Singular Spectrum Analysis

Using R

Hossein Hassani, Rahim Mahmoudvand

• Publisher: Palgrave Pivot
• Year: 2018
• Print ISBN: 9781137409508
• eBook ISBN: 9781137409515
• Topic: Business
• Subtopic: Business General
• Index: Business

This book provides a broad introduction to computational aspects of Singular Spectrum Analysis (SSA) which is a non-parametric technique and requires no prior assumptions such as stationarity, normality or linearity of the series. This book is unique as it not only details the theoretical aspects underlying SSA, but also provides a comprehensive guide enabling the user to apply the theory in practice using the R software. Further, it provides the user with step- by- step coding and guidance for the practical application of the SSA technique to analyze their time series databases using R. The first two chapters present basic notions of univariate and multivariate SSA and their implementations in R environment. The next chapters discuss the applications of SSA to change point detection, missing-data imputation, smoothing and filtering. This book is appropriate for researchers, upper level students (masters level and beyond) and practitioners wishing to revive their knowledge of times series analysis or to quickly learn about the main mechanisms of SSA.

© The Author(s) 2018

Hossein Hassani and Rahim MahmoudvandSingular Spectrum AnalysisPalgrave Advanced Texts in Econometricshttps://doi.org/10.1057/978-1-137-40951-5_1

Begin Abstract

1. Univariate Singular Spectrum Analysis

Hossein Hassani¹ and Rahim Mahmoudvand²

(1)

Research Institute of Energy Management and Planning, University of Tehran, Tehran, Iran

(2)

Department of Statistics, Bu-Ali Sina University, Hamedan, Iran

Hossein Hassani

Email: [email protected]

Abstract

A concise description of univariate Singular Spectrum Analysis (SSA) is presented in this chapter. A step-by-step guide for performing filtering, forecasting as well as forecasting interval using univariate SSA and associated R codes is also provided. After reading this chapter, the reader will be able to select two basic, but very important, choices of SSA: window length and number of singular values. The similarity and dissimilarity between SSA and principal component analysis (PCA) is also briefly deliberated.

Keywords

Univariate SSAWindow lengthSingular valuesReconstructionForecasting

End Abstract

1.1 Introduction

There are several different methods for analysing time series all of which have sensible applications in one or more areas. Many of these methods are largely parametric, for example, requiring linearity or nonlinearity of a particular form. An alternative approach uses non-parametric techniques that are neutral with respect to problematic areas of specification, such as linearity, stationarity and normality. As a result, such techniques can provide a reliable and often better means of analysing time series data. Singular Spectrum Analysis (SSA) is a relatively new non-parametric method that has proved its capability in many different time series applications ranging from economics to physics. For the history of SSA, see Broomhead et al. (1987), and Broomhead and King (1986a, b). SSA has subsequently been developed in several ways including multivariate SSA (Hassani and Mahmoudvand 2013), SSA based on minimum variance (Hassani 2010) and SSA based on perturbation (Hassani et al. 2011b) (for more information, see San...

Table of contents

• Cover
• Front Matter
• 1. Univariate Singular Spectrum Analysis
• 2. Multivariate Singular Spectrum Analysis
• 3. Applications of Singular Spectrum Analysis
• 4. More on Filtering and Forecasting by SSA
• Back Matter