论文标题
使用时空信息的高维矢量自动回归模型中的正则估计
Regularized Estimation in High-Dimensional Vector Auto-Regressive Models using Spatio-Temporal Information
论文作者
论文摘要
向量自动回归(VAR)模型通常用于对多元时间序列进行建模,并且有许多惩罚方法来处理高维度。但是,就时空数据而言,大多数方法并未考虑数据的空间和时间结构,这可能导致不可靠的网络检测和不准确的预测。本文提出了针对时空var模型的数据驱动的加权L1正则方法。进行了广泛的仿真研究,以将所提出的方法与四种现有的高维var模型方法进行比较,从而在参数估计,网络检测和样本外预测中证明了我们方法比其他方法的改进。我们还将方法应用于流量数据集,以评估其在实际应用程序中的性能。此外,我们探讨了在弱稀疏方案下L1正规化VAR模型的理论特性,其中确切的稀疏性可以看作是一种特殊情况。据我们所知,文献尚未考虑这个方向。对于一般的固定VAR工艺,我们在弱稀疏场景下的L1正则估计误差上得出了非反应上限,提供了估计一致性的条件,并为特殊的VAR(1)情况进一步简化了这些条件。
A Vector Auto-Regressive (VAR) model is commonly used to model multivariate time series, and there are many penalized methods to handle high dimensionality. However in terms of spatio-temporal data, most methods do not take the spatial and temporal structure of the data into consideration, which may lead to unreliable network detection and inaccurate forecasts. This paper proposes a data-driven weighted l1 regularized approach for spatio-temporal VAR model. Extensive simulation studies are carried out to compare the proposed method with four existing methods of high-dimensional VAR model, demonstrating improvements of our method over others in parameter estimation, network detection and out-of-sample forecasts. We also apply our method on a traffic data set to evaluate its performance in real application. In addition, we explore the theoretical properties of l1 regularized estimation of VAR model under the weakly sparse scenario, in which the exact sparsity can be viewed as a special case. To the best of our knowledge, this direction has not been considered yet in the literature. For general stationary VAR process, we derive the non-asymptotic upper bounds on l1 regularized estimation errors under the weakly sparse scenario, provide the conditions of estimation consistency, and further simplify these conditions for a special VAR(1) case.