Cheng Yu, Dong Li, Feiyu Jiang, Ke Zhu
arXiv 8 Jun 2023 · Statistics — Methodology · publishedJournal of the American Statistical Association (2024) · 6 citations (OpenAlex)
arXiv:2306.05169 · PDF · DOI · OpenAlex · Extracted main text
Matrix-variate time series data are largely available in applications. However, no attempt has been made to study their conditional heteroskedasticity that is often observed in economic and financial data. To address this gap, we propose a novel matrix generalized autoregressive conditional heteroskedasticity (GARCH) model to capture the dynamics of conditional row and column covariance matrices of matrix time series. The key innovation of the matrix GARCH model is the use of a univariate GARCH specification for the trace of conditional row or column covariance matrix, which allows for the identification of conditional row and column covariance matrices. Moreover, we introduce a quasi maximum likelihood estimator (QMLE) for model estimation and develop a portmanteau test for model diagnostic checking. Simulation studies are conducted to assess the finite-sample performance of the QMLE and portmanteau test. To handle large dimensional matrix time series, we also propose a matrix factor GARCH model. Finally, we demonstrate the superiority of the matrix GARCH and matrix factor GARCH models over existing multivariate GARCH-type models in volatility forecasting and portfolio allocations using three applications on credit default swap prices, global stock sector indices, and future prices.
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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 | Yu, L., He, Y., Kong, X., Zhang, X (2022) Projected estimation for large-dimensional matrix factor models | 1.000 | 5 | 3 | 100% |
| 2 | Wang, D., Liu, X., Chen, R (2019) Factor models for matrix-valued high-dimensional time series | 0.737 | 3 | 2 | 100% |
| 3 | Bollerslev, T (1986) Generalized autoregressive conditional heteroskedasticity | 0.737 | 3 | 2 | 100% |
| 4 | Engle, R. F., Kroner, K. F (1995) Multivariate simultaneous generalized ARCH | 0.737 | 3 | 2 | 100% |
| 5 | Chen, E. Y., Fan, J (2021) Statistical inference for high-dimensional matrix-variate factor models | 0.644 | 2 | 2 | 100% |
| 6 | Chen, R., Yang, D., Zhang, C.-H (2022) Factor models for high-dimensional tensor time series | 0.644 | 2 | 2 | 100% |
| 7 | Engle, R. F (2002) Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models | 0.644 | 2 | 2 | 100% |
| 8 | Engle, R. F., Ledoit, O., Wolf, M (2019) Large dynamic covariance matrices | 0.511 | 2 | 1 | 100% |
| 9 | Hafner, C. M., Preminger, A (2009) On asymptotic theory for multivariate GARCH models | 0.511 | 2 | 1 | 100% |
| 10 | Chen, R., Xiao, H., Yang, D (2021) Autoregressive models for matrix-valued time series | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 37 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Tensor dynamic conditional correlation model: A new way to pursuit “Holy Grail of investing” | 0.874 | 6 | 2 |