A new parsimonious recurrent forecasting model in singular spectrum analysis

• Published date: 01 March 2018
• Date: 01 March 2018
• Author: Paulo Canas Rodrigues,Rahim Mahmoudvand
• DOI: http://doi.org/10.1002/for.2484

Received: 15 October 2015 Revised: 29 November 2016 Accepted: 26 May 2017

DOI: 10.1002/for.2484

RESEARCH ARTICLE

A new parsimonious recurrent forecasting model in singular

spectrum analysis

Rahim Mahmoudvand1,2 Paulo Canas Rodrigues2,3

1Department of Statistics, Bu-Ali Sina

University,Hamedan, Iran

2Department of Statistics, Federal

University of Bahia, Salvador,BA, Brazil

3Center for Applied Statistics and Data

Analytics, Faculty of Natural Sciences,

University of Tampere, Tampere,Finland

Correspondence

Rahim Mahmoudvand, Department of

Statistics, Bu-Ali Sina University,Hamedan,

Iran. P.O.Box6517838695

Email: r.mahmodvand@gmail.com

Abstract

Singular spectrum analysis (SSA) is a powerful nonparametric method in the area of

time series analysis that has shown its capability in different applications areas. SSA

depends on two main choices: the window length Land the number of eigentriples

used for grouping r. One of the most important issues when analyzing time series

is the forecast of new observations. When using SSA for time series forecasting

there are several alternative algorithms, the most widely used being the recurrent

forecasting model, which assumes that a given observation can be written as a linear

combination of the L−1 previous observations. However, when the windowlengt h

Lis large, the forecasting model is unlikely to be parsimonious. In this paper we

propose a new parsimonious recurrent forecasting model that uses an optimal m(<

L−1) coefficients in the linear combination of the recurrent SSA. Our results support

the idea of using this new parsimonious recurrent forecasting model instead of the

standard recurrent SSA forecasting model.

KEYWORDS

bootstrap, singular spectrum analysis, window length

1INTRODUCTION

The whole procedure of singular spectrum analysis (SSA)

depends upon two basic, but very important, choices: (i) the

window length, L; and (ii) the number of eigenvalues rthat

need to be selected to reconstruct a noise-free series from a

noisy time series. The choice of Ldepends on the dataset to

be analyzed and on the kind of analysis to be performed. An

improper choice of Limplies an inferior decomposition and/or

a less parsimonious forecasting model.

Elsner and Tsonis (1997) provide some discussion on the

choice of window length and remark that choosing L=T∕4

(where Tis series length) is a common practice. Golyandina,

Nekrutkin, and Zhigljavsky (2001) recommend that Lshould

be large enough but not larger than T∕2. Another general rec-

ommendation is to choose a value of Lproportional to the

number of periods (i.e., proportional to 12 for a monthly time

series), which is especially important while doing the recon-

struction. Large values of Lallow longer period oscillations

to be resolved, but choosing Ltoo large leaves too few obser-

vations to estimate the covariance matrix of the Lvariabl es.

Although considerable attempts and various techniques have

been considered for selecting the proper value of L,thereis

not enough algebraic and theoretical materials for choosing L.

The choice of Lis closely related to the most widely used

forecasting algorithm for SSA—the recurrent SSA—as it

assumes that a given observation/forecast can be written as a

linear combination of the L−1 previous observations. In this

paper we propose a new parsimonious recurrent forecasting

model that uses an optimal m(<L−1) coefficients in the

linear combination of the recurrent SSA, aiming at more pre-

cise forecasts. Although our proposal is more time consuming

than the standard recurrent SSA forecasting model, we expect

a major improvement in forecast accuracy.

The rest of the paper is structured as follows. In Section

2 we give a brief description of the SSA, including smooth-

Journal of Forecasting.2018;37:191–200. wileyonlinelibrary.com/journal/for Copyright © 2017 John Wiley & Sons, Ltd. 191