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，时间序列分析中的现有推理方法往往依赖于不切实际的，有时无法验证的假设。这项研究继续主要研究者正在进行的研究，在时间序列分析的推理方法的发展，不依赖于不切实际的或无法验证的模型假设。恢复和二次抽样方法提供了可行的方法来获得有效的分布近似值，同时假设很少的随机机制产生的时间序列数据，与现有的方法，使不切实际的分布假设的数据。为了使这些现代方法安全准确地应用，许多重要的问题仍然需要解决。本研究主要探讨四个问题：（a）精确残差自举和局部块自举方案的核设计以及最佳带宽/块大小的选择问题：（B）非标准/非平稳情形下的残差自举方案;（c）在集合下进行强有力的自助假设检验以及准确的再估计推断（如置信区间）的方法-可能整合的单变量时间序列;（4）多元时间序列的合理回归机制及其在协整检验和伪回归中的应用。研究结果将有助于时间序列分析的几个领域，包括在残差自举的上下文中和在用于最精确的带宽/块大小选择的导频估计器中使用胖顶核，以及开发两种不同的自举方案，一种基于局部阻塞技术而另一种基于残差，从局部（而不是全局）平稳序列中处理数据。(The研究还将确定在线性回归中进行最强大的自助假设检验的方法，并且除了不管是否存在单位根都有效的二次抽样程序之外，还设计了一致/强大的自助单位根检验。 最后，研究还定义了一个连续路径块Bootstrap的多变量数据，其有效性在几个感兴趣的统计量的分布近似。这项研究将提供重要的结果，有效地分析时间序列数据与最小的假设有关的数据生成过程。 这项研究的结果将在几个领域有实际应用，如汇率，股票市场收益率和利率变化的分析。

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.