Computationally efficient segmentation for non-stationary time series with oscillatory patterns
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917235134562304 |
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| author | Bianco, Nicolas Cappello, Lorenzo |
| author_facet | Bianco, Nicolas Cappello, Lorenzo |
| contents | We propose a novel approach for change-point detection and parameter learning in multivariate non-stationary time series exhibiting oscillatory behaviour. We approximate the process through a piecewise function defined by a sum of sinusoidal functions with unknown frequencies and amplitudes plus noise. The inference for this model is non-trivial. However, discretising the parameter space allows us to recast this complex estimation problem into a more tractable linear model, where the covariates are Fourier basis functions. Then, any change-point detection algorithms for segmentation can be used. The advantage of our proposal is that it bypasses the need for trans-dimensional Markov chain Monte Carlo algorithms used by state-of-the-art methods. Through simulations, we demonstrate that our method is significantly faster than existing approaches while maintaining comparable numerical accuracy. We also provide high probability bounds on the change-point localization error. We apply our methodology to climate and EEG sleep data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_22999 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Computationally efficient segmentation for non-stationary time series with oscillatory patterns Bianco, Nicolas Cappello, Lorenzo Methodology Computation We propose a novel approach for change-point detection and parameter learning in multivariate non-stationary time series exhibiting oscillatory behaviour. We approximate the process through a piecewise function defined by a sum of sinusoidal functions with unknown frequencies and amplitudes plus noise. The inference for this model is non-trivial. However, discretising the parameter space allows us to recast this complex estimation problem into a more tractable linear model, where the covariates are Fourier basis functions. Then, any change-point detection algorithms for segmentation can be used. The advantage of our proposal is that it bypasses the need for trans-dimensional Markov chain Monte Carlo algorithms used by state-of-the-art methods. Through simulations, we demonstrate that our method is significantly faster than existing approaches while maintaining comparable numerical accuracy. We also provide high probability bounds on the change-point localization error. We apply our methodology to climate and EEG sleep data. |
| title | Computationally efficient segmentation for non-stationary time series with oscillatory patterns |
| topic | Methodology Computation |
| url | https://arxiv.org/abs/2601.22999 |