All Times ET
Keywords: Singular Spectrum Analysis, Functional Singular Value Decomposition, Time Series Data, Functional Data Analysis
In this work, we develop two novel algorithms designed to provide nonparametric forecasts of multivariate functional time series (MFTS) data. The methodologies are extensions to the multivariate functional singular spectrum analysis (MFSSA) technique which is used to decompose a MFTS into informative trend, periodic, and mean components. It was found that the MFSSA approach is the ideal algorithm in performing signal extraction of a MFTS. In addition the MFSSA algorithm was developed to be able to handle MFTS whose variables might be observed over different dimensional domains allowing for decomposition of smoothed images and functional curves in a joint fashion. Since MFSSA provided the best results for signal extraction of a MFTS and the approach is flexible, it is expected that the proposed MFSSA-based forecasting algorithms of MFSSA recurrent and MFSSA vector forecasting (MFSSA R-forecasting and MFSSA V-forecasting respectively) will give more accurate and flexible forecasts as compared to other approaches. In the following, we first provide the theoretical details that support the methods. In addition, we also provide a real data study showcasing that the MFSSA R-forecasting and MFSSA V-forecasting approaches are superior in terms of accuracy in forecasting MFTS as compared to univariate functional singular spectrum analysis-based forecasting approaches applied to variables in an independent fashion. The goal is to continue to develop the MFSSA-based forecasting approaches to incorporate the flexibility of MFSSA so that predictions of smoothed image data and functional curves in a joint fashion may be made and to compare the novel approaches to other nonparametric techniques used in the forecasting of MFTS signals.