A Survey of Estimation Methods for Sparse High-dimensional Time Series Models
稀疏高维时间序列模型估计方法综述AI 解读 ↓
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稀疏高维时间序列模型估计方法综述
- 研究问题
- 在变量维度较高、时间相关样本数量较少时，如何估计大型时间序列模型，稀疏方法面临哪些统计理论与实践挑战？
- 方法与思路
- 作者综述基于 lasso 的估计进展，重点讨论随机回归和向量自回归两类多元时间序列模型，并整理技术难点与研究方向。
- 材料陈述的贡献
- 摘要所述贡献是汇总稀疏时间序列估计的近期进展，梳理时间依赖带来的挑战；并未声称提出统一的新估计量。
- 阅读关注点
- 核对各类方法对稀疏性、时间依赖和维度增长的条件，区分估计、变量选择与预测保证，并检查综述覆盖范围。
- 阅读边界
- 所据为 arXiv 预印本，不能确认同行评审或期刊接收；摘要未列出具体理论条件、方法比较结果或文献筛选标准。
原文摘要
High-dimensional time series datasets are becoming increasingly common in many areas of biological and social sciences. Some important applications include gene regulatory network reconstruction using time course gene expression data, brain connectivity analysis from neuroimaging data, structural analysis of a large panel of macroeconomic indicators, and studying linkages among financial firms for more robust financial regulation. These applications have led to renewed interest in developing principled statistical methods and theory for estimating large time series models given only a relatively small number of temporally dependent samples. Sparse modeling approaches have gained popularity over the last two decades in statistics and machine learning for their interpretability and predictive accuracy. Although there is a rich literature on several sparsity inducing methods when samples are independent, research on the statistical properties of these methods for estimating time series models is still in progress. We survey some recent advances in this area, focusing on empirically successful lasso based estimation methods for two canonical multivariate time series models - stochastic regression and vector autoregression. We discuss key technical challenges arising in high-dimensional time series analysis and outline several interesting research directions.