Given observations from a stationary time series, permutation tests allow one to construct exactly level $\alpha$ tests under the null hypothesis of an i.i.d. (or, more generally, exchangeable) distribution. On the other hand, when the null hypothesis of interest is that the underlying process is an uncorrelated sequence, permutation tests are not necessarily level $\alpha$, nor are they approximately level $\alpha$ in large samples. In addition, permutation tests may have large Type 3, or directional, errors, in which a two-sided test rejects the null hypothesis and concludes that the first-order autocorrelation is larger than 0, when in fact it is less than 0. In this article, under weak assumptions on the mixing coefficients and moments of the sequence, we provide a test procedure for which the asymptotic validity of the permutation test holds, while retaining the exact rejection probability $\alpha$ in finite samples when the observations are independent and identically distributed. A Monte Carlo simulation study, comparing the permutation test to other tests of autocorrelation, is also performed, along with an empirical example of application to financial data.

中文翻译：

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时间序列相关性的排列测试

给定来自平稳时间序列的观察结果，置换测试允许人们准确地构建水平$\alpha$在独立同分布（或更一般地说，可交换）分布的零假设下进行检验。另一方面，当感兴趣的零假设是基础过程是不相关的序列时，置换检验不一定是水平的$\alpha$, 也不是近似水平的$\alpha$在大样本中。此外，置换检验可能存在较大的第 3 类或定向误差，其中双边检验拒绝原假设并得出一阶自相关大于 0 的结论，而实际上它小于 0。本文在对序列的混合系数和矩的弱假设下，提供了一个置换检验的渐近有效性成立的检验程序，同时保留了准确的拒绝概率$\alpha$在有限样本中，当观测值独立且同分布时。还进行了一项蒙特卡罗模拟研究，将置换检验与其他自相关检验进行了比较，以及一个应用于金融数据的经验示例。