A review on singular spectrum analysis for economic and financial time series

In recent years Singular Spectrum Analysis (SSA), a relatively novel but powerful technique in time series analysis, has been developed and applied to many practical problems across different fields. In this paper we review recent developments in the theoretical and methodological aspects of the SSA from the perspective of analyzing and forecasting economic and financial time series, and also represent some new results. In particular, we (a) show what are the implications of SSA for the, frequently invoked, unit root hypothesis of economic and financial times series; (b) introduce two new versions of SSA, based on the minimum variance estimator and based on perturbation theory; (c) discuss the concept of causality in the context of SSA; and (d) provide a variety of simulation results and real world applications, along with comparisons with other existing methodologies.