论文标题
高维时间序列的套索推断
Lasso Inference for High-Dimensional Time Series
论文作者
论文摘要
在本文中，我们开发了高维时间序列的有效推断。我们将DeSparsified Lasso扩展到近期依赖性（NED）假设下的时间序列设置，允许非高斯，串行相关和异性恋过程，其中回归器的数量可能比时间维度更快。我们首先得出一个弱稀疏下绑定的误差，该误差与NED假设相结合，意味着这种不平等也可以应用于在DeSparsified Lasso中执行的（固有错误指定的）鼻子回归。这使我们能够在一般条件下建立脱骨套索的均匀渐近正态性，包括推断尺寸增加的参数。此外，我们显示了长期差异估计器的一致性，从而提供了一组完整的工具，用于在高维线性时间序列模型中进行推断。最后，我们进行了模拟练习，以证明普通时间序列设置中脱毛的套索的较小样品特性。
In this paper we develop valid inference for high-dimensional time series. We extend the desparsified lasso to a time series setting under Near-Epoch Dependence (NED) assumptions allowing for non-Gaussian, serially correlated and heteroskedastic processes, where the number of regressors can possibly grow faster than the time dimension. We first derive an error bound under weak sparsity, which, coupled with the NED assumption, means this inequality can also be applied to the (inherently misspecified) nodewise regressions performed in the desparsified lasso. This allows us to establish the uniform asymptotic normality of the desparsified lasso under general conditions, including for inference on parameters of increasing dimensions. Additionally, we show consistency of a long-run variance estimator, thus providing a complete set of tools for performing inference in high-dimensional linear time series models. Finally, we perform a simulation exercise to demonstrate the small sample properties of the desparsified lasso in common time series settings.
