Joint Recurrence Analysis for Synchronized Market Regimes
Summary
The document introduces Joint Recurrence Quantification Analysis (JRQA) as a way to examine whether two time series revisit their own past states at the same time indices. It distinguishes this from cross-recurrence analysis, which compares states across the two series. JRQA builds self-recurrence conditions for each series and combines them, requiring both to recur together. The method uses aligned series, shared embedding settings, and a separate recurrence threshold for each series so differences in scale do not dominate the comparison.
The article defines a joint recurrence matrix and explains metrics for recurrence frequency, diagonal structure, vertical structure, and changes in joint behavior over time. It describes a library and indicator that calculate these metrics on rolling windows, with normalization, timestamp alignment, and GPU acceleration plus CPU fallback. The proposed interpretations—such as treating changes in joint trend as possible coupling shifts—are exploratory. The document presents an analytical tool rather than a trading strategy, and it supplies no evidence that these measures predict returns or improve trading results.
Key ideas
- JRQA marks a recurrence only when both series revisit their respective past states at the same time indices.
- Separate thresholds allow recurrence analysis across series with different scales.
- Joint recurrence is stricter than recurrence in either series on its own.
- Diagonal and vertical line metrics describe structure and persistence in simultaneous recurrences.
- The described rolling indicator is an analysis tool, and its regime interpretations require empirical testing.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.