Multiplicative random cascades with additional stochastic process in financial markets

TL;DR

This paper empirically investigates multiplicative random cascade models in financial markets, finds negative correlations in multiplicative factors, and proposes an extended model with an additional stochastic term that aligns with observed data.

Contribution

It introduces an extended multiplicative cascade model incorporating an extra stochastic process, improving the fit to empirical financial data.

Findings

Empirical data confirms intermittency and multifractality in financial time series.

Negative correlations are observed among multiplicative factors.

The extended model with an added stochastic term matches empirical observations.

Abstract

Multiplicative random cascade model naturally reproduces the intermittency or multifractality, which is frequently shown among hierarchical complex systems such as turbulence and financial markets. As described herein, we investigate the validity of a multiplicative hierarchical random cascade model through an empirical study using financial data. Although the intermittency and multifractality of the time series are verified, random multiplicative factors linking successive hierarchical layers show strongly negative correlation. We extend the multiplicative model to incorporate an additional stochastic term. Results show that the proposed model is consistent with all the empirical results presented here.