Measuring Volatility Memory, Asymmetry, Jumps, and Multifractality

Summary

This article presents MQL5 measures for studying intraday futures volatility: realized and duration-based volatility, fractional and FIGARCH-inspired volatility, clustering, leverage asymmetry, jump intensity, and multifractal spectrum width. It revises an MFDFA measure to estimate the Legendre-transform spectrum width Δα and reports mean regression R² as a confidence indicator. A GJR-GARCH model is fitted for the leverage effect, while the FIGARCH-inspired measure is explicitly a power-law weighted proxy rather than a full fitted FIGARCH model. Jump intensity uses bipower variation as a threshold baseline, but is not a formal jump test.

The empirical study uses two years of NQ M1 data across 514 New York sessions. It reports mean jump intensity of 1.4%, with a 90th percentile of 2.1%, and discusses how multifractal width can indicate when average long-memory statistics may mask changing regimes. The measures are intended as diagnostics for decisions such as sizing and stop placement, not standalone trading signals. Assumptions include applying a return-based memory estimate to squared returns, and the authors caution that low scaling-fit confidence makes multifractal estimates unreliable.

Key ideas

• Volatility clustering can be measured through autocorrelation in squared returns.
• The article estimates multifractal width through a Legendre transform and pairs it with mean regression R².
• Its FIGARCH-inspired volatility measure is a computational proxy, not a fitted FIGARCH model.
• Leverage asymmetry is estimated with GJR-GARCH, while jumps are flagged relative to bipower variation.
• The empirical results use NQ M1 data, and the measures remain diagnostics with stated modeling limits.

Tags

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