Cacorr

Cacorr is a statistical framework and software library designed for correcting autocorrelation and cross-channel dependencies in multivariate time-series data. The name is an acronym for Canonical Autocorrelation Correction, reflecting its core idea of decomposing and removing serial correlation while preserving cross-channel structure. In practice, Cacorr provides adjusted estimates and significance tests that are more reliable when residuals are autocorrelated.

The concept arose in discussions of time-series inference where standard methods assume independent errors. Cacorr generalizes the idea of canonical correlation to the temporal domain, using a two-stage approach: first, it estimates channel-wise autocovariance; second, it applies a canonical transformation to decorrelate channels and stabilize variance across lags.

Computationally, Cacorr typically involves the following steps: fit autoregressive models to each channel; construct a cross-channel correction matrix from estimated canonical correlations; apply the transformation to the data; re-estimate model parameters on the corrected series. It outputs corrected residuals, standard errors, and adjusted p-values.

History and usage: Although described in theoretical works and tutorials, Cacorr is primarily presented as a conceptual tool in textbooks and demonstrations for improving inference in multivariate time-series analysis. Implementations vary and may adopt Bayesian, frequentist, or hybrid strategies.

Applications: It has potential use in finance for high-frequency asset data, engineering sensor networks, and neuroscience where multiple brain signal channels are analyzed jointly. See also: Autocorrelation, Canonical correlation, Cross-correlation, Time-series analysis.