Topics on time series resampling and subsampling

时间序列的统计分析在计量经济学中占有重要地位。然而，在时间序列分析中，现有的推断方法往往依赖于不切实际的假设，有时甚至是无法验证的假设。这项研究继续了首席研究员正在进行的研究，即开发不依赖于不现实或不可验证的模型假设的时间序列分析的推理方法。重采样和次采样方法提供了获得有效分布近似的可行方法，而与对数据做出不切实际的分布假设的现有方法相比，对生成时间序列数据的随机机制假设很少。仍有许多重要问题需要解决，以便安全和准确地应用这些现代方法。研究了四个主要问题：(A)精确剩余Bootstrap和局部块Bootstrap方案中的核设计以及最优带宽/块大小选择问题；(B)非标准/非平稳情况下的重采样方案；(C)在可能积分的单变量时间序列下进行强大Bootstrap假设检验和精确重采样推断的方法；这些研究结果将有助于时间序列分析的几个领域，包括在残差Bootstrap和导频估计器中使用胖顶核以实现最准确的带宽/块大小选择，以及开发两种不同的Bootstrap方案，一个基于局部分块技术，另一个基于残差，以处理来自局部(但不是全局)平稳序列的数据。(研究还将确定在线性回归中进行最强大的自举假设检验的方法，并且除了子抽样程序之外，还将设计一致/强大的自举单位根检验，该子抽样程序无论是否存在单位根都有效。最后，本研究还定义了一种多变量数据的连续路径块Bootstrap，并证明了其在逼近感兴趣的几个统计量的分布方面的有效性。这项研究将为有效地分析时间序列数据提供重要的结果，而对数据生成过程的假设最少。本文的研究成果将在汇率分析、股市收益分析、利率波动分析等领域具有实际应用价值。

The statistical analysis of time series is of central importance in econometrics. Existing methods for inference in time series analysis, however, often rely on unrealistic and sometimes unverifiable assumptions. This research continues the principal investigator's on-going research in the development of methods of inference for time series analysis that do not rely on unrealistic or unverifiable model assumptions. Resampling and subsampling methods offer viable approaches to obtaining valid distributional approximations while assuming very little about the stochastic mechanism generating time series data, in contrast to existing methods that make unrealistic distributional assumptions about the data. Many important questions still need to be addressed in order for these modern approaches to be applied safely and accurately. This research investigates four main issues: (a) kernel design in accurate residual bootstrap and local block bootstrap schemes as well as the problem of optimal bandwidth/block size choice; (b) resampling schemes for nonstandard/nonstationary situations; (c) methods for conducting powerful bootstrap hypothesis testing as well as accurate resampling inference-such as confidence intervals-under the set-up of a possibly integrated univariate time series; and (d) appropriate resampling mechanisms for multivariate time series with applications to cointegration testing and spurious regressions.The research results will contribute to several areas of time series analysis, including the use of fat-top kernels both in the context of residual bootstrap and in pilot estimators for most accurate bandwidth/block size choice and the development of two different bootstrap schemes, one based on a local blocking technique and the other on residuals, to address data from locally (but not globally) stationary series. (The research will also identify a way to conduct most powerful bootstrap hypothesis tests in linear regressions and consistent/ powerful bootstrap unit root tests are devised in addition to a subsampling procedure that works regardless of the presence of a unit root. Finally, the research also defines a Continuous-Path Block Bootstrap for multivariate data, and its validity in approximating the distribution of several statistics of interest is shown. This research will provide important results for effectively analyzing time series data with minimal assumptions about the data generating process. The results of this research will have practical applications in several areas, such as the analysis of exchange rates, stock market returns, and interest rates variability.