Monitoring Time Series for Relevant Changes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909799326679040 |
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| author | Bastian, Patrick Kutta, Tim Basu, Rupsa Dette, Holger |
| author_facet | Bastian, Patrick Kutta, Tim Basu, Rupsa Dette, Holger |
| contents | We consider the problem of sequentially testing for changes in the mean parameter of a time series, compared to a benchmark period. Most tests in the literature focus on the null hypothesis of a constant mean versus the alternative of a single change at an unknown time. Yet in many applications it is unrealistic that no change occurs at all, or that after one change the time series remains stationary forever. We introduce a new setup, modeling the sequence of means as a piecewise constant function with arbitrarily many changes. Instead of testing for a change, we ask whether the evolving sequence of means, say $(μ_n)_{n \geq 1}$, stays within a narrow corridor around its initial value, that is, $μ_n \in [μ_1-Δ, μ_1+Δ]$ for all $n \ge 1$. Combining elements from multiple change point detection with a Hölder-type monitoring procedure, we develop a new online monitoring tool. A key challenge in both construction and proof of validity is that the risk of committing a type-I error after any time $n$ fundamentally depends on the unknown future of the time series. Simulations support our theoretical results and we present two real-world applications: (1) healthcare monitoring, with a focus on blood glucose tracking, and (2) political consensus analysis via citizen opinion polls. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_01756 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monitoring Time Series for Relevant Changes Bastian, Patrick Kutta, Tim Basu, Rupsa Dette, Holger Methodology Statistics Theory We consider the problem of sequentially testing for changes in the mean parameter of a time series, compared to a benchmark period. Most tests in the literature focus on the null hypothesis of a constant mean versus the alternative of a single change at an unknown time. Yet in many applications it is unrealistic that no change occurs at all, or that after one change the time series remains stationary forever. We introduce a new setup, modeling the sequence of means as a piecewise constant function with arbitrarily many changes. Instead of testing for a change, we ask whether the evolving sequence of means, say $(μ_n)_{n \geq 1}$, stays within a narrow corridor around its initial value, that is, $μ_n \in [μ_1-Δ, μ_1+Δ]$ for all $n \ge 1$. Combining elements from multiple change point detection with a Hölder-type monitoring procedure, we develop a new online monitoring tool. A key challenge in both construction and proof of validity is that the risk of committing a type-I error after any time $n$ fundamentally depends on the unknown future of the time series. Simulations support our theoretical results and we present two real-world applications: (1) healthcare monitoring, with a focus on blood glucose tracking, and (2) political consensus analysis via citizen opinion polls. |
| title | Monitoring Time Series for Relevant Changes |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2509.01756 |