A novel two-sample test within the space of symmetric positive definite matrix distributions and its application in finance

TL;DR

This paper presents a new two-sample test for symmetric positive definite matrix distributions, with applications in finance and cryptocurrency data analysis, demonstrating its practical utility in algorithmic trading contexts.

Contribution

It introduces the first two-sample test for orthogonally equivalent positive definite matrix distributions and derives its asymptotic distribution, filling a gap in statistical methodology.

Findings

Test successfully applied to cryptocurrency and stock data

Demonstrates applicability in algorithmic trading

Provides a new tool for matrix distribution comparison

Abstract

This paper introduces a novel two-sample test for a broad class of orthogonally equivalent positive definite symmetric matrix distributions. Our test is the first of its kind and we derive its asymptotic distribution. To estimate the test power, we use a warp-speed bootstrap method and consider the most common matrix distributions. We provide several real data examples, including the data for main cryptocurrencies and stock data of major US companies. The real data examples demonstrate the applicability of our test in the context closely related to algorithmic trading. The popularity of matrix distributions in many applications and the need for such a test in the literature are reconciled by our findings.