Long-Term Outlier Prediction Through Outlier Score Modeling

Abstract

This study addresses an important gap in time series outlier detection by proposing a novel problem setting: long-term outlier prediction. Conventional methods primarily focus on immediate detection by identifying deviations from normal patterns. As a result, their applicability is limited when forecasting outlier events far into the future. To overcome this limitation, we propose a simple and unsupervised two-layer method that is independent of specific models. The first layer performs standard outlier detection, and the second layer predicts future outlier scores based on the temporal structure of previously observed outliers. This framework enables not only pointwise detection but also long-term forecasting of outlier likelihoods. Experiments on synthetic datasets show that the proposed method performs well in both detection and prediction tasks. These findings suggest that the method can serve as a strong baseline for future work in outlier detection and forecasting.

Figures (6)

• Figure 1: Illustrative example of the proposed approach. The time series (including outliers) is given up to time $T = 500$. Conventional methods calculate outlier scores using only past values, which prevents the detection of future anomalies. However, if a regular pattern such as periodicity exists in the outlier scores, this structure can be used to anticipate future scores.
• Figure 2: The Beijing temperature dataset used in our experiments. The top plot shows the original time series with artificially inserted periodic outliers. The bottom plot shows the outlier scores calculated by the detection layer (left half) and the predicted scores produced by the prediction layer (right half), starting at time point 1000.
• Figure 3: Predicted outlier scores for the synthetic time series in the test interval ($t = 1000$ to $1500$). The solid line shows the original time series with periodic anomalies. The dashed line shows the predicted outlier scores. Their peaks align with the injected outliers, indicating perfect long-term prediction.
• Figure 4: Predicted outlier scores for the Beijing temperature data during the test interval. The solid line represents the original series with periodic outliers, and the dashed line represents the predicted scores. The synchronization between the two indicates successful long-term forecasting. All values are normalized.
• Figure 5: Bivariate real dataset (Beijing temperature and pressure) with correlated outliers. The blue and orange lines indicate temperature and pressure, respectively. The pressure series consistently shows outliers 10 time steps after the temperature spikes. All values are normalized.