A Simple Distribution-Free Algorithm for Generating Simulated High-Dimensional Correlated Data with an Autoregressive Structure

A distribution-free method to generate high-dimensional sequences of dependent variables with an autoregressive structure is presented. The quantile or fractile correlation (i.e., the moment correlation of the quantiles) is used as measure of dependence among a set of contiguous variables. The proposed algorithm breaks the sequence in small parts and avoids having to define one large correlation matrix for the entire high-dimensional sequence of variables. Simulations based on proteomics data are presented. Results suggest that negligible or no loss of fractile correlation occurs by splitting the generation of a sequence into small parts.