Fat tails, long-range correlations and multifractality as emergent properties in nonstationary time series

¹ Instituto de Física, Universidade Federal de Alagoas - 57.072-970, Maceió-AL, Brazil
² Departamento de Física, Centro de Ciências Exatas e Tecnologia, Universidade Federal de Sergipe 49.100-000, Sao Cristóvao-SE, Brazil
³ Departamento de Economia, Universidade Federal de Santa Catarina - 88.049-970, Florianópolis-SC, Brazil
⁴ Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte 59072-970, Natal-RN, Brazil

^a fredsp7@gmail.com

Received: 18 October 2010
Accepted: 10 February 2011

Abstract

An important open problem concerns the physical origin of long-range correlations, multifractality and fat-tailed distributions observed in heteroscedastic time series associated with complex systems. Financial stylized facts provides one useful example usually not explained by traditional economic models. We investigate the behavior of an agent-based model consisting of N agents which interact with each other via fixed rules. We show that fat-tailed distributions, long-range correlations, heteroscedasticity and multifractality arise as N becomes large. Our findings suggest that such stylized facts can in principle arise as emergent properties.