Vector and recurrent singular spectrum analysis: which is better at forecasting?

Abstract

Singular Spectrum Analysis (SSA) is an increasingly popular and widely adopted filtering and forecasting technique which is currently exploited in a variety of fields. Given its increasing application and superior performance in comparison to other methods, it is pertinent to study and distinguish between the two forecasting variations of SSA. These are referred to as Vector SSA (SSA-V) and Recurrent SSA (SSA-R). The general notion is that SSA-V is more robust and provides better forecasts than SSA-R. This is especially true when faced with time series which are non-stationary and asymmetric, or affected by unit root problems, outliers or structural breaks. However, currently there exists no empirical evidence for proving the above notions or suggesting that SSA-V is better than SSA-R. In this paper, we evaluate out-of-sample forecasting capabilities of the optimised SSA-V and SSA-R forecasting algorithms via a simulation study and an application to 100 real data sets with varying structures, to provide a statistically reliable answer to the question of which SSA algorithm is best for forecasting at both short and long run horizons based on several important criteria.

The Effect of Data Transformation on Singular Spectrum Analysis for Forecasting

“…There are two different algorithms for forecasting with SSA, namely recurrent forecasting and vector forecasting [12,28]. Those interested in a comparison of the performance of both algorithms are referred to [25]. Both of these forecasting algorithms require that one follows two common steps of SSA, the decomposition and reconstruction of a time series [12,28].…”

“…Regardless of its wide and varied applications, researchers have yet to explore the effect of data transformations on the forecasting performance of this nonparametric forecasting technique. Previously, in [25], the authors evaluated the forecasting performance of the two basic SSA algorithms under different data structures. However, their work did not extend to evaluating the impact of data transformations to provide empirical evidence for future research.…”

A New Signal Processing Approach for Discrimination of EEG Recordings

“…In contrast to the popular binary approach for eigenvalue selection in SSA, [46] introduced a new approach based on Colonial Theory, which appreciates that for more complex time series, a binary approach to reconstruction would not suffice. Ghodsi et al [47] considered an extensive study of the characteristics underlying 100 real data sets and its influence on the selection of SSA choices when decomposition and reconstruction are based on the [44] algorithm. They found the distribution of data, stationarity, frequencies and series length to be factors enabling differentiation between the best SSA forecasting approaches.…”

Weighted Linear Recurrent Forecasting in Singular Spectrum Analysis

“…Moreover, the SSA-V approach has shown better performance in the presence of outliers [27]. Recently, a comprehensive investigation was conducted in [28] to compare the forecasting capabilities of SSA-R and SSA-V forecasting algorithms via a simulation study and an application to 100 real data sets with varying structures from different fields. Statistically reliable results in [28] indicate that on average, SSA-V forecasts are better in comparison to SSA-R as reported in [23,29].…”

“…Recently, a comprehensive investigation was conducted in [28] to compare the forecasting capabilities of SSA-R and SSA-V forecasting algorithms via a simulation study and an application to 100 real data sets with varying structures from different fields. Statistically reliable results in [28] indicate that on average, SSA-V forecasts are better in comparison to SSA-R as reported in [23,29]. However, it is noteworthy that sample sizes and forecasting horizons were found to have an influence on which algorithm is more appropriate for forecasting with SSA.…”