# Detection of collective and point anomalies at the presence of trend and seasonality

## TL;DR

This paper introduces a new method for detecting both collective and point anomalies in time series data that accounts for trends and seasonality, with proven statistical accuracy and practical effectiveness.

## Contribution

It presents a novel approach that simultaneously detects various anomaly types in complex time series, overcoming limitations of existing methods.

## Key findings

- Accurately decomposes time series into anomaly, trend, seasonality, and residual components.
- Consistently estimates the number and locations of anomalies with minimal error.
- Demonstrates strong detection performance in simulations and real energy price data.

## Abstract

Detecting anomalies in time series data is a challenging task with broad relevance in many applications. Existing methods work effectively only under idealized conditions, typically focusing on point anomalies or assuming a constant baseline. Our approach overcomes these limitations by detecting both collective and point anomalies, while allowing for polynomial trends and seasonal patterns. We establish statistical theory demonstrating that our method accurately decomposes the time series into anomaly, trend, seasonality, and a remainder component. We further show that it estimates the number of anomalies consistently and their locations with minimal error. Simulation studies confirm its strong detection performance with finite samples, and an application to energy price data illustrates its practical utility. An R package is available on request.