Computer-intensive Methods for Nonparametric Time Series Analysis

非参数时间序列分析的计算机密集型方法

• 批准号: 0104059
• 负责人: Dimitris Politis
• 金额: $ 9.45万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-07-01 至 2004-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0104059&HistoricalAwards=false
• 关键词: Computer; intensive; Methods; Nonparametric; Time

Resampling and subsampling offer viable approaches to obtaining valid distributional approximations in the context of dependent data while assuming very little about the underlying stochastic mechanism. Many important questions still need to be addressed in order for these modern approaches to be applied safely and accurately in practice. The main issues the investigator wishes to tackle include the following: (a) Extend the realm of applicability of subsampling by considering self-normalized statistics and/or extrema of time series with possibly heavy tails together with extrapolation/interpolation of subsampling estimators. (b) Investigate the performance of the Local Bootstrap in forming confidence bands for conditional moments and prediction intervals for future values of a Markov process, as well as constructing hypothesis tests for time-reversibility. (c) Show that nonparametric estimation of conditional moments via flat-top kernel smoothing is not appreciably affected by the curse of dimensionality when the underlying function is ultra-smooth. (d) Investigate the performance of the newly proposed Local Block-Bootstrap in the case of a nonstationary series with a slowly-changing stochastic structure. (e) Propose the Tapered Block-Bootstrap algorithm, and show that it achieves superior performance as compared to the well-known Block-Bootstrap. (f) Propose a new block/bandwidth choice estimator with superior rate of convergence. And finally (g) consider the issue of a possibly integrated time series, and propose a new computer-intensive procedure, the Continuous-Path Block-Bootstrap, for statistical inference. Correlated data, such as time series and spatial data, are often encountered in many diverse scientific disciplines including economics, meteorology, electrical engineering, etc. The general goal of this project is to further the development of computer-intensive statistical analysis methods that are applicable in the setting of correlated data but do not rely on unrealistic or unverifiable model assumptions. Addressing this issue fruitfully will have many practical applications. For example, in a daily series of exchange rates or stock returns spanning a decade (or more), there may be evidence that the stochastic structure of the series has not been invariant over such a long stretch of time. Creating a practical way to model such nonstationarities and devising appropriate resampling methods for inference would be most helpful for economic applications. For a different application, consider the problem of stochastic simulation of manufacturing systems or a Gibbs-type sampler simulation; the development of subsampling/resampling for `almost' stationary time series would be most helpful in order to assess convergence and accuracy of the simulation. In the context of spatial statistics (e.g., mining and geostatistics, atmospheric and environmental science, etc.), the data typically correspond to measurements obtained at spatial points that are irregularly spaced. For example, a measurement may indicate the quality or quantity of the ore found in some location X, or a measurement of precipitation or air quality at location Y during a fixed time interval. The irregular nature of the measurement locations presents an added complication that, however, can be by-passed by specially designed versions of resampling/subsampling.

重采样和子采样提供了在相关数据的背景下获得有效分布近似的可行方法，同时对底层随机机制的假设很少。 为了使这些现代方法在实践中安全、准确地应用，仍然需要解决许多重要问题。 研究者希望解决的主要问题包括以下内容：（a）通过考虑自归一化统计和/或可能具有重尾的时间序列极值以及二次抽样估计量的外推/内插来扩展二次抽样的适用范围。 (b) 研究局部引导在形成马尔可夫过程的条件矩的置信带和未来值的预测区间以及构建时间可逆性的假设检验方面的性能。 (c) 表明，当基础函数超平滑时，通过平顶核平滑对条件矩进行非参数估计不会明显受到维数灾难的影响。 (d) 研究新提出的局部块引导程序在具有缓慢变化的随机结构的非平稳序列的情况下的性能。 (e) 提出 Tapered Block-Bootstrap 算法，并表明与众所周知的 Block-Bootstrap 相比，它具有更优越的性能。 (f) 提出一种具有优异收敛速度的新块/带宽选择估计器。 最后 (g) 考虑可能集成的时间序列问题，并提出一种新的计算机密集型程序，即连续路径块引导程序，用于统计推断。相关数据，如时间序列和空间数据，经常在许多不同的科学学科中遇到，包括经济学、气象学、电气工程等。该项目的总体目标是进一步开发计算机密集型统计分析方法，这些方法适用于相关数据的设置，但不依赖于不切实际或无法验证的模型假设。 有效地解决这个问题将有许多实际应用。 例如，在跨越十年（或更长）的每日汇率或股票收益序列中，可能有证据表明该序列的随机结构在如此长的一段时间内并不是一成不变的。 创建一种实用的方法来对此类非平稳性进行建模并设计适当的重采样方法进行推理将对经济应用最有帮助。 对于不同的应用，考虑制造系统的随机模拟或吉布斯型采样器模拟的问题；为了评估模拟的收敛性和准确性，开发“几乎”平稳时间序列的子采样/重采样将是最有帮助的。 在空间统计（例如采矿和地质统计学、大气和环境科学等）背景下，数据通常对应于在不规则间隔的空间点处获得的测量结果。 例如，测量结果可以指示在某个位置 X 发现的矿石的质量或数量，或者在固定时间间隔期间在位置 Y 处的降水量或空气质量的测量结果。 测量位置的不规则性质带来了额外的复杂性，但是可以通过专门设计的重采样/子采样版本来绕过。