Andrea Bucci, Michele Palma, Chao Zhang
arXiv 12 Dec 2024 · Finance — Computational
arXiv:2412.09517 · PDF · DOI · OpenAlex · Extracted main text
Traditional methods employed in matrix volatility forecasting often overlook the inherent Riemannian manifold structure of symmetric positive definite matrices, treating them as elements of Euclidean space, which can lead to suboptimal predictive performance. Moreover, they often struggle to handle high-dimensional matrices. In this paper, we propose a novel approach for forecasting realized covariance matrices of asset returns using a Riemannian-geometry-aware deep learning framework. In this way, we account for the geometric properties of the covariance matrices, including possible non-linear dynamics and efficient handling of high-dimensionality. Moreover, building upon a Fr\'echet sample mean of realized covariance matrices, we are able to extend the HAR model to the matrix-variate. We demonstrate the efficacy of our approach using daily realized covariance matrices for the 50 most capitalized companies in the S&P 500 index, showing that our method outperforms traditional approaches in terms of predictive accuracy.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Huang, Z. and Van Gool, L (2017) A Riemannian network for SPD matrix learning | 1.000 | 7 | 4 | 100% |
| 2 | Corsi, F (2009) A Simple Approximate Long-Memory Model of Realized Volatility | 1.000 | 5 | 3 | 100% |
| 3 | Andersen, T. G., Bollerslev, T., Diebold, F. X., and Labys, P (2003) Modeling and Forecasting Realized Volatility | 0.737 | 3 | 2 | 100% |
| 4 | Reiss, M. and Winkelmann, L (2021) Inference on the maximal rank of time-varying covariance matrices using high-frequency data | 0.644 | 2 | 2 | 100% |
| 5 | Bucci, A., Ippoliti, L., and Valentini, P (2022) Comparing unconstrained parametrization methods for return covariance matrix prediction self | 0.644 | 2 | 2 | 100% |
| 6 | Halbleib-Chiriac, R. and Voev, V (2011) Modelling and Forecasting Multivariate Realized Volatility | 0.644 | 2 | 2 | 100% |
| 7 | Dryden, I. L., Koloydenko, A., and Zhou, D (2009) Non-Euclidean Statistics for Covariance Matrices, with Applications to Diffusion Tensor Imaging | 0.585 | 3 | 1 | 100% |
| 8 | Zhang, C., Pu, X., Cucuringu, M., and Dong, X (2024) Graph-Based Methods for Forecasting Realized Covariances self | 0.511 | 2 | 1 | 100% |
| 9 | Andersen, T. G., Bollerslev, T., Diebold, F. X., and Labys, P (2001) The distribution of realized exchange rate volatility | 0.405 | 1 | 1 | 100% |
| 10 | Arsigny, V., Fillard, P., Pennec, X., and Ayache, N (2007) Geometric Means in a Novel Vector Space Structure on Symmetric Positive‐Definite Matrices | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 48 scored citations.