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.

翻译：本文提出了一种新颖的方法，用于检测具有振荡行为的多元非平稳时间序列中的变点并学习其参数。我们通过一个分段函数来近似该过程，该函数由具有未知频率和振幅的正弦函数之和加上噪声构成。该模型的推断并非易事。然而，通过对参数空间进行离散化，我们可以将这个复杂的估计问题转化为一个更易处理的线性模型，其中协变量是傅里叶基函数。随后，任何用于分割的变点检测算法均可应用。我们方法的优势在于，它绕过了当前最先进方法所使用的跨维度马尔可夫链蒙特卡洛算法的需求。通过模拟实验，我们证明我们的方法在保持可比数值精度的同时，速度显著快于现有方法。我们还给出了变点定位误差的高概率界。我们将我们的方法应用于气候数据和脑电图睡眠数据。