We improve upon the two-stage sparse vector autoregression (sVAR) method in Davis et al. (2016) by proposing an alternative two-stage modified sVAR method which relies on time series graphical lasso to estimate sparse inverse spectral density in the first stage, and the second stage refines non-zero entries of the AR coefficient matrices using a false discovery rate (FDR) procedure. Our method has the advantage of avoiding the inversion of the spectral density matrix but has to deal with optimization over Hermitian matrices with complex-valued entries. It significantly improves the computational time with a little loss in forecasting performance. We study the properties of our proposed method and compare the performance of the two methods using simulated and a real macro-economic dataset. Our simulation results show that the proposed modification or msVAR is a preferred choice when the goal is to learn the structure of the AR coefficient matrices while sVAR outperforms msVAR when the ultimate task is forecasting.
翻译:我们改进了Davis等人的两阶段稀散矢量自动递增方法(sVAR),建议采用两阶段修改的 SVAR 替代方法,该方法依靠时间序列图形拉索来估计第一阶段的稀薄反光谱密度,而第二阶段则使用虚假的发现率(FDR)程序改进AR系数矩阵的非零条目。我们的方法有避免光谱密度矩阵反转的优势,但必须处理对具有复杂价值条目的Hermitian矩阵的优化问题。该方法大大改进计算时间,在预测性能方面略为损失。我们用模拟和真正的宏观经济数据集研究拟议方法的特性并比较这两种方法的性能。我们的模拟结果显示,在最终任务预测时,在SVAR 超越 msVAR 时,拟议修改或 msVAR 是一个首选项目。