Cross-Recurrence Analysis for Comparing Financial Time Series
Summary
The article explains cross-recurrence quantification analysis (CRQA), a nonlinear way to compare the evolving states of two time series. Each series is embedded separately using matching dimension and delay settings; pairwise distances between embedded vectors form a rectangular cross-recurrence matrix, which is thresholded to identify similar states. Unlike single-series recurrence analysis, the matrix need not be symmetric and has no guaranteed self-matching diagonal.
It describes ten metrics, including cross-recurrence rate, determinism, laminarity, trapping time, line lengths, entropy, divergence, and a determinism-to-recurrence ratio. Diagonal patterns represent similar sequences of evolution, while vertical patterns capture periods when one series stays near states visited by the other. The article also discusses normalization and threshold selection when series use different scales, and outlines a library with rolling-window CPU and GPU computation and a chart indicator. Examples involving currency pairs and other markets are illustrative; the document does not establish that CRQA predicts returns or produces profitable trades. Results will depend on preprocessing, parameter choices, and alignment between the series.
Key ideas
- CRQA compares separately embedded states from two series in a rectangular matrix of pairwise distances.
- Matching embedding dimensions and delays are needed for meaningful comparisons.
- Cross-recurrence rate measures state-space overlap, while diagonal-line metrics capture similar sequences of evolution.
- Vertical-line metrics describe trapping near states visited by the other series.
- Normalization and threshold choice matter when the two series have different scales.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.