自回归模型
估计员
数学
系列(地层学)
推论
星型
统计推断
渐近分布
背景(考古学)
抽样分布
时间序列
应用数学
算法
计算机科学
统计
自回归积分移动平均
人工智能
古生物学
生物
作者
Jonas Krampe,Jens-Peter Kreiß,Efstathios Paparoditis
出处
期刊:Bernoulli
[Bernoulli Society for Mathematical Statistics and Probability]
日期:2021-05-01
卷期号:27 (3)
被引量:13
摘要
Fitting sparse models to high-dimensional time series is an important area of statistical inference. In this paper, we consider sparse vector autoregressive models and develop appropriate bootstrap methods to infer properties of such processes. Our bootstrap methodology generates pseudo time series using a model-based bootstrap procedure which involves an estimated, sparsified version of the underlying vector autoregressive model. Inference is performed using so-called de-sparsified or de-biased estimators of the autoregressive model parameters. We derive the asymptotic distribution of such estimators in the time series context and establish asymptotic validity of the bootstrap procedure proposed for estimation and, appropriately modified, for testing purposes. In particular, we focus on testing that large groups of autoregressive coefficients equal zero. Our theoretical results are complemented by simulations which investigate the finite sample performance of the bootstrap methodology proposed. A real-life data application is also presented.
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