Advanced Spectral Methods and Their Potential in Forecasting Fuzzy-Valued and Multivariate Financial Time Series

In this paper we explore the effectiveness of two nonparametric methods, based upon a matrix spectral decomposition approach, namely the Independent Component Analysis (ICA) and the Singular Spectrum Analysis (SSA). The intended area of applications is that of forecasting fuzzy-valued and multivariate time series. Given a multivariate time series, ICA assumes that each of its components is a mixture of several independent underlying factors. Separating such distinct time-varying causal factors becomes crucial in multivariate financial time series analysis, when attempting to explain past co-movements and to predict future evolutions. The multivariate extension of SSA (MSSA) can be employed as a powerful prediction tool, either separately, or in conjunction with ICA. As a first application, we use MSSA to recurrently forecasting triangular-shaped fuzzy monthly exchange rates, thus aiming at capturing both the randomness and the fuzziness of the financial process. A hybrid ICA-SSA approach is also proposed. The primarily role of ICA is to reveal certain fundamental factors behind several parallel series of foreign exchange rates. More accurate predictions can be performed via these independent components, after their separation. MSSA is employed to compute forecasts of independent factors. Afterwards, these forecasts of underlying factors are remixed into the forecasts of observable foreign exchange rates.