A method for generating realistic correlation matrices

TL;DR

This paper introduces a novel algorithm for generating realistic correlation matrices by adding controlled noise, improving upon traditional methods and enabling better assessment of statistical methodologies.

Contribution

The authors develop a flexible algorithm for generating correlation matrices with controlled noise, surpassing Gaussian simulation methods in realism and applicability.

Findings

The proposed method produces more realistic correlation matrices than Gaussian data simulation.

The algorithm can be customized for various correlation models.

Simulated correlation matrices aid in evaluating statistical methods.

Abstract

Simulating sample correlation matrices is important in many areas of statistics. Approaches such as generating Gaussian data and finding their sample correlation matrix or generating random uniform $[-1,1]$ deviates as pairwise correlations both have drawbacks. We develop an algorithm for adding noise, in a highly controlled manner, to general correlation matrices. In many instances, our method yields results which are superior to those obtained by simply simulating Gaussian data. Moreover, we demonstrate how our general algorithm can be tailored to a number of different correlation models. Using our results with a few different applications, we show that simulating correlation matrices can help assess statistical methodology.