    2. Anton J. Heckens & Thomas Guhr, 2021. "A New Attempt to Identify Long-term Precursors for Endogenous Financial Crises in the Market Correlation Structures," Papers 2107.09048, arXiv.org, revised Aug 2022.
    3. Gaunersdorfer, Andrea & Hommes, Cars H. & Wagener, Florian O.O., 2008. "Bifurcation routes to volatility clustering under evolutionary learning," Journal of Economic Behavior & Organization, Elsevier, vol. 67(1), pages 27-47, July.
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    Cited by:

    1. Martin He{ss}ler & Tobias Wand & Oliver Kamps, 2023. "Efficient Multi-Change Point Analysis to decode Economic Crisis Information from the S&P500 Mean Market Correlation," Papers 2308.00087, arXiv.org.
    2. El-Nabulsi, Rami Ahmad & Anukool, Waranont, 2025. "Modeling stochastic Langevin dynamics in fractal dimensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 667(C).
    3. Martin Heßler & Oliver Kamps, 2025. "Quantifying local stability and noise levels from time series in the US Western Interconnection blackout on 10th August 1996," Nature Communications, Nature, vol. 16(1), pages 1-14, December.

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