Large Volatility Matrix Prediction using Tensor Factor Structure

TL;DR

This paper introduces a tensor-based model for predicting large volatility matrices that accounts for time-varying eigenvectors, improving upon existing methods by capturing more complex dynamics in financial data.

Contribution

It generalizes the factor structure to a tensor form and proposes the PT-POET procedure, with proven asymptotic properties, for better volatility matrix prediction.

Findings

PT-POET outperforms existing methods in simulations.

Application to high-frequency data improves portfolio allocation.

Model captures time-varying eigenvector processes.

Abstract

Several approaches for predicting large volatility matrices have been developed based on high-dimensional factor-based It\^o processes. These methods often impose restrictions to reduce the model complexity, such as constant eigenvectors or factor loadings over time. However, several studies indicate that eigenvector processes are also time-varying. To address this feature, this paper generalizes the factor structure by representing the integrated volatility matrix process as a cubic (order-3 tensor) form, which is decomposed into low-rank tensor and idiosyncratic tensor components. To predict conditional expected large volatility matrices, we propose the Projected Tensor Principal Orthogonal componEnt Thresholding (PT-POET) procedure and establish its asymptotic properties. The advantages of PT-POET are validated through a simulation study and demonstrated in an application to minimum variance portfolio allocation using high-frequency trading data.