CorrXt

CorrXt is a statistical framework used to measure time-varying correlations between pairs of time-series. By integrating local windowing and lag structure, CorrXt seeks to reveal transient relationships that may be masked by global measures. The term is used in theoretical discussions and in some applied analyses of sequential data.

CorrXt computes a localized correlation function over a sliding window. A typical formulation is CorrXt(t, lag) = sum_s W(s) x(t+s) y(t+s+lag) divided by the square root of [sum_s W(s) x(t+s)^2] [sum_s W(s) y(t+s+lag)^2], where W is a window weight. The method supports a range of lags and can be extended to more than two series to form a correlation tensor. Variants include Pearson-like and rank-based (nonparametric) correlations.

Implementation requires choosing a window length and lag bounds, and handling missing data. Efficient versions use convolution or FFT-based approaches and can output time-local matrices or tensors for downstream analysis.

Applications include neuroscience, where it helps identify delayed coupling between brain regions; finance, for detecting lead-lag relationships between assets; and engineering or climate science, for feature extraction in predictive models and anomaly detection, especially when relationships evolve over time.

Limitations include sensitivity to window size, non-stationarity, and potential spurious correlations from common drivers. Interpretations should rely on domain knowledge and, when possible, corroboration with complementary methods.

See also: cross-correlation, dynamic time warping, coherence, mutual information.