Evaluating Randomness Assumption: A Novel Graph Theoretic Approach

TL;DR

This paper introduces a new graph-theoretic method using random interval graphs to test the assumption of randomness in data, capable of detecting complex dependencies beyond traditional tests.

Contribution

It develops two novel tests based on RIG properties that are distribution-independent and more effective at identifying various data dependencies than existing methods.

Findings

RIG-based tests detect complex dependencies like heteroskedasticity and chaos.

The RIG-DD test outperforms most existing randomness tests.

The methods are applicable to real-world data examples.

Abstract

Randomness or mutual independence is a fundamental assumption forming the basis of statistical inference across disciplines such as economics, finance, and management. Consequently, validating this assumption is essential for the reliable application of statistical methods. However, verifying randomness remains a challenge, as existing tests in the literature are often restricted to detecting specific types of data dependencies. In this paper, we propose a novel graph-theoretic approach to testing randomness using random interval graphs (RIGs). The key advantage of RIGs is that their properties are independent of the underlying distribution of the data, relying solely on the assumption of independence between observations. By using two key properties of RIGs-edge probability and vertex degree distribution-we develop two new randomness tests: the RIG-Edge Probability test and the RIG-Degree Distribution (RIG-DD) test. Through extensive simulations, we demonstrate that these tests can detect a broad range of dependencies, including complex phenomena such as conditional heteroskedasticity and chaotic behavior, beyond simple correlations. Furthermore, we show that the RIG-DD test outperforms most of the existing tests of randomness in the literature. We also provide real-world examples to illustrate the practical applicability of these tests.