A note on modelling cross-correlations: Hyperbolic secant regression

Abstract

SUMMARY: The problem of determining if a bivariate normal correlation changes with respect to time or some other covariate is considered. It is assumed that the means and standard deviations of the normal random variables can be consistently estimated from the entire data run, and do not need to be re-estimated for each covariate value. A new estimator of a bivariate normal correlation is given that has useful performance down to samples of size one. This allows regression type modelling of the correlation without unnecessary loss of resolution. The arc-tanh transformation of this estimator has a symmetric Fisher's z-distribution about the arc-tanh correlation. A method of smoothing the corr..