# Structural Classification of Locally Stationary Time Series Based on Second-order Characteristics

arXiv: https://arxiv.org/abs/2507.04237 · HTML: https://mlsanity.com/paper/2507.04237/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 52 references that are in the map.
- First posted on arXiv 6 Jul 2025.

## Builds on (most cited first, 10 of 10)

- [Deep learning for time series classification: a review](https://mlsanity.com/paper/1809.04356/) (2018)
- [Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network](https://mlsanity.com/paper/1808.03314/) (2018)
- [ROCKET: Exceptionally fast and accurate time series classification using random convolutional kernels](https://mlsanity.com/paper/1910.13051/) (2019)
- [MultiRocket: Multiple pooling operators and transformations for fast and effective time series classification](https://mlsanity.com/paper/2102.00457/) (2021)
- [A Time Series Forest for Classification and Feature Extraction](https://mlsanity.com/paper/1302.2277/) (2013)
- [HYDRA: Competing convolutional kernels for fast and accurate time series classification](https://mlsanity.com/paper/2203.13652/) (2022)
- [Discriminant Analysis of Time Series in the Presence of Within-Group Spectral Variability](https://mlsanity.com/paper/1509.06358/) (2015)
- [Predictive, finite-sample model choice for time series under stationarity and non-stationarity](https://mlsanity.com/paper/1611.04460/) (2016)
- [Prediction in locally stationary time series](https://mlsanity.com/paper/2001.00419/) (2020)
- [On the partial autocorrelation function for locally stationary time series: characterization, estimation and inference](https://mlsanity.com/paper/2401.15778/) (2024)

## Built on by (most cited first, 2 of 2)

- [Beyond In-Domain Detection: SpikeScore for Cross-Domain Hallucination Detection](https://mlsanity.com/paper/2601.19245/) (2026)
- [TimEE: End-to-end Time Series Classification via In-Context Learning](https://mlsanity.com/paper/2607.07500/) (2026)

## Abstract (arXiv)

Time series classification is crucial for numerous scientific and engineering applications. In this article, we present a numerically efficient, practically competitive, and theoretically rigorous classification method for distinguishing between two classes of locally stationary time series based on their time-domain, second-order characteristics. Our approach builds on the autoregressive approximation for locally stationary time series, combined with an ensemble aggregation and a distance-based threshold for classification. It imposes no requirement on the training sample size, and is shown to achieve zero misclassification error rate asymptotically when the underlying time series differ only mildly in their second-order characteristics. The new method is demonstrated to outperform a variety of state-of-the-art solutions, including wavelet-based, tree-based, convolution-based methods, as well as modern deep learning methods, through intensive numerical simulations and a real EEG data analysis for epilepsy classification.