Econ Papers Daily / 期刊论文
高维多元随机波动率模型的实用估计方法
Practical estimation methods for high-dimensional multivariate stochastic volatility models
摘要
We propose computationally inexpensive and efficient estimators for multivariate stochastic volatility (MSV) models with cross-dependence, Granger causality, and higher-order persistence in latent volatilities. The proposed class of estimators is based on a small set of moment equations derived from the weak VARMA representations of MSV models. Except for the cross-dependence parameters, closed-form expressions are obtained for the remaining parameters, so that no numerical optimization is required. To improve the stability and efficiency of the volatility-persistence parameter estimates, we develop shrinkage-type VARMA estimators based on averaging different simple estimates (winsorization) and matrix-variate regressions (MVR). We also derive the asymptotic distribution of these estimators. Due to their computational simplicity, VARMA estimators make reliable — possibly exact — simulation-based inference tractable through Monte Carlo test techniques. We formulate volatility commonality as a testable common-C-space restriction on the MSV transition matrices, and develop finite-sample Monte Carlo tests for this hypothesis. Simulation results show that the proposed shrinkage-type VARMA-MVR estimators compare favorably with Bayesian and QML benchmarks in terms of bias, RMSE, and computational cost. They also remain feasible in very high dimensions, and, using auxiliary particle filtering, deliver accurate latent-state recovery and covariance forecasts even under model misspecification. In empirical applications to stock returns, we find that unrestricted higher-order MSV models perform well for covariance forecasting and portfolio building, while the data provide little support for an exact low-dimensional common dynamic subspace.
中文摘要
我们提出计算成本低且高效的多变量随机波动率（MSV）模型估计量，适用于具有交叉依赖、Granger因果性以及潜在波动率中高阶持续性的情形。所提出的估计量类别基于由MSV模型的弱VARMA表示导出的一小组矩方程。除交叉依赖参数外，其余参数均获得闭式表达式，因此无需数值优化。为提高波动率持续性参数估计的稳定性和效率，我们开发了收缩型VARMA估计量，其基于对不同简单估计进行平均（缩尾处理）以及矩阵变量回归（MVR）。我们还推导了这些估计量的渐近分布。由于其计算简便性，VARMA估计量使基于模拟的可靠——可能精确——推断通过蒙特卡罗检验技术变得可行。我们将波动率共性表述为MSV转移矩阵上可检验的共同C空间约束，并为该假设开发有限样本蒙特卡罗检验。模拟结果表明，所提出的收缩型VARMA-MVR估计量在偏差、RMSE和计算成本方面优于贝叶斯和QML基准。它们在极高维度下仍然可行，并且使用辅助粒子滤波，即使在模型误设下也能提供准确的潜在状态恢复和协方差预测。在股票收益的经验应用中，我们发现无约束的高阶MSV模型在协方差预测和投资组合构建方面表现良好，而数据对精确的低维共同动态子空间提供了很少支持。