Large Volatility Matrix Prediction with High-Frequency Data

TL;DR

This paper introduces a new eigen-decomposition based method for predicting large volatility matrices using high-frequency data, leveraging ARMA models to capture eigenvalue dynamics for improved financial forecasting.

Contribution

The paper proposes a novel approach combining eigen-decomposition and ARMA modeling for large volatility matrix prediction from high-frequency data, enhancing accuracy in financial applications.

Findings

Improved volatility prediction accuracy.

Enhanced portfolio allocation strategies.

Effective modeling of eigenvalue dynamics.

Abstract

We provide a novel method for large volatility matrix prediction with high-frequency data by applying eigen-decomposition to daily realized volatility matrix estimators and capturing eigenvalue dynamics with ARMA models. Given a sequence of daily volatility matrix estimators, we compute the aggregated eigenvectors and obtain the corresponding eigenvalues. Eigenvalues in the same relative magnitude form a time series and the ARMA models are further employed to model the dynamics within each eigenvalue time series to produce a predictor. We predict future large volatility matrix based on the predicted eigenvalues and the aggregated eigenvectors, and demonstrate the advantages of the proposed method in volatility prediction and portfolio allocation problems.