Robust singular spectrum analysis: comparison between classical and robust approaches for model fit and forecasting

Singular spectrum analysis is a powerful and widely used non-parametric method to analyse and forecast time series. Although singular spectrum analysis has proven to outperform traditional parametric methods for model fit and model forecasting, one of the steps of this algorithm is the singular value decomposition of the trajectory matrix, which is very sensitive to the presence of outliers because it uses the $$L_{2}$$ L 2 norm optimization. Therefore the presence of outlying observations have a significant impact on the singular spectrum analysis reconstruction and forecasts. The main aim of this paper is to introduce four robust alternatives to the singular spectrum analysis, where the singular value decomposition is replaced by the: (i) robust regularized singular value decomposition; (ii) robust principal component analysis algorithm, which combines projection pursuit ideas with robust scatter matrix estimation; (iii) robust principal component analysis based on the grid algorithm and projection pursuit; and (iv) robust principal component analysis based on a robust covariance matrix. The four proposed robust singular spectrum analysis alternatives are compared with the classical singular spectrum analysis and other available robust singular spectrum analysis algorithms, in terms of model fit and model forecasting via Monte Carlo simulations based on synthetic and real data, considering several contamination scenarios.