论文标题
Martingale Z检验
The martingale Z-test
论文作者
论文摘要
我们描述了两个自相关时间序列的关联的统计检验，其中一个是在每个时间点随机生成的，从已知但可能与历史有关的分布产生。零假设是，在每个时间点，两个变量是独立的，以历史为条件，直到该时间点为止。我们定义了一个测试统计量，该统计量是零假设下的Martingale，并根据Martingale Central Limit定理描述了它的渐近测试。如果我们拒绝该无效假设，则可以推断随机变量对测量变量的立即因果关系。
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.
