Agent based reasoning for the non-linear stochastic models of long-range memory

TL;DR

This paper extends Kirman's agent-based model with a variable time scale to better represent trading activity in financial markets, linking microscopic agent behavior to macroscopic long-range memory phenomena.

Contribution

It introduces a flexible, variable time scale into Kirman's model, bridging microscopic agent dynamics with macroscopic long-range memory in financial markets.

Findings

The extended model matches empirical power law statistics.

Agent-based approach explains long-range memory phenomena.

Flexible time scale captures variable trading activity.

Abstract

We extend Kirman's model by introducing variable event time scale. The proposed flexible time scale is equivalent to the variable trading activity observed in financial markets. Stochastic version of the extended Kirman's agent based model is compared to the non-linear stochastic models of long-range memory in financial markets. Agent based model providing matching macroscopic description serves as a microscopic reasoning of the earlier proposed stochastic model exhibiting power law statistics.