An Application of the EM-algorithm to Approximate Empirical Distributions of Financial Indices with the Gaussian Mixtures

TL;DR

This paper demonstrates that Gaussian mixture models can accurately approximate the empirical distributions of major financial indices, with high-quality fits validated by statistical testing, suggesting further applications in financial data analysis.

Contribution

The paper applies Gaussian mixture models to financial indices and shows they provide high-quality approximations validated by Kolmogorov-Smirnov tests.

Findings

Gaussian mixtures fit financial index distributions well

High-quality approximation confirmed by statistical testing

Potential for broader application in financial data modeling

Abstract

In this study I briefly illustrate application of the Gaussian mixtures to approximate empirical distributions of financial indices (DAX, Dow Jones, Nikkei, RTSI, S&P 500). The resulting distributions illustrate very high quality of approximation as evaluated by Kolmogorov-Smirnov test. This implies further study of application of the Gaussian mixtures to approximate empirical distributions of financial indices.