Modeling stylized facts for financial time series

TL;DR

This paper develops a multivariate probability density function model that captures key stylized facts of financial returns, including heavy tails, volatility clustering, and leverage effects, validated on over a century of Dow Jones data.

Contribution

It introduces a comprehensive model that accurately describes multiple stylized facts of financial time series in a unified framework.

Findings

Successfully fits joint distributions of 100+ years of daily returns

Captures heavy tails and volatility clustering

Models leverage effect effectively

Abstract

Multivariate probability density functions of returns are constructed in order to model the empirical behavior of returns in a financial time series. They describe the well-established deviations from the Gaussian random walk, such as an approximate scaling and heavy tails of the return distributions, long-ranged volatility-volatility correlations (volatility clustering) and return-volatility correlations (leverage effect). The model is tested successfully to fit joint distributions of the 100+ years of daily price returns of the Dow Jones 30 Industrial Average.