Abstract: We consider the problem of two-sample testing for time series with staggered observation periods, where the two time series can have different starting and ending observation times and can be of different lengths. In addition, we allow the two time series to depend on each other in a general way, which makes the staggered observation periods nontrivial to deal with as it now requires accommodating the joint dependence in the presence of overlapping and nonoverlapping segments when designing a valid inference protocol. This also makes existing self-normalization methods inapplicable to the current problem. To address this, we propose a warped self-normalized two-sample test, which uses warped self-normalized subsamples to provide uncertainty quantification of the global two-sample statistic. The method can be readily applied to compare quantities beyond the mean such as the variance or quantiles, and the associated asymptotic theory has been established. Numerical experiments including a simulation study and a real data analysis are also provided to further illustrate the proposed method.

Key words and phrases: Self-normalization, staggered time series, subsampling, two-sample test.