Two important issues characterize the design of bootstrap methods to construct confidence intervals for the correlation between two time series sampled (unevenly or evenly spaced) on different time points: (i) ordinary block bootstrap methods that produce bootstrap samples have been designed for time series that are coeval (i.e., sampled on identical time points) and must be adapted; (ii) the sample Pearson correlation coefficient cannot be readily applied, and the construction of the bootstrap confidence intervals must rely on alternative estimators that unfortunately do not have the same asymptotic properties. In this paper it is argued that existing proposals provide an unsatisfactory solution to issue (i) and ignore issue (ii). This results in procedures with poor coverage whose limitations and potential applications are not well understood. As a first step to address these issues, a modification of the bootstrap procedure underlying existing methods is proposed, and the asymptotic properties of the estimator of the correlation are investigated. It is established that the estimator converges to a weighted average of the cross-correlation function in a neighborhood of zero. This implies a change in perspective when interpreting the results of the confidence intervals based on this estimator. Specifically, it is argued that with the proposed modification of the bootstrap, the existing methods have the potential to provide a useful lower bound for the absolute correlation in the non-coeval case and, in some special cases, confidence intervals with approximately the correct coverage. The limitations and implications of the results presented are demonstrated with a simulation study. The extension of the proposed methodology to the problem of estimating the cross-correlation function is straightforward and is illustrated with a real data example. Related applications include the estimation of the autocorrelation function and the periodogram of a time series.

引导程序设计的两个重要问题是构建用于在不同时间点采样的两个时间序列（不均匀或均匀间隔）之间的相关性的置信区间：（i）针对时间序列设计了产生引导程序样本的普通块引导程序方法，是同时代的（即在相同的时间点采样），并且必须进行调整；（ii）样本Pearson相关系数不能轻易应用，并且自举置信区间的构造必须依赖于可替代的估计量，这些估计量不幸地没有相同的渐近性质。在本文中，有人争辩说，现有建议为问题（i）提供了不令人满意的解决方案，而忽略了问题（ii）。这导致覆盖范围较差的程序，其局限性和潜在应用尚不为人所知。作为解决这些问题的第一步，提出了对现有方法基础的自举程序的修改，并研究了相关估计的渐近性质。可以确定，估计量收敛到互相关函数的加权平均值（在零附近​​）。这意味着在基于此估计器解释置信区间的结果时，观点将发生变化。特别是，有人认为，通过对引导程序进行提议的修改，现有方法有可能为非同等情况下的绝对相关性提供有用的下界，在某些特殊情况下，具有近似正确覆盖率的置信区间。仿真研究证明了所提出结果的局限性和含义。将所提出的方法扩展到估计互相关函数的问题很简单，并用一个真实的数据示例进行了说明。相关应用包括自相关函数的估计和时间序列的周期图。