Explicit minimal representation of variance matrices, and its implication for dynamic volatility models
提出一种方差矩阵的最小显式表示，将参数化与正定性条件显式化，应用于动态多元波动率模型，使协方差参数数量减半，避免维度灾难，在最小方差组合预测中风险降低2-3倍且收益提升。
Summary We propose a minimal representation of variance matrices of dimension k, where parameterization and positive-definiteness conditions are both explicit. Then we apply it to the specification of dynamic multivariate volatility processes. Compared to the most parsimonious unrestricted formulation currently available, the required number of covariance parameters (hence processes) is reduced by about a half, which makes them estimable in full parametric generality if needed. Our conditions are easy to implement: there are only k of them, and they are explicit and univariate. To illustrate, we forecast minimum-variance portfolios and show that risk is always reduced (by a factor of 2 to 3 in spite of us using the simplest dynamics) compared to the standard benchmark used in finance, while also improving returns on the investment. Because of our representation, we do not get the usual dimensionality problems of existing unrestricted models, and the performance relative to the benchmark is actually improved substantially as k increases.