Singular Spectrum Analysis

Over the last 15 years, singular spectrum analysis (SSA) has proven very successful. It has already become a standard tool in climatic and meteorological time series analysis and well known in nonlinear physics and signal processing.

This book presents two new decomposition methods to decompose a time series in intrinsic components of low and high frequencies. The methods are based on Singular Value Decomposition (SVD) of a Hankel matrix (HSVD). The proposed decomposition is used to improve the accuracy of linear and nonlinear auto-regressive models.

This book presents two new decomposition methods to decompose a time series in intrinsic components of low and high frequencies. The methods are based on Singular Value Decomposition (SVD) of a Hankel matrix (HSVD). The proposed decomposition is used to improve the accuracy of linear and nonlinear auto-regressive models.

This book presents two new decomposition methods to decompose a time series in intrinsic components of low and high frequencies. The methods are based on Singular Value Decomposition (SVD) of a Hankel matrix (HSVD). The proposed decomposition is used to improve the accuracy of linear and nonlinear auto-regressive models.

The main goal of this comprehensive textbook is to cover the core techniques required to understand some of the basic and most popular model learning algorithms available for engineers, then illustrate their applicability directly with stationary time series. A multi-step approach is introduced for modeling time series which differs from the mainstream in the literature. Singular spectrum analysis of univariate time series, trend and seasonality modeling with least squares and residual analysis, and modeling with ARMA models are discussed in more detail.