Robust Estimation of Transition Matrices in High Dimensional Heavy-tailed Vector Autoregressive Processes

Area of Science:

• Statistics
• Econometrics
• Time Series Analysis

Background:

• Gaussian vector autoregressive (VAR) models are widely used but assume normal distributions.
• Real-world financial and economic data often exhibit heavy tails, violating Gaussian assumptions.
• Existing methods struggle with heavy-tailed time series, limiting their applicability.

Purpose of the Study:

• To develop a unified framework for modeling and estimating heavy-tailed VAR processes.
• To introduce a robust statistical method for analyzing time series with non-Gaussian distributions.
• To extend the analysis of Granger causality to heavy-tailed VAR models.

Main Methods:

• Generalizing Gaussian VAR to elliptical VAR models to accommodate heavy tails.
• Developing a quantile-based robust estimator for the transition matrix.
• Analyzing the theoretical properties of the estimator, including convergence rates in high dimensions.

Main Results:

• The proposed estimator achieves parametric rates of convergence in high-dimensional settings.
• This is the first analysis of heavy-tailed, high-dimensional VAR processes.
• The robust estimator leads to sign-consistent Granger causality estimation.

Conclusions:

• The elliptical VAR framework provides a robust alternative to Gaussian VAR for heavy-tailed data.
• The developed methodology is effective for both synthetic and real-world financial data.
• The approach demonstrates superior performance in stock price prediction tasks.