l1-regularization of high-dimensional time-series models with non-Gaussian and heteroskedastic errors
l1-regularization of high-dimensional time-series models with non-Gaussian and heteroskedastic errors
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DOI：
10.1016/j.jeconom.2015.10.011
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发表时间：
2016-03-01
影响因子：
6.3
通讯作者：
Mendes, Eduardo F.
中科院分区：
文献类型：
--
作者：
Medeiros, Marcelo C.;Mendes, Eduardo F.
研究了稀疏、高维、线性时间序列模型中自适应LASSO（adaLASSO）的渐近性质。adaLASSO是折叠凹惩罚最小二乘家族的一步实现。我们假设模型中协变量的数量和候选变量的数量都可以随着样本量的增加而增加（多项式或几何）。换句话说，我们让候选变量的数量大于观测值的数量。我们表明，adaLASSO一致地选择相关变量的观测数量的增加（模型选择的一致性），并具有预言属性，即使当错误是非高斯和条件异方差。这使得adaLASSO可以应用于经验金融和宏观经济学的无数应用。仿真研究表明，该方法在非常一般的设置与t分布和异方差误差以及高度相关的回归。最后，我们考虑一个应用程序来预测月度美国通货膨胀与许多预测。adaLASSO估计的模型比传统的基准竞争对手（如自回归和因子模型）提供上级的预测。(C)2015爱思唯尔B.V.保留所有权利。
We study the asymptotic properties of the Adaptive LASSO (adaLASSO) in sparse, high-dimensional, linear time-series models. The adaLASSO is a one-step implementation of the family of folded concave penalized least-squares. We assume that both the number of covariates in the model and the number of candidate variables can increase with the sample size (polynomially or geometrically). In other words, we let the number of candidate variables to be larger than the number of observations. We show the adaLASSO consistently chooses the relevant variables as the number of observations increases (model selection consistency) and has the oracle property, even when the errors are non-Gaussian and conditionally heteroskedastic. This allows the adaLASSO to be applied to a myriad of applications in empirical finance and macroeconomics. A simulation study shows that the method performs well in very general settings with t-distributed and heteroskedastic errors as well with highly correlated regressors. Finally, we consider an application to forecast monthly US inflation with many predictors. The model estimated by the adaLASSO delivers superior forecasts than traditional benchmark competitors such as autoregressive and factor models. (C) 2015 Elsevier B.V. All rights reserved.