# Real-time and adaptive anomaly detection algorithm for cyclostationary models

arXiv: https://arxiv.org/abs/2609.09326 · HTML: https://mlsanity.com/paper/2609.09326/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 39 references that are in the map.
- First posted on arXiv 8 Sep 2026.

## Builds on (most cited first, 8 of 8)

- [Anomaly Transformer: Time Series Anomaly Detection with Association Discrepancy](https://mlsanity.com/paper/2110.02642/) (2021)
- [PyOD: A Python Toolbox for Scalable Outlier Detection](https://mlsanity.com/paper/1901.01588/) (2019)
- [PyOD 2: A Python Library for Outlier Detection with LLM-powered Model Selection](https://mlsanity.com/paper/2412.12154/) (2024)
- [Research on Cloud Platform Network Traffic Monitoring and Anomaly Detection System based on Large Language Models](https://mlsanity.com/paper/2504.17807/) (2025)
- [Empirical study of periodic autoregressive models with additive noise -- estimation and testing](https://mlsanity.com/paper/2302.07070/) (2023)
- [Identification and validation of periodic autoregressive model with additive noise: finite-variance case](https://mlsanity.com/paper/2308.11265/) (2023)
- [Fractional lower-order covariance-based measures for cyclostationary time series with heavy-tailed distributions: application to dependence testing and model order identification](https://mlsanity.com/paper/2604.13689/) (2026)
- [A systematic framework for the identification and statistical quantification of impulsivity in condition monitoring signals](https://mlsanity.com/paper/2608.08391/) (2026)

## Abstract (arXiv)

This article introduces PeriodicCALM, an effective real-time anomaly detection framework designed for cyclostationary data streams. While classical cyclostationary processes feature periodically time-varying statistical properties, real-world signals often contain recurring impulsive components that conceal abnormal behavior. Existing real-time methods for struggle with these dynamics, frequently misinterpreting phase-dependent variability as non-cyclic anomalies and causing excessive false alarms. To address this, PeriodicCALM incorporates cycle-dependent variability to systematically ignore regular cyclic impulses while accurately isolating genuine anomalies. Operating in real time with continuous retraining capabilities, the method adapts dynamically to evolving signal characteristics. Comparative evaluations against the baseline CALM framework using simulated data demonstrate significant improvements in detection accuracy and training efficiency, alongside a reduction in prediction latency. Furthermore, the practical utility of PeriodicCALM is validated on real-world vibration signals collected from a compressor monitoring system.