IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2609.13698.html

Spectral Design of Random-Duration Switchbacks

Author

Listed:
  • Yuchen Hu

Abstract

A switchback experiment alternates an entire system between treatment and control over time. It is especially useful when interactions between units can undermine standard unit-level experiments. Switchback experiments are commonly implemented on fixed temporal grids, which impose highly structured restrictions on when treatment can switch. We study a broader class of random-duration switchbacks, in which treatment and control alternate across runs whose durations are drawn from a common distribution. Under finite carryover, we show that the mean squared error of the Horvitz-Thompson estimator has a simple frequency-domain representation governed by how temporal outcome patterns align with design-induced imbalance and contamination patterns. This representation yields a tractable worst-case design criterion that can be computed directly from the duration distribution. Optimizing over even a simple two-rate family produces a run-age-dependent switching rule that reduces the asymptotic worst-case mean squared error by at least 32\% relative to the standard independently randomized fixed-block switchback.

Suggested Citation

  • Yuchen Hu, 2026. "Spectral Design of Random-Duration Switchbacks," Papers 2609.13698, arXiv.org.
    • Handle: RePEc:arx:papers:2609.13698
    as

    Download full text from publisher

    File URL: https://arxiv.org/pdf/2609.13698
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Iavor Bojinov & David Simchi-Levi & Jinglong Zhao, 2023. "Design and Analysis of Switchback Experiments," Management Science, INFORMS, vol. 69(7), pages 3759-3777, July.
    2. Guillaume W Basse & Yi Ding & Panos Toulis, 2023. "Minimax designs for causal effects in temporal experiments with treatment habituation," Biometrika, Biometrika Trust, vol. 110(1), pages 155-168.
    3. Chengchun Shi & Xiaoyu Wang & Shikai Luo & Hongtu Zhu & Jieping Ye & Rui Song, 2023. "Dynamic Causal Effects Evaluation in A/B Testing with a Reinforcement Learning Framework," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(543), pages 2059-2071, July.
    4. Michael P. Leung, 2021. "Rate-Optimal Cluster-Randomized Designs for Spatial Interference," Papers 2111.04219, arXiv.org, revised Sep 2022.
    5. Ugander Johan & Yin Hao, 2023. "Randomized graph cluster randomization," Journal of Causal Inference, De Gruyter, vol. 11(1), pages 1-53, January.
    6. Marcel F. Neuts & H. Sitaraman, 1989. "The square-wave spectral density of a stationary renewal process," International Journal of Stochastic Analysis, Hindawi, vol. 2, pages 1-14, January.
    7. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jinglong Zhao, 2024. "Experimental Design For Causal Inference Through An Optimization Lens," Papers 2408.09607, arXiv.org, revised Aug 2024.
    2. Ke Sun & Linglong Kong & Hongtu Zhu & Chengchun Shi, 2024. "ARMA-Design: Optimal Treatment Allocation Strategies for A/B Testing in Partially Observable Time Series Experiments," Papers 2408.05342, arXiv.org, revised Jan 2025.
    3. Shuze Chen & David Simchi-Levi & Chonghuan Wang, 2024. "Improving the Estimation of Lifetime Effects in A/B Testing via Treatment Locality," Papers 2407.19618, arXiv.org, revised Sep 2025.
    4. Xinqi Chen & Xingyu Bai & Zeyu Zheng & Nian Si, 2025. "Experimental Designs for Multi-Item Multi-Period Inventory Control," Papers 2501.11996, arXiv.org, revised Jul 2026.
    5. Jinglong Zhao, 2023. "Adaptive Neyman Allocation," Papers 2309.08808, arXiv.org, revised Jan 2026.
    6. repec:ehl:lserod:138897 is not listed on IDEAS
    7. Ruoxuan Xiong & Susan Athey & Mohsen Bayati & Guido Imbens, 2024. "Optimal Experimental Design for Staggered Rollouts," Management Science, INFORMS, vol. 70(8), pages 5317-5336, August.
    8. Zikun Ye & Zhiqi Zhang & Dennis J. Zhang & Heng Zhang & Renyu Zhang, 2026. "Deep Learning-Based Causal Inference for Large-Scale Combinatorial Experiments: Theory and Empirical Evidence," Management Science, INFORMS, vol. 72(7), pages 5611-5634, July.
    9. Zhexiao Lin & Peng Ding, 2025. "Unifying regression-based and design-based causal inference in time-series experiments," Papers 2510.22864, arXiv.org.
    10. Michael Thomas & Marcel Goic & Kirthi Kalyanam, 2025. "Long Lags and Large Returns: Experimental Evidence from Advertising to Businesses," Management Science, INFORMS, vol. 71(10), pages 8750-8766, October.
    11. Jizhou Liu & Liang Zhong, 2026. "Randomization Tests in Switchback Experiments," Papers 2602.23257, arXiv.org, revised Sep 2026.
    12. Sadegh Shirani & Mohsen Bayati, 2025. "On Evolution-Based Models for Experimentation Under Interference," Papers 2511.21675, arXiv.org.
    13. Gao, Mengsi & Ding, Peng, 2025. "Causal inference in network experiments: Regression-based analysis and design-based properties," Journal of Econometrics, Elsevier, vol. 252(PA).
    14. Chonghuan Wang, 2026. "Experimental Design for Matching," Papers 2601.21036, arXiv.org.
    15. Jacob Carlson & Neil Shephard, 2026. "When are time series predictions causal? The potential system and dynamic causal effects," Papers 2603.20394, arXiv.org.
    16. Hongyu Chen & David Simchi-Levi, 2026. "Efficient Switchback Experiments with Surrogate Variables: Estimation and Experimental Design," Management Science, INFORMS, vol. 72(6), pages 4854-4870, June.
    17. Shan Huang & Chen Wang & Yuan Yuan & Jinglong Zhao & Brocco & Zhang, 2023. "Estimating Effects of Long-Term Treatments," Papers 2308.08152, arXiv.org, revised Dec 2025.
    18. Ruohan Zhan & Shichao Han & Yuchen Hu & Zhenling Jiang, 2024. "Estimating Treatment Effects under Algorithmic Interference: A Structured Neural Networks Approach," Papers 2406.14380, arXiv.org, revised Mar 2026.
    19. Makoto Nakakita & Teruo Nakatsuma, 2026. "Calibrated Horizon-Weighted Local Projection Designs for Markov Switchbacks," Papers 2607.11694, arXiv.org.
    20. Li, Ting & Shi, Chengchun & Wen, Qianglin & Sui, Yang & Qin, Yongli & Lai, Chunbo & Zhu, Hongtu, 2024. "Combining experimental and historical data for policy evaluation," LSE Research Online Documents on Economics 125588, London School of Economics and Political Science, LSE Library.
    21. Nian Si, 2023. "Tackling Interference Induced by Data Training Loops in A/B Tests: A Weighted Training Approach," Papers 2310.17496, arXiv.org, revised Apr 2024.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2609.13698. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: https://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.