Time Series Outlier Detection using Penalised Regression

Abstract

Outliers in time series data pose challenges for both accurate outlier detection and reliable parameter estimation. 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 parameter ensures nonzero values are only retained at the location of the outliers. We develop different model specifications for innovative outliers, where the effect of the outlier propagates into the future, and additive outliers, where the effect of the outlier is only present at the current period. We use proximal gradient descent to achieve efficient estimation, and the effect of outlier identification is examined with both soft thresholding and hard thresholding. A Bayesian information criterion is used to select between different penalty parameters, thresholding functions, and the specifications of the type of outlier. Simulations show that our method outperforms the existing robust estimation methods of time series models in both outlier identification and model estimation.