Stylized Facts Generated Through Cellular Automata Models. Case of Study: The Game of Life

TL;DR

This paper introduces a simple geometrical method using cellular automata, specifically Conway's Game of Life, to generate anomalous random walks that exhibit stylized facts similar to financial time series.

Contribution

It presents a novel approach to produce stylized facts through cellular automata, offering insights into their formation mechanisms in complex systems.

Findings

Generated anomalous random walks with properties similar to financial stylized facts

Projection to 1D reveals statistical similarities to real financial data

Method demonstrates simplicity and potential for understanding stylized facts

Abstract

In the present work, a geometrical method to generate a two dimensional random walk by means of a bidimensional Cellular Automaton is presented. We illustrate it by means of Conway's Game of Life with periodical borders, with a large lattice of 3000 x 3000 cells. The obtained random walk is of character anomalous, and its projection to a one dimensional random walk is analyzed, showing that it presents some statistical properties similar to the so-called stylized facts observed in financial time series. We consider that the procedure presented here is important not only because of its simplicity, but also because it could help us to understand and shed light on the stylized facts formation mechanism.