Large Volatility Matrix Prediction using Tensor Factor Structure

Sung Hoon Choi; Donggyu Kim

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arXiv · 2412.04293

Large Volatility Matrix Prediction using Tensor Factor Structure

Sung Hoon Choi·Donggyu Kim

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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.

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BibTeX RIS

Sung Hoon Choi, Donggyu Kim. 2024-12-05. Large Volatility Matrix Prediction using Tensor Factor Structure. https://arxiv.org/abs/2412.04293

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