corrgre

Corrgre is a term used in time-series analysis to quantify the dynamic relationship between two variables by measuring the instantaneous rate of change of their correlation over time. It is not a standard single statistic, but a construct used to study evolving dependence in sequential data.

Definition and computation: Corrgre is defined as the instantaneous rate of change of the correlation between two time series. It is typically estimated from rolling correlations: r_t is the Pearson correlation within a window centered at time t, and corrgre_t is approximated by the finite-difference change in r_t over time, often after smoothing to reduce noise. Values generally fall near [-1, 1], with positive corrgre indicating a strengthening relationship and negative corrgre indicating a weakening or reversal.

Interpretation and limitations: Corrgre signals changing dependence but does not imply causality. It is sensitive to the choice of window length, data length, and outliers, and it captures changes in linear association unless nonlinear extensions are used. Interpretation should consider the broader context and potential confounders.

Applications: In finance, corrgre tracks shifting co-movements between assets. In climatology and ecology, it helps detect regime shifts in teleconnections or species interactions. In neuroscience, corrgre can describe evolving functional connectivity between brain regions, aiding the study of dynamic networks.

History: The idea of measuring dynamic changes in correlation has appeared in time-series literature since the early 2010s, with corrgre-related analyses used alongside rolling correlations and dynamic conditional correlation models to study nonstationary dependence.

See also: dynamic correlation, rolling correlation, time-series analysis, Granger causality.