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Large Volatility Matrix Prediction using Tensor Factor Structure

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  • Sung Hoon Choi
  • Donggyu Kim

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.

Suggested Citation

  • Sung Hoon Choi & Donggyu Kim, 2024. "Large Volatility Matrix Prediction using Tensor Factor Structure," Papers 2412.04293, arXiv.org, revised May 2025.
    • Handle: RePEc:arx:papers:2412.04293
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    References listed on IDEAS

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