Abstract
Dynamic covariance matrix estimation is pivotal in various domains such as finance, economics, and statistics, facilitating risk assessment, asset allocation, and portfolio optimization. However, challenges arise in accurately estimating covariance matrices, particularly in high-dimensional and nonstationary data settings.This thesis proposes innovative methodologies to address these challenges. Firstly, nonparametric methods are employed to capture complex data structures without imposing restrictive assumptions, enhancing adaptability to diverse data environments, including those exhibiting nonstationarity.
Secondly, to mitigate the curse of dimensionality and singularity issues in high-dimensional data, the thesis utilizes techniques based on matrix decomposition and dynamic group-LASSO approach. By decomposing the dynamic covariance matrix into low-rank and sparse components, effective parameter reduction is achieved while preserving crucial data characteristics. Additionally, regularization techniques ensures the positive definiteness of the estimated dynamic covariance matrix, enhancing its reliability.
Theoretical analyses of the proposed methodologies establish their asymptotic properties, providing insights into their performance under various conditions. Empirical evaluations using simulated and real-world datasets demonstrate the effectiveness and practical utility of the proposed approaches.
In summary, this thesis contributes novel techniques for dynamic covariance matrix estimation tailored for high-dimensional and nonstationary data settings. These methodologies have the potential to improve decision-making processes in finance, economics, and related fields by providing more accurate and reliable estimates of dynamic covariance matrices.
| Date of Award | 29 Aug 2024 |
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| Original language | English |
| Awarding Institution |
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| Supervisor | Junhui WANG (Supervisor), Xiao QIAO (Supervisor) & Liyuan CUI (Co-supervisor) |