Subset selection for vector autoregressive processes using Lasso
Subset selection for vector autoregressive processes using Lasso
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DOI：
10.1016/j.csda.2007.12.004
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发表时间：
2008-03
期刊：
影响因子：
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通讯作者：
Nan-Jung Hsu;Hung Hung-Hung;Ya-Mei Chang
中科院分区：
文献类型：
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作者：
Nan-Jung Hsu;Hung Hung-Hung;Ya-Mei Chang
使用Lasso [Tibshirani， R.(1996)]提出了向量自回归（VAR）过程的子集选择方法。通过套索收缩和选择。皇家统计学会杂志，B辑58,267 - 288]技术。简单地说，Lasso是回归设置中的收缩方法，它同时选择模型和估计参数。与AIC和BIC等传统的基于信息的方法相比，Lasso方法避免了计算密集型和穷举搜索。另一方面，与已有的带有参数约束的子集选择方法（如自顶向下和自底向上策略）相比，Lasso方法计算效率高，其结果对自回归模型中包含的序列的阶数具有鲁棒性。给出了VAR过程下Lasso估计量的渐近定理。仿真结果表明，在不同设置下，Lasso方法在预测均方误差和估计误差方面都优于几种传统的小样本子集选择方法。该方法用于对美国宏观经济数据进行建模以说明。
A subset selection method is proposed for vector autoregressive (VAR) processes using the Lasso [Tibshirani, R. (1996). Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society, Series B 58, 267–288] technique. Simply speaking, Lasso is a shrinkage method in a regression setup which selects the model and estimates the parameters simultaneously. Compared to the conventional information-based methods such as AIC and BIC, the Lasso approach avoids computationally intensive and exhaustive search. On the other hand, compared to the existing subset selection methods with parameter constraints such as the top-down and bottom-up strategies, the Lasso method is computationally efficient and its result is robust to the order of series included in the autoregressive model. We derive the asymptotic theorem for the Lasso estimator under VAR processes. Simulation results demonstrate that the Lasso method performs better than several conventional subset selection methods for small samples in terms of prediction mean squared errors and estimation errors under various settings. The methodology is applied to modeling U.S. macroeconomic data for illustration.