Collaborative Research: Asymptotic Statistical Inference for High-dimensional Time Series

合作研究:高维时间序列的渐近统计推断

基本信息

  • 批准号:
    1916351
  • 负责人:
  • 金额:
    $ 19万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2019
  • 资助国家:
    美国
  • 起止时间:
    2019-08-01 至 2023-07-31
  • 项目状态:
    已结题

项目摘要

The information era has witnessed an explosion in the collection of high dimensional time series data across a wide range of areas, including finance, signal processing, neuroscience, meteorology, seismology, among others. For low dimensional time series, there is a well-developed estimation and inference theory. Inference theory in the high dimensional setting is of fundamental importance and has wide applications, but has been rarely studied. Researchers face a number of challenges in solving real-world problems: (i) complex dynamics of data generating systems, (ii) temporal and cross-sectional dependencies, (iii) high dimensionality and (iv) non-Gaussian distributions. The goal of this project is to develop and advance inference theory for high dimensional time series data by concerning all the above characteristics. The project will provide training to graduate students and publicly avaialble statistical packages. This project involves developing a systematic asymptotic theory for estimation and inference for high dimensional time series, including parameter estimation, construction of simultaneous confidence intervals, prediction, model selection, Granger causality test, hypothesis testing, and spectral domain estimation. To this end, a new methodology for the estimation of parameters and second-order characteristics for high dimensional time series will be proposed. New tools and concentration inequalities for the asymptotic analysis of high-dimensional time series will be developed. To perform simultaneous inference and significance testing, the PIs will investigate the very deep Gaussian approximation problem and the high dimensional central limit theorems by taking both high dimensionality and temporal and cross-sectional dependencies into account.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
信息时代见证了广泛领域的高维时间序列数据收集的爆炸式增长,包括金融、信号处理、神经科学、气象学、地震学等。对于低维时间序列,已有较完善的估计和推理理论。高维环境下的推理理论具有重要的基础和广泛的应用,但目前研究较少。研究人员在解决现实问题时面临许多挑战:(i)数据生成系统的复杂动力学,(ii)时间和截面依赖性,(iii)高维性和(iv)非高斯分布。本课题的目标是发展和推进高维时间序列数据的推理理论。该项目将向研究生提供培训,并向公众提供统计资料包。本项目涉及发展高维时间序列估计和推理的系统渐近理论,包括参数估计、同时置信区间的构建、预测、模型选择、格兰杰因果检验、假设检验和谱域估计。为此,提出了一种新的高维时间序列参数和二阶特征估计方法。为高维时间序列的渐近分析将发展新的工具和浓度不等式。为了同时进行推理和显著性检验,pi将研究非常深的高斯近似问题和高维中心极限定理,同时考虑高维、时间和截面依赖关系。该奖项反映了美国国家科学基金会的法定使命,并通过使用基金会的知识价值和更广泛的影响审查标准进行评估,被认为值得支持。

项目成果

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Wei Biao Wu其他文献

High-dimensional Simultaneous Inference of Quantiles
Optimal Multivariate EWMA Chart for Detecting Common Change in Mean
Recursive estimation of time-average variance constants
时间平均方差常数的递归估计
  • DOI:
  • 发表时间:
    2009
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Wei Biao Wu
  • 通讯作者:
    Wei Biao Wu
Asymptotic theory for QMLE for the real‐time GARCH(1,1) model
实时 GARCH(1,1) 模型的 QMLE 渐近理论
Simultaneous Confidence Bands in Nonlinear Regression Models with Nonstationarity
非平稳非线性回归模型中的联立置信带
  • DOI:
  • 发表时间:
    2017
  • 期刊:
  • 影响因子:
    1.4
  • 作者:
    Degui Li;Weidong Liu;Qiying Wang;Wei Biao Wu
  • 通讯作者:
    Wei Biao Wu

Wei Biao Wu的其他文献

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{{ truncateString('Wei Biao Wu', 18)}}的其他基金

Collaborative Research: Non-Parametric Inference of Temporal Data
合作研究:时态数据的非参数推理
  • 批准号:
    2311249
  • 财政年份:
    2023
  • 资助金额:
    $ 19万
  • 项目类别:
    Standard Grant
ATD: Collaborative Research: Inference of Human Dynamics from High-Dimensional Data Streams: Community Discovery and Change Detection
ATD:协作研究:从高维数据流推断人类动力学:社区发现和变化检测
  • 批准号:
    2027723
  • 财政年份:
    2020
  • 资助金额:
    $ 19万
  • 项目类别:
    Standard Grant
Collaborative Research: Second Order Inference for High-Dimensional Time Series and Its Applications
合作研究:高维时间序列的二阶推理及其应用
  • 批准号:
    1405410
  • 财政年份:
    2014
  • 资助金额:
    $ 19万
  • 项目类别:
    Continuing Grant
Covariance Matrix Estimation in Time Series and Its Applications
时间序列中的协方差矩阵估计及其应用
  • 批准号:
    1106790
  • 财政年份:
    2011
  • 资助金额:
    $ 19万
  • 项目类别:
    Continuing Grant
Statistical Inference of Models with Time-Varying Parameters
时变参数模型的统计推断
  • 批准号:
    0906073
  • 财政年份:
    2009
  • 资助金额:
    $ 19万
  • 项目类别:
    Continuing Grant
CAREER: Asymptotics of random processes and their applications
职业:随机过程的渐近及其应用
  • 批准号:
    0448704
  • 财政年份:
    2005
  • 资助金额:
    $ 19万
  • 项目类别:
    Continuing Grant

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