Multivariate Functional Singular Spectrum Analysis Over Different Dimensional Domains

A common problem in time series analysis is detection, extraction, and exploration of mean, seasonal, trend, and noise components in time series data. A technique known as singular spectrum analysis (SSA) has been developed as a nonparametric, exploratory method which can be used to identify such interesting components in ordinary time series where observations are scalars (Golyandina et al., 2001). Often times, many variables are observed as a result of a single stochastic process and investigation of time series components can be made richer by performing a multivariate analysis of these vector observations. The MSSA algorithm is a technique that has seen success over its univariate SSA counterpart in decomposing a multidimensional time series into components if the covariates are moderately correlated (Golyandina and Stepanov, 2012). MSSA also has been broken up into two approaches of vertical MSSA (VMSSA) and horizontal MSSA (HMSSA) where VMSSA involves the vertical stacking of univariate Hankel trajectory matrices while HMSSA works with the horizontal stacking of the same elements (Hassani and Mahmoudvand, 2018). Over the course of the last 15 years, MSSA has seen significant success in various areas of application see Groth and Ghil (2011); Golyandina and Stepanov (2012); Silva et al. (2018); Hassani et al. (2019). Functional data analysis embodies the evaluation and exploration of data that is comprised of functions such as curves or surfaces (Ramsay and Silverman, 2005). Functional PCA (FPCA) is a technique that is used to find the most informative directions in a timeindependent collection of functional subjects (Ramsay and Silverman, 2005). Univariate Functional Singular Spectrum Analysis (FSSA) was developed by Haghbin et al. (2019) as a novel technique that is used to decompose a time-dependent collection of functional