Testing for Unspecified Periodicities in Binary Time Series
针对二元时间序列，检验其成功概率是否恒定或存在未知长度的周期性，基于Fisher经典检验构造统计量，并证明渐近性质。
ABSTRACT Given random variables with we test the hypothesis whether the underlying success probabilities are constant or whether they are periodic with an unspecified period length of . The test relies on an auxiliary integer which can be chosen arbitrarily, using which a new time series of length is constructed. For this new time series, the test statistic is derived according to the classical test by Fisher. Under the null hypothesis of a constant success probability and if the sequence is independent, it is shown that the test keeps the level asymptotically, while it has power for most alternatives, that is, typically in the case of and where and have common divisors. We also discuss extensions to more general distributions than binary ones and prove related limit theorems when the independence assumption is replaced by some weak dependence.