Fast and Accurate Anomaly Detection in Time Series

2026-07-02

AI Summary

This study addresses the challenges in time series anomaly detection posed by extreme class imbalance and scarce labeled data, which hinder supervised approaches and lead to high false positive rates in unsupervised methods. To overcome these limitations, the authors propose an unsupervised detection framework that integrates Haar discrete wavelet transform with a tailored t-test. By decomposing the signal across multiple scales and applying statistically grounded significance testing, the method effectively identifies anomalies without requiring labeled data. This work is the first to synergistically combine Haar wavelets with theoretically justified t-tests, substantially reducing false positives while enhancing detection accuracy. Extensive experiments on 343 real-world datasets demonstrate that the proposed approach outperforms current state-of-the-art unsupervised and self-supervised methods in both detection speed and accuracy.

Abstract

Anomaly detection is a critical and evolving field in Machine Learning, with applications targeting different domains such as cybersecurity, finance, healthcare, manufacturing and IoT (Internet of Things) systems. Traditionally, anomaly detection algorithms have been designed using both supervised and unsupervised learning paradigms. The fundamental challenge in real-world anomaly detection scenarios is related to the inherent class imbalance (anomalies are typically rare) and, for supervised methods, to the scarcity of labelled anomalous data. Indeed, labelling is both expensive and time-consuming. Conversely unsupervised methods do not require labelling, but may suffer from high false positive rates when deployed in safety-critical applications. In this work we introduce a novel unsupervised algorithm for anomaly detection in time series based on the Haar discrete wavelet and a suitably designed $t$-test. We establish the theoretical foundation of the proposed $t$-test and, through extensive experimentation across 343 datasets, demonstrate that our algorithm outperforms state-of-the-art unsupervised and self-supervised benchmarks.

Problem

• anomaly detection
• time series
• class imbalance
• unsupervised learning
• false positive rate

Innovation

• Haar wavelet
• t-test
• unsupervised anomaly detection
• time series
• class imbalance