A Simulation Analysis of Herding and Unifractal Scaling Behaviour

Abstract

We model the financial market using a class of agent-based models in which agents' expectations are driven by heuristic forecasting rules (in contrast to the rational expectations models used in traditional theories of financial markets). We show that within this framework, we can reproduce unifractal scaling with respect to three well-known power-laws relating: (i) moments of the absolute price-change to the time-scale over which they are measured; (ii) magnitude of returns with respect to their probability; (iii) the autocorrelation of absolute returns with respect to lag. In contrast to previous studies, we systematically analyse all three power-laws simultaneously using the same underlying model by making observations at different time-scales. We show that the first two scaling laws are remarkably robust to the time-scale over which observations are made, irrespective of the model configuration.However, in contrast to previous studies, we show that herding may explain why long-memory is observed at all frequencies. *

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