Time Series Components Separation Based on Singular Spectral Analysis Visualization: an HJ-biplot Method Application

Abstract

The extraction of essential features of any real-valued time series is crucial for exploring, modeling and producing, for example, forecasts. Taking advantage of the representation of a time series data by its trajectory matrix of Hankel constructed using Singular Spectrum Analysis, as well as of its decomposition through Principal Component Analysis via Partial Least Squares, we implement a graphical display employing the biplot methodology. A diversity of types of biplots can be constructed depending on the two matrices considered in the factorization of the trajectory matrix. In this work, we discuss the called HJ-biplot which yields a simultaneous representation of both rows and columns of the matrix with maximum quality. Interpretation of this type of biplot on Hankel related trajectory matrices is discussed from a real-world data set.