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

TL;DR

This paper demonstrates that market correlations in the S&P 500 exhibit significant memory effects over three weeks, and incorporating these effects into models improves prediction and stability analysis of market states.

Contribution

It introduces a generalized Langevin equation model with a memory kernel for market correlation, revealing slow time scales and non-Markovian dynamics in financial markets.

Findings

Memory kernel improves forecasting accuracy

Evidence of non-Markovianity in market data

Existence of slow market state dynamics

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.