Computationally efficient segmentation for non-stationary time series with oscillatory patterns

TL;DR

This work tackles offline change-point detection in high-dimensional time series with oscillatory structure by discretizing the frequency content into a finite Fourier grid and recasting within-segment inference as a sparse linear regression. It combines SuSiE-based variable selection with marginal-likelihood gains for segmentation, employing optimistic search to achieve substantial computational gains over trans-dimensional MCMC methods while preserving uncertainty quantification within segments. Theoretical guarantees yield a localization rate of order $\log T$ for the change-point estimator under realistic conditions, and simulations show CPVS matches or approaches state-of-the-art accuracy with dramatically faster runtimes. Real-data applications to EEG sleep and ENSO demonstrate interpretable, segment-specific frequency content and reliable change-point localization, highlighting the method’s scalability and practical impact for climate and neuroscience data.

Abstract

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.

Figures (15)

• Figure 1: Feature selection uncertainty with SuSiE. Uncertainty quantification around features selected using SuSiE ($N_E=2$). $T=100$ observations are generated from model \ref{['eq:model']} with $d=1$, no change points, and $\omega_1=1/30$ and $\omega_2=1/15$ ($L=2$). Panels depict $q(\gamma_e)$ obtained running the algorithms with equally spaced grid $\Omega$ for $p=250,500,1000$.
• Figure 2: Scenario 2.a: Average runtime. Left panel depicts the case with varying $(T,m)$, right panel the case with fixed $T=1000$ and varying $m$.
• Figure 3: EEG sleep data: segmentation by MCPVS and ADA-X. Segmentation provided by MCPVS and the ADA-X of bertolacci2022adaptspec. Three panels refer to distinct EEG channels (FP1-A1, C3-A1, O1-A1). Black lines depict the first-order difference of EEG recordings. Vertical lines represent the change point estimated by MCPVS (blue) and ADA-X (yellow). Sleep spindles annotated by the experts are highlighted in red.
• Figure 4: EEG sleep data: estimated frequencies and intensities by segment ($N_E=2$). Vertical lines depict the change points estimated by MCPVS. Within each segment, horizontal bars depict the maximum a posteriori frequency, the colour gradient depicts the corresponding intensity.
• Figure 5: ENSO data: estimated frequencies and intensities ($N_E=2$). Vertical lines depict the change points estimated by MCPVS. Within each segment, horizontal bars depicts the maximum a posterior frequency, the color gradient depicts the corresponding intensity.

Theorems & Definitions (7)

• Theorem 1
• Proposition 1
• Lemma 1
• proof
• Definition 1
• Lemma 2
• proof