The consentaneous model of the financial markets exhibiting spurious nature of long-range memory

TL;DR

This paper investigates whether the observed long-range memory in financial market volatility is genuine or spurious, using a non-linear stochastic model that reproduces empirical data and analyzes burst duration statistics.

Contribution

It demonstrates that the statistical properties of volatility bursts can be explained by non-linear stochastic differential equations, suggesting the long-range memory may be spurious.

Findings

Empirical burst and inter-burst durations align with model predictions.

Long-range memory in volatility may be a spurious effect.

The model reproduces empirical probability and spectral densities.

Abstract

It is widely accepted that there is strong persistence in the volatility of financial time series. The origin of the observed persistence, or long-range memory, is still an open problem as the observed phenomenon could be a spurious effect. Earlier we have proposed the consentaneous model of the financial markets based on the non-linear stochastic differential equations. The consentaneous model successfully reproduces empirical probability and power spectral densities of volatility. This approach is qualitatively different from models built using fractional Brownian motion. In this contribution we investigate burst and inter-burst duration statistics of volatility in the financial markets employing the consentaneous model. Our analysis provides an evidence that empirical statistical properties of burst and inter-burst duration can be explained by non-linear stochastic differential equations driving the volatility in the financial markets. This serves as an strong argument that long-range memory in finance can have spurious nature.