Detecting Parameter Instabilities in Functional Concurrent Linear Regression
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914328496570368 |
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| author | Basu, Rupsa Otto, Sven |
| author_facet | Basu, Rupsa Otto, Sven |
| contents | We develop methodology to detect structural breaks in the slope function of a concurrent functional linear regression model for functional time series in $C[0,1]$. Our test is based on a CUSUM process of regressor-weighted OLS residual functions. To accommodate both global and local changes, we propose $L^2$- and sup-norm versions, with the sup-norm particularly sensitive to spike-like changes. Under Hölder regularity and weak dependence conditions, we establish a functional strong invariance principle, derive the asymptotic null distribution, and show that the resulting tests are consistent against a broad class of alternatives with breaks in the slope function. Simulation studies illustrate finite-sample size and power. We apply the method to sports data obtained via body-worn sensors from running athletes, focusing on hip and knee joint-angle trajectories recorded during a fatiguing run. As fatigue accumulates, runners adapt their movement patterns, and sufficiently pronounced adjustments are expected to appear as a change point in the regression relationship. In this manner, we illustrate how the proposed tests support interpretable inference for biomechanical functional time series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13152 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Detecting Parameter Instabilities in Functional Concurrent Linear Regression Basu, Rupsa Otto, Sven Methodology Statistics Theory We develop methodology to detect structural breaks in the slope function of a concurrent functional linear regression model for functional time series in $C[0,1]$. Our test is based on a CUSUM process of regressor-weighted OLS residual functions. To accommodate both global and local changes, we propose $L^2$- and sup-norm versions, with the sup-norm particularly sensitive to spike-like changes. Under Hölder regularity and weak dependence conditions, we establish a functional strong invariance principle, derive the asymptotic null distribution, and show that the resulting tests are consistent against a broad class of alternatives with breaks in the slope function. Simulation studies illustrate finite-sample size and power. We apply the method to sports data obtained via body-worn sensors from running athletes, focusing on hip and knee joint-angle trajectories recorded during a fatiguing run. As fatigue accumulates, runners adapt their movement patterns, and sufficiently pronounced adjustments are expected to appear as a change point in the regression relationship. In this manner, we illustrate how the proposed tests support interpretable inference for biomechanical functional time series. |
| title | Detecting Parameter Instabilities in Functional Concurrent Linear Regression |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2602.13152 |