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Using Partition Functions to Test for Multifractality in Market Data

Article MQL5 articles
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Summary

This article begins a native MQL5 implementation of the Multifractal Model of Asset Returns (MMAR), focusing on partition analysis. For each moment order, the method calculates partition functions across multiple time scales, fits lines to their logarithms, and uses the slopes to estimate the scaling function tau(q). It also describes estimating the Hurst exponent and applying diagnostics to assess whether a price series displays multifractal behavior.

The implementation is organized as a library, with an ordinary least squares component using an SVD-based pseudo-inverse, a generalized Hurst exponent estimator, and a partition analysis engine. A script applies the pipeline to historical market bars. The article situates this module within a larger MMAR research project and reports that earlier Python work compared MMAR favorably with GARCH, but the supplied discussion here is primarily about implementation and analysis architecture. The excerpt does not provide enough detail to independently assess the earlier comparison, and detecting multifractal scaling alone does not establish forecasting or trading value.

Key ideas

  • Partition functions are computed over multiple time scales and moment orders.
  • Log-log regression slopes are used to estimate tau(q).
  • The analysis includes Hurst estimation and diagnostics for multifractal behavior.
  • An SVD-based pseudo-inverse is used for regression stability.
  • The MQL5 module is one stage in a broader MMAR pipeline, not evidence of trading profitability.

Tags

StatisticsVolatilityMachine learning

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