High Dimensional Forecasting via Interpretable Vector Autoregression
High Dimensional Forecasting via Interpretable Vector Autoregression
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发表时间：
2014-12
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通讯作者：
William B. Nicholson;I. Wilms;J. Bien;D. Matteson
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作者：
William B. Nicholson;I. Wilms;J. Bien;D. Matteson
矢量自动进度（VAR）是建模多元时间序列的基本工具。但是，随着组件系列的数量增加，VAR模型变得过度参数化。几位作者通过将正规化方法（例如var估算中的拉索（Lasso））结合在一起来解决了这个问题。传统方法假设通用滞后顺序适用于所有组件，从而根据短距离依赖性的假设选择低滞后顺序来解决过度参数化。这种方法限制了组件之间的关系和阻碍预测性能。基于套索的方法在高维情况下工作得更好，但不包含滞后订单选择的概念。我们提出了一类新的分层滞后结构（HLAG），该结构将滞后选择概念嵌入到凸正则器中。关键建模工具是一个具有嵌套组的组套索，可确保滞后系数的稀疏模式尊重VAR的有序结构。 HLAG框架提供了三个结构，可以具有不同水平的灵活性。一项仿真研究表明，与以前的方法相比，预测和滞后订单选择的性能提高了，宏观经济应用进一步突出了预测改进以及HLAG方便，可解释的输出。
Vector autoregression (VAR) is a fundamental tool for modeling multivariate time series. However, as the number of component series is increased, the VAR model becomes overparameterized. Several authors have addressed this issue by incorporating regularized approaches, such as the lasso in VAR estimation. Traditional approaches address overparameterization by selecting a low lag order, based on the assumption of short range dependence, assuming that a universal lag order applies to all components. Such an approach constrains the relationship between the components and impedes forecast performance. The lasso-based approaches work much better in high-dimensional situations but do not incorporate the notion of lag order selection. We propose a new class of hierarchical lag structures (HLag) that embed the notion of lag selection into a convex regularizer. The key modeling tool is a group lasso with nested groups which guarantees that the sparsity pattern of lag coefficients honors the VAR's ordered structure. The HLag framework offers three structures, which allow for varying levels of flexibility. A simulation study demonstrates improved performance in forecasting and lag order selection over previous approaches, and a macroeconomic application further highlights forecasting improvements as well as HLag's convenient, interpretable output.