论文标题
时间序列中依赖的置换测试
Permutation Testing for Dependence in Time Series
论文作者
论文摘要
给定从固定时间序列的观察结果，置换测试允许在i.i.d的零假设下构建精确水平$α$测试。 （或更普遍的，可交换的）分布。另一方面，当未兴趣的零假设是基础过程是一个不相关的序列时，置换测试不一定是$α$的水平，在大型样本中也不是$α$。此外，置换测试可能具有大型3型或方向性错误，其中双面测试拒绝零假设，并得出结论，结论是，一阶自相关大于0，而实际上它小于0。当观测值独立且分布相同时，有限样品的概率$α$。还进行了一项蒙特卡洛模拟研究，将置换测试与其他自相关测试进行比较，以及对财务数据应用的经验示例。
Given observations from a stationary time series, permutation tests allow one to construct exactly level $α$ 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 $α$, nor are they approximately level $α$ 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 paper, 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 $α$ 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.
