Time Series Outlier Detection using Penalised Regression
Abstract
Outliers in time series data pose challenges for both accurate outlier detection and reliable parameter estimation, which can in turn affect forecasting performance. We adopt a penalised regression approach to reliably estimate ARMA models in the presence of outliers, which are identified through mean shift parameters assigned to each time period. Regularisation of the mean shift parameters ensures that nonzero values are retained only at the locations of outliers. We develop different model specifications for innovative outliers, where the effect propagates into future observations, and additive outliers, where the effect is confined to the current period. Estimation is carried out using proximal gradient descent to achieve computational efficiency, and the effect of outlier identification is examined using both soft and hard thresholding. Simulations show that our method outperforms existing robust estimation approaches in terms of outlier identification and model estimation.