Recurrent Forecasting in Singular Spectrum Decomposition †

Abstract

In this paper, the Recurrent Singular Spectrum Decomposition (R-SSD) algorithm is proposed as an improvement over the Recurrent Singular Spectrum Analysis (R-SSA) algorithm for forecasting non-linear and non-stationary narrowband time series. R-SSD modifies the embedding step of the basic SSA method to reduce energy residuals. This paper conducts simulations and real-case studies to investigate the properties of the R-SSD method and compare its performance with R-SSA. The results show that R-SSD yields more accurate forecasts in terms of ratio root mean squared errors (RRMSEs) and ratio mean absolute errors (RMAEs) criteria. Additionally, the Kolmogorov–Smirnov Predictive Accuracy (KSPA) test indicates significant accuracy gains with R-SSD over R-SSA, as it measures the maximum distance between the empirical cumulative distribution functions of recurrent prediction errors and determines whether a lower error leads to stochastically less error. Finally, the non-parametric Wilcoxon test confirms that R-SSD outperforms R-SSA in filtering and forecasting new data points.