rollingrelated

Rollingrelated is a term used in data analysis to describe the evolving relationship between two time series as observed through rolling window transformations. It refers to how the strength and nature of association between variables change over time when computed on successive, overlapping time segments.

Definition and scope

Rollingrelated encompasses a family of statistics computed on moving windows. The most common example is rolling correlation, but the concept also includes rolling regression coefficients, rolling mutual information, and other dependence measures. Each window yields a snapshot of the relationship, and concatenating these snapshots forms a time series of windowed relationships.

Calculation

Choose a window length w and a step size s. For each window position, compute a dependence statistic between the segments X[t-w+1..t] and Y[t-w+1..t]. This produces a new time series of R values. Variants include centered windows, expanding windows (where the window grows over time), and multi-scale analyses using several window lengths. Handling missing data, detrending, and standardization are common preprocessing steps.

Interpretation and use

Rollingrelated highlights how relationships change over time, potentially signaling regime shifts, structural breaks, or evolving causal linkages. In finance, it helps track dynamic correlations among asset returns; in climatology or neuroscience, it can reveal time-varying couplings between variables.

Limitations

The approach is sensitive to window size and overlap, can suffer from edge effects, and may produce noisy estimates in short windows. Non-stationarity and data sparsity complicate interpretation, and multiple testing concerns arise with many overlapping windows.

See also

Rolling statistics, dynamic correlation, rolling regression, time-varying parameter models.