cs.LGMar 22, 2026

Long-Term Outlier Prediction Through Outlier Score Modeling

Authors: Yuma Aoki, Joon Park, Koh Takeuchi, Hisashi Kashima, Shinya Akimoto, Ryuichi Hashimoto, Takahiro Adachi, Takeshi Kishikawa, +1 more

Organizations: Nara Institute of Science and Technology · Kyoto University · Panasonic Holdings Corporation

Read PDF
Ask AI
Cite

Copy citation

DOINot available for this paper

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 & tables

Figure 1: Illustrative example of the proposed approach. The time series (including outliers) is given up to time T=500T=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=1000t=1000 to 15001500 ). 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.
Prediction horizon kk1234567891011121314
Variable x(1)x^{(1)}1.001.001.001.001.001.001.001.001.001.000.450.450.490.49
Variable x(2)x^{(2)}0.400.390.390.420.430.440.450.480.500.510.490.450.460.46
Table 1: Long-term prediction accuracy for the synthetic bivariate time series. The AUC for each prediction horizon kk is shown. The first variable is predictable up to k=10k=10 due to the known delay, while the second variable remains unpredictable.
Prediction horizon kk1234567891011121314
Pressure0.830.870.960.870.870.970.970.970.970.960.520.450.480.47
Temperature0.410.340.390.400.430.460.490.500.490.490.490.490.480.45
Table 2: Long-term prediction accuracy for the Beijing bivariate time series. The AUC for each prediction horizon kk is shown. As in the synthetic data, the pressure series is predictable up to k=10k=10 due to its causal dependency, while the temperature series remains unpredictable.
Figure 6: Example of long-term outlier score prediction in the Beijing bivariate dataset. The prediction is made at T=10600T=10600 . The solid lines show the true outlier scores before prediction time. A spike in the temperature score at 1059710597 indicates an outlier. The dashed lines show the predicted scores, and the rise in the pressure score at 1060710607 confirms successful forecasting.

Explore similar work

CardsList

  1. Forecasting Anomaly Precursors via Uncertainty-Aware Time-Series Ensembles

    Feb 19, 2026Hyeongwon Kang, Jinwoo Park, Seunghun Han +1Time-Series Anomaly DetectionUnsupervised Anomaly Detection

    Department of Industrial & Management Engineering, Korea University, 126-16 Anam-dong 5-ga, Seongbuk-gu, Seoul, Republic of Korea · Department of Industrial Engineering, Seoul National University, Gwanak-ro 1, Gwanak-gu, Seoul, Republic of Korea · LG CNS, 71, Magokjungang 8-ro, Gangseo-gu, Seoul, Republic of Korea

  2. XLinear: Frequency-Enhanced MLP with CrossFilter for Robust Long-Range Forecasting

    Mar 4, 2026Xiang AoTime Series ForecastingLong-Term Time Series Forecasting

    School of Software Engineering, Beijing Jiaotong University, Beijing, China

  3. TA-SparseMG: Trend-Aware Sparse Forecasting via Multi-Scale Gating for Long-Term Time Series

    Jun 26, 2026Wenchao Liu, Hongbing Wang, Youji Zhu +2Long-Term Time Series ForecastingNon-Stationary Time Series Forecasting

    School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China. · School of Big Data and Computer Science, Guizhou Normal University, Guiyang 550025, China.