The switchback is an experimental design that measures treatment effects by repeatedly turning an intervention on and off for a whole system. Switchback experiments are a robust way to overcome cross-unit spillover effects; however, they are vulnerable to bias from temporal carryovers. In this paper, we consider properties of switchback experiments in Markovian systems that mix at a geometric rate. We find that, in this setting, standard switchback designs suffer considerably from carryover bias: Their estimation error decays as $T^{-1/3}$ in terms of the experiment horizon $T$, whereas in the absence of carryovers a faster rate of $T^{-1/2}$ would have been possible. We also show, however, that judicious use of burn-in periods can considerably improve the situation, and enables errors that decay as $\log(T)^{1/2}T^{-1/2}$. Our formal results are mirrored in an empirical evaluation.

翻译：开关回溯是一种实验设计，通过在整个系统中反复开启和关闭干预措施来测量处理效应。开关回溯实验是克服跨单元溢出效应的稳健方法；然而，它们易受时间延迟效应的影响而产生偏差。本文研究了在几何速率混合的马尔可夫系统中开关回溯实验的性质。我们发现，在此设定下，标准开关回溯设计显著受延迟效应偏差的影响：其估计误差以$T^{-1/3}$的速率随实验时间范围$T$衰减，而在无延迟效应情况下本可实现更快的$T^{-1/2}$衰减速率。但我们同时证明，合理使用预热期可大幅改善该情况，并实现以$\log(T)^{1/2}T^{-1/2}$衰减的误差。我们的理论结果与实证评估结果一致。