Theoretical advancements and applications in singular spectrum analysis.

Abstract

Singular Spectrum Analysis (SSA) is a nonparametric time series analysis and forecasting technique which has witnessed an augment in applications in the recent past. The increased application of SSA is closely associated with its superior filtering and signal extraction capabilities which also differentiates it from the classical time series methods. In brief, the SSA process consists of decomposing a time series for signal extraction and then reconstructing a less noisy series which is used for forecasting. The aim of this research is to develop theoretical advancements in SSA, supported by empirical evidence to further promote the value, effectiveness and applicability of the technique in the field of time series analysis and forecasting. To that end, this research has four main contributions. Initially, given the reliance of this research towards improving forecasting processes, it is mandatory to compare and distinguish between the predictive accuracy of forecasts for statistically significant differences. The first contribution of this research is the introduction of a complement statistical test for comparing between the predictive accuracy of two forecasts. The proposed test is based on the principles of cumulative distribution functions and stochastic dominance, and is evaluated via both a simulation study and empirical evidence. Governments, practitioners, researchers and private organizations publish a variety of forecasts each year. Such forecasts are generally computed using multivariate models and are widely used in decision making processes given the considerably high level of anticipated forecast accuracy. The classical multivariate methods consider modelling multiple information pertaining to the same time period or with a time lag into the past. Multivariate Singular Spectrum Analysis (MSSA) is a relatively new and alternative technique for generating forecasts from multiple time series. The second contribution of this research is the introduction of a novel theoretical development which seeks to exploit the information contained in published forecasts (which represent data with a time lag into the future) for generating a new and improved (comparatively more accurate) forecast by taking advantage of the MSSA technique’s capability at modelling time series with different series lengths. In brief, the proposed multivariate theoretical development seeks to exploit the forecastability of forecasts by considering not only official and professional forecasts, but also forecasts obtained via other time series models. The productive application of SSA and MSSA depends largely on the selection of SSA and MSSA parameters, i.e. the Window Length, L, and the number of eigenvalues r which are used for decomposition and reconstruction of time series. Over the years, a variety of mathematically complex, time consuming and labour intensive approaches which require detailed knowledge on the theory underlying SSA have been proposed and developed for the selection of SSA and MSSA parameters. However, the highly labour intensive and complex nature of such approaches have not only discouraged the application of this method by those not conversant with the underlying theory, but also limited SSA and MSSA to offline applications. The third and final contribution of this research proposes new, automated and optimized, SSA and MSSA algorithms for the selection of SSA parameters and thereby enables obtaining optimal SSA and MSSA forecasts (optimized by minimising a loss function). This development opens up the possibility of using SSA and MSSA for online forecasting in the future.