Recurrence Quantification Analysis (RQA)
Also known as: RQA, Recurrence Plot Analysis, Nonlinear Recurrence Analysis, Tekrarlama Kantifikasyon Analizi
Recurrence Quantification Analysis (RQA) is a nonlinear method for characterizing the dynamics of a time series by quantifying the small-scale structure of its recurrence plot. Introduced in its modern, comprehensive form by Marwan, Romano, Thiel, and Kurths in 2007, RQA extracts scalar measures — such as recurrence rate, determinism, laminarity, and Shannon entropy — that capture periodicity, chaos, stationarity, and transitions in complex dynamical systems.
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When to use it
RQA is appropriate when the time series is suspected to be nonlinear, non-stationary, or of unknown dynamics — contexts where classical spectral methods or linear autocorrelation are insufficient. It suits relatively short records (hundreds to low thousands of points) from physiological, geophysical, financial, or engineering sources. Key assumptions are that the data arise from a deterministic or stochastic dynamical system and that embedding parameters (m, tau, epsilon) can be estimated from the data. Limitations include sensitivity to the threshold epsilon, computational cost scaling as O(N^2), and interpretive ambiguity when signal length is short. Alternatives include sample entropy, detrended fluctuation analysis, or wavelet-based nonlinear methods.
Strengths & limitations
- Works with short, noisy, non-stationary time series where Fourier or linear AR methods fail.
- Produces multiple interpretable scalar indices (RR, DET, LAM, ENTR, TT) from a single analysis.
- No assumption of stationarity or linearity; applicable to real-world complex systems.
- Recurrence plots provide an intuitive visual complement to the quantitative measures.
- Results are sensitive to the choice of embedding dimension m, time delay tau, and threshold epsilon — poor choices distort all derived measures.
- Computational complexity is O(N^2) in memory and time, limiting applicability to very long time series without windowing strategies.
- No universal threshold-selection criterion exists; practice often relies on heuristics (e.g., 10% recurrence rate) that may not generalize.
- Statistical significance testing of RQA measures requires careful surrogate-data procedures, adding analytical overhead.
Frequently asked
How do I choose the threshold epsilon for the recurrence matrix?
A common heuristic is to select epsilon such that the recurrence rate (RR) falls between 2% and 10% of all possible point pairs, ensuring the plot is neither too sparse nor too dense. Alternatively, epsilon can be set as a fixed percentage of the attractor diameter or chosen via a fixed nearest-neighbor fraction. Sensitivity analysis across a range of epsilon values is strongly recommended before interpreting results.
What is the minimum time series length required for reliable RQA?
There is no strict universal minimum, but most practitioners recommend at least N = 500 data points after embedding to ensure sufficient diagonal and vertical line statistics. For very short series (N < 200), RQA measures exhibit high variance and should be interpreted cautiously, ideally supplemented by bootstrap confidence intervals or surrogate testing.
How does RQA differ from sample entropy?
Both methods quantify regularity in time series without assuming linearity, but they differ in structure. Sample entropy counts template matches up to a fixed tolerance and length, producing a single scalar reflecting predictability. RQA constructs a full recurrence matrix and extracts multiple measures (RR, DET, LAM, ENTR, TT), each capturing a distinct aspect of the dynamics — determinism, laminarity, and entropy of line-length distributions — providing a richer, multi-faceted characterization.
Sources
- Marwan, N., Romano, M. C., Thiel, M., & Kurths, J. (2007). Recurrence plots for the analysis of complex systems. Physics Reports, 438(5–6), 237–329. DOI: 10.1016/j.physrep.2006.11.001 ↗
How to cite this page
ScholarGate. (2026, June 2). Recurrence Quantification Analysis (RQA). ScholarGate. https://scholargate.app/en/complex-systems/recurrence-quantification-analysis
Which method?
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