Large Volatility Matrix Prediction using Tensor Factor Structure
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912356783620096 |
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| author | Choi, Sung Hoon Kim, Donggyu |
| author_facet | Choi, Sung Hoon Kim, Donggyu |
| contents | Several approaches for predicting large volatility matrices have been developed based on high-dimensional factor-based Itô 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_04293 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large Volatility Matrix Prediction using Tensor Factor Structure Choi, Sung Hoon Kim, Donggyu Econometrics Several approaches for predicting large volatility matrices have been developed based on high-dimensional factor-based Itô 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. |
| title | Large Volatility Matrix Prediction using Tensor Factor Structure |
| topic | Econometrics |
| url | https://arxiv.org/abs/2412.04293 |