MMAR and GARCH: Testing Financial Returns for Multifractal Scaling

Summary

This article introduces the Multifractal Model of Asset Returns (MMAR) as an alternative framework for volatility modeling, contrasting its construction with standard GARCH. GARCH estimates conditional variance from past shocks and variance, capturing volatility clustering, but the article argues that its conventional form has limitations around extreme returns, persistent volatility memory, and consistency across time scales. Extensions can address some issues, though they remain within the GARCH family.

MMAR represents log prices as fractional Brownian motion evaluated on multifractal trading time, a clock that changes speed with market activity. The article explains how this setup is intended to produce heavy tails, long memory, clustering, and scaling behavior. Its practical focus is the first step of an implementation pipeline: load return data and use partition-function analysis to assess whether multifractal scaling is present. It cites prior work reporting better MMAR forecasts across stocks, but the supplied text is incomplete and does not provide the current article’s test results. Evidence of scaling is a prerequisite, not proof of forecasting advantage in a particular market or sample.

Key ideas

• GARCH models conditional variance using past squared shocks and variance, which creates volatility clustering.
• The article identifies thin tails, short memory, and weak cross-scale consistency as limitations of standard GARCH.
• MMAR models returns through fractional Brownian motion evaluated on multifractal trading time.
• The proposed pipeline tests for multifractal scaling with partition-function analysis before fitting the broader model.
• The supplied excerpt reports no results from its own fractality test, and the cited comparative evidence is not independently assessed.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.