Simultaneous detection of change points and outliers

In time series analysis, the coexistence of structural mean shifts and transient anomalies can distort statistical inference, making it essential to distinguish and estimate both phenomena simultaneously.However, existing methods typically handle change points and outliers separately or focus exclusively on only one type of variation, failing to provide an integrated solution.In this paper, we extend a standard mean-shift change point model to concurrently detect both change points and outliers by incorporating either an ℓ 0 (hard-thresholding) or an ℓ 1 (soft-thresholding) penalty for outlier identification.We compare their empirical performance through simulations across varying noise levels and outlier frequencies, evaluating change point detection accuracy and outlier identification rates.We also analyze how each penalty's theoretical properties are reflected in practice.Finally, we apply our method to real accelerometer sensor data, demonstrating its practical utility in accurately localizing both activity transitions and transient sensor spikes within a unified framework.