New Frontiers in Time Series Analysis

大数据现在几乎在每个领域都很流行。虽然收缩和稀疏估计器对于缓解大数据集带来的体积问题至关重要，但需要创新的模型来解决它们的多样性和速度需求。的确，改进的监测和测量系统现在提供的数据分辨率足够高，观测结果通常可以被认为是本质上连续的或功能性的。大量的环境、生物、工业和计算网络正在被动态地记录下来，以便它们复杂的演变可以被简洁地监测、研究和维护。每天都会产生大量的数据集，从大型卫星和遥感仪器、应急系统和能源基础设施，到纳米级电磁传感器、医疗设备和成像设备。这些系统提供了关于我们人类-自然世界的丰富信息，大多数是顺序的，或按时间排序的，并表现出复杂的趋势、过渡和依赖关系。多元统计中的标准方法不合适，适应性不足。首席研究员（PI）将开发新的方法和计算工具，以帮助数据驱动的科学发现和工业应用。PI还将培训和指导研究生和本科生的研究，在应用领域自由传播新的软件和方法，并促进统计学与广泛领域之间的合作，包括经济学、生态学、物理学、金融学、空间天气、水文学、农业、能源、环境工程、生物物理学、数学、电气工程、人类发展和计算机科学。大多数时间索引数据表现出异方差噪声、异常、变化点、局部和全局趋势以及线性和非线性依赖，并且明显缺乏适合对这种复杂性建模的分析工具。收缩、稀疏和自适应估计器是例外，它们已经成为重要的工具。全局-局部和正则化估计，通过自适应稀疏性/平滑性诱导惩罚/先验，是必不可少的-它允许复杂模型的计算可处理估计，具有更大的可解释性和减少估计不确定性。PI将开发：(i)新的方法和计算框架，通过允许全局和特定段参数，增加灵活性，用于变化点检测；（ii）对隐马尔可夫模型较少探索的方面进行新的理论和应用驱动的研究；（iii）扩展动态收缩过程，在存在异常值、相关网络时间序列的溢出效应和因果推理以及分布趋势过滤的情况下对变化点进行鲁棒和自适应估计；(4)对具有长距离依赖性和随机波动性等复杂特征的动态功能数据进行同步建模和推理的新方法。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。

Big data are now prevalent in nearly every domain. While shrinkage and sparse estimators are essential to mitigate the volume issues posed by big datasets, innovative models are needed to address their variety and velocity demands. Indeed, enhanced monitoring and measurement systems now provide data at high enough resolutions that observations can often be considered intrinsically continuous or functional. Massive environmental, biological, industrial, and computational networks are being dynamically recorded such that their intricate evolution might be succinctly monitored, studied, and maintained. Vast datasets are generated every day, ranging from large-scale satellites and remote sensing instruments, emergency systems, and energy infrastructure, to nanoscale electromagnetic sensors, medical devices, and imaging devices. These systems provide rich information about our human-natural world, and most is sequential, or time-ordered and exhibit complex trends, transitions, and dependencies. Standard methods in multivariate statistics are unsuitable and insufficiently adaptable. The Principal Investigator (PI) will develop new methods and computational tools to aid data-driven scientific discovery and industry applications. The PI will also train and mentor graduate and undergraduate student research, freely disseminate new software and methodology across application areas, and foster collaboration between statistics and a wide range of fields, including economics, ecology, physics, finance, space weather, hydrology, agriculture, energy, environmental engineering, biophysics, mathematics, electrical engineering, human development, and computer science.Most time-indexed data exhibit heteroskedastic noise, anomalies, change points, local and global trends, and both linear and nonlinear dependence, and there is a striking shortage of analytical tools suitable for modeling such complexity. Shrinkage, sparse, and adaptive estimators are exceptions and have become vital tools. Global-local and regularized estimation, via adaptive sparsity/smoothness-inducing penalties/priors, is essential — it allows computationally tractable estimation of complex models, with greater interpretability and reduced estimation uncertainty. The PI will develop: (i) new methods and computational frameworks for change-point detection with increased flexibility by allowing global and segment-specific parameters; (ii) new theoretical and application-driven investigations into less explored aspects of hidden Markov models; (iii) extensions of dynamic shrinkage process for robust and adaptive estimation of change-points in the presence of outliers, spillover effects and causal inference on dependent network time series, and distributional trend filtering; (iv) new methods for simultaneous modeling and inference of dynamic functional data with complex features such as long range dependence and stochastic volatility.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.