We describe a statistical test for association of two autocorrelated time series, one of which generated randomly at each time point from a known but possibly history-dependent distribution. The null hypothesis is that at each time point, the two variables are independent, conditional on history until that time point. We define a test statistic that is a martingale under the null hypothesis and describe an asymptotic test for it based on the martingale central limit theorem. If we reject this null hypothesis, we may infer an immediate causal effect of the randomized variable on the measured variable.
翻译:我们描述两个与电离相关时间序列关联的统计测试, 其中之一从已知但可能取决于历史的分布的每个时间点随机生成。 无效的假设是,在每一个时间点,这两个变量都是独立的, 取决于历史直到那个时间点。 我们定义一个根据无效假设的测试统计, 并描述一个基于马丁格尔中心定理的无症状测试。 如果我们拒绝这个无效假设, 我们可以推断随机变量对测量的变量的直接因果关系 。