Skip to main content
SpringerLink
Log in

Introduction: Overview

  • Chapter
  • First Online:
Singular Spectrum Analysis with R

Part of the book series: Use R! ((USE R))

  • 2338 Accesses

Abstract

Chapter 1 is introductory; it outlines the main principles and ideas of SSA, presents a unified view on SSA, reviews its computer implementation in the form of the Rssa package, compares SSA with other methods of time series analysis, gives a short literature review, and provides references to all data sources used. In this chapter, the main concepts and generic structure of all methods of the book are introduced and explained; hence, the material of Chap. 1 is essential for the rest of the book.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 64.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 84.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Alexandrov T (2009) A method of trend extraction using singular spectrum analysis. RevStat 7(1):1–22

    Google Scholar 

  • Allen M, Smith L (1996) Monte Carlo SSA: Detecting irregular oscillations in the presence of colored noise. J Clim 9(12):3373–3404

    Article  Google Scholar 

  • Andrews D, Herzberg A (1985) Data. A collection of problems from many fields for the student and research worker. Springer, New York

    Google Scholar 

  • Barrios-Muriel J, Romero F, Alonso FJ, Gianikellis K (2016) A simple SSA-based de-noising technique to remove ECG interference in EMG signals. Biomed Signal Process Control 30:117–126

    Article  Google Scholar 

  • Bozzo E, Carniel R, Fasino D (2010) Relationship between singular spectrum analysis and Fourier analysis: Theory and application to the monitoring of volcanic activity. Comput Math Appl 60(3):812–820

    Article  MathSciNet  Google Scholar 

  • Broomhead D, King G (1986) Extracting qualitative dynamics from experimental data. Physica D 20:217–236

    Article  MathSciNet  Google Scholar 

  • Broomhead D, King G (1986b) On the qualitative analysis of experimental dynamical systems. In: Sarkar S (ed) Nonlinear phenomena and chaos. Adam Hilger, Bristol, pp 113–144

    Google Scholar 

  • von Buttlar J, Zscheischler J, Mahecha MD (2014) An extended approach for spatiotemporal gapfilling: dealing with large and systematic gaps in geoscientific datasets. Nonlinear Process Geoph 21:203–215

    Google Scholar 

  • Cadzow JA (1988) Signal enhancement: a composite property mapping algorithm. IEEE Trans Acoust 36(1):49–62

    Article  MathSciNet  Google Scholar 

  • Chen Q, Weigelt M, Sneeuw N, van Dam T (2016) On time-variable seasonal signals: Comparison of SSA and Kalman filtering based approach. Springer International Publishing, Cham, pp 75–80

    Google Scholar 

  • Cleveland WS (1993) Visualizing data. Hobart Press

    Google Scholar 

  • Danilov D, Zhigljavsky A (eds) (1997) Principal components of time series: the “Caterpillar” method. St. Petersburg Press (in Russian)

    Google Scholar 

  • Filho ASF, Lima GAR (2016) Gap filling of precipitation data by SSA - singular spectrum analysis. J Phys Conf Ser 759(1):012,085

    Google Scholar 

  • Fraedrich K (1986) Estimating dimensions of weather and climate attractors. J Atmos Sci 43: 419–432

    Google Scholar 

  • Frigo M, Johnson SG (2005) The design and implementation of FFTW3. Proc IEEE 93(2):216–231

    Article  Google Scholar 

  • Genkin D, Pachmanov L, Pipman I, Tromer E, Yarom Y (2016) Ecdsa key extraction from mobile devices via nonintrusive physical side channels. In: Proceedings of the 2016 ACM SIGSAC conference on computer and communications security. ACM, New York, NY, USA, CCS ’16, pp 1626–1638

    Google Scholar 

  • Ghil M, Allen RM, Dettinger MD, Ide K, Kondrashov D, Mann ME, Robertson A, Saunders A, Tian Y, Varadi F, Yiou P (2002) Advanced spectral methods for climatic time series. Rev Geophys 40(1):1–41

    Google Scholar 

  • Golub GH, Van Loan CF (1996) Matrix computations, 3rd edn. Johns Hopkins University Press, Baltimore, MD, USA

    Google Scholar 

  • Golyandina N, Korobeynikov A (2013) Basic singular spectrum analysis and forecasting with R. Comput Stat Data Anal 71:943–954

    Google Scholar 

  • Golyandina N, Osipov E (2007) The “Caterpillar”-SSA method for analysis of time series with missing values. J Stat Plan Inference 137(8):2642–2653

    Article  MathSciNet  Google Scholar 

  • Golyandina N, Shlemov A (2015) Variations of singular spectrum analysis for separability improvement: Non-orthogonal decompositions of time series. Stat Interface 8(3):277–294

    Article  MathSciNet  Google Scholar 

  • Golyandina N, Shlemov A (2017) Semi-nonparametric singular spectrum analysis with projection. Stat Interface 10(1):47–57

    Article  MathSciNet  Google Scholar 

  • Golyandina N, Stepanov D (2005) SSA-based approaches to analysis and forecast of multidimensional time series. In: Proceedings of the 5th St.Petersburg workshop on simulation, June 26–July 2, 2005. St. Petersburg State University, St. Petersburg, pp 293–298

    Google Scholar 

  • Golyandina N, Usevich K (2010) 2D-extension of singular spectrum analysis: algorithm and elements of theory. In: Olshevsky V, Tyrtyshnikov E (eds) Matrix methods: Theory, algorithms and applications. World Scientific Publishing, pp 449–473

    Chapter  Google Scholar 

  • Golyandina N, Zhigljavsky A (2013) Singular apectrum analysis for time series. Springer briefs in statistics. Springer

    Chapter  Google Scholar 

  • Golyandina N, Nekrutkin V, Zhigljavsky A (2001) Analysis of time series structure: SSA and related techniques. Chapman&Hall/CRC

    Book  Google Scholar 

  • Golyandina N, Korobeynikov A, Shlemov A, Usevich K (2015) Multivariate and 2D extensions of singular spectrum analysis with the Rssa package. J Stat Softw 67(2):1–78

    Google Scholar 

  • Groth A, Ghil M (2015) Monte Carlo singular spectrum analysis (SSA) revisited: Detecting oscillator clusters in multivariate datasets. J Climate 28(19):7873–7893

    Article  Google Scholar 

  • Hall MJ (1998) Combinatorial theory. Wiley, New York

    Google Scholar 

  • Harris T, Yan H (2010) Filtering and frequency interpretations of singular spectrum analysis. Physica D 239:1958–1967

    Article  MathSciNet  Google Scholar 

  • Hassani H, Heravi S, Zhigljavsky A (2009) Forecasting European industrial production with singular spectrum analysis. Int J Forecast 25(1):103–118

    Article  Google Scholar 

  • Hassani H, Heravi S, Zhigljavsky A (2013) Forecasting UK industrial production with multivariate singular spectrum analysis. J Forecast 32(5):395–408

    Article  MathSciNet  Google Scholar 

  • Hassani H, Webster A, Silva ES, Heravi S (2015) Forecasting U.S. tourist arrivals using optimal singular spectrum analysis. Tourism Manag 46:322–335

    Article  Google Scholar 

  • Hudson IL, Keatley MR (2017) Singular spectrum analytic (ssa) decomposition and reconstruction of flowering: Signatures of climatic impacts. Environ Model Assess 22(1):37–52

    Article  Google Scholar 

  • Hyndman R, Athanasopoulos G (2013) Forecasting: principles and practice. OTexts, URL http://otexts.org/fpp/, accessed on 28.07.2017

  • Hyndman RJ (2013) Time Series Data Library. URL http://data.is/TSDLdemo, accessed on 10/08/2013

  • Iqelan BM (2017) A singular spectrum analysis technique to electricity consumption forecasting. Int J Eng Res Appl 7(3):92–100

    Article  Google Scholar 

  • Karnjana J, Unoki M, Aimmanee P, Wutiwiwatchai C (2017) Tampering detection in speech signals by semi-fragile watermarking based on singular-spectrum analysis. Springer International Publishing, Cham, pp 131–140

    Google Scholar 

  • Kondrashov D, Ghil M (2006) Spatio-temporal filling of missing points in geophysical data sets. Nonlinear Process Geophys 13(2):151–159

    Article  Google Scholar 

  • Korobeynikov A (2010) Computation- and space-efficient implementation of SSA. Stat Interface 3(3):357–368

    Article  MathSciNet  Google Scholar 

  • Korobeynikov A, Larsen RM, Wu KJ, Yamazaki I (2016) svd: Interfaces to various state-of-art SVD and eigensolvers. URL http://CRAN.R-project.org/package=svd, R package version 0.4

  • Korobeynikov A, Shlemov A, Usevich K, Golyandina N (2017) Rssa: A collection of methods for singular spectrum analysis. URL http://CRAN.R-project.org/package=Rssa, R package version 1.0

  • Kumar KS, Rajesh R, Tiwari RK (2017) Regional and residual gravity anomaly separation using the singular spectrum analysis-based low pass filtering: a case study from Nagpur, Maharashtra, India. Explor Geophys.

    Google Scholar 

  • Kurakin V, Kuzmin A, Mikhalev A, Nechaev A (1995) Linear recurring sequences over rings and modules. J Math Sci 76(6):2793–2915

    Article  MathSciNet  Google Scholar 

  • Lakshmi K, Rao ARM, Gopalakrishnan N (2016) Singular spectrum analysis combined with ARMAX model for structural damage detection. Struct Control Health Monit. https://doi.org/10.1002/stc.1960

  • Lisi F, Nicolis O, Sandri M (1995) Combining singular-spectrum analysis and neural networks for time series forecasting. Neural Process Lett 2(4):6–10

    Article  Google Scholar 

  • Makridakis S, Wheelwright S, Hyndman R (1998) Forecasting: Methods and applications, 3rd edn. Wiley, New York

    Google Scholar 

  • Monselesan DP, O’Kane TJ, Risbey JS, Church J (2015) Internal climate memory in observations and models. Geophys Res Lett 42(4):1232–1242

    Article  Google Scholar 

  • Mudersbach C, Wahl T, Haigh ID, Jensen J (2013) Trends in high sea levels of German North Sea gauges compared to regional mean sea level changes. Cont Shelf Res 65:111–120

    Article  Google Scholar 

  • Pepelyshev A, Zhigljavsky A (2017) Ssa analysis and forecasting of records for earth temperature and ice extents. Stat Interface 10(1):151–163

    Article  MathSciNet  Google Scholar 

  • de Prony G (1795) Essai expérimental et analytique sur les lois de la dilatabilité des fluides élastiques et sur celles de la force expansive de la vapeur de l’eau et la vapeur de l’alkool à différentes températures. J de l’Ecole Polytechnique 1(2):24–76

    Google Scholar 

  • Salgado D, Cambero I, Olivenza JH, Sanz-Calcedo JG, López PN, Plaza EG (2013) Tool wear estimation for different workpiece materials using the same monitoring system. Procedia Eng 63:608–615

    Article  Google Scholar 

  • Sella L, Vivaldo G, Groth A, Ghil M (2016) Economic cycles and their synchronization: A comparison of cyclic modes in three European countries. J Bus Cycle Res 12(1):25–48

    Article  Google Scholar 

  • Shlemov A, Golyandina N (2014) Shaped extensions of singular spectrum analysis. In: 21st international symposium on mathematical theory of networks and systems, July 7–11, 2014. Groningen, The Netherlands, pp 1813–1820

    Google Scholar 

  • Sivapragasam C, Liong SY, Pasha M (2001) Rainfall and runoff forecasting with SSA–SVM approach. J Hydroinform 3(3):141–152

    Article  Google Scholar 

  • Vautard M, Ghil M (1989) Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series. Physica D 35:395–424

    Article  MathSciNet  Google Scholar 

  • Vautard R, Yiou P, Ghil M (1992) Singular-spectrum analysis: A toolkit for short, noisy chaotic signals. Physica D 58:95–126

    Article  Google Scholar 

  • Vile JW J L nnd Gillard, Harper PR, Knight VA (2012) Predicting ambulance demand using singular spectrum analysis. J Oper Res Soc 63(11):1556–1565

    Article  Google Scholar 

  • Wang S, Tang HL, turk LIA, Hu Y, Sanei S, Saleh GM, Peto T (2017) Localizing microaneurysms in fundus images through singular spectrum analysis. IEEE Trans Biomed Eng 64(5):990–1002

    Article  Google Scholar 

  • Wang X, Wu J, Liu C, Wang S, Niu W (2016) A hybrid model based on singular spectrum analysis and support vector machines regression for failure time series prediction. Qual Reliab Eng Int 32(8):2717–2738, qRE-16-0186.R2

    Article  Google Scholar 

  • Watson PJ (2016) Identifying the best performing time series analytics for sea level research. Springer International Publishing, Cham, pp 261–278

    Google Scholar 

  • Weigend A, Gershenfeld N (eds) (1993) Time series prediction: Forecasting the future and understanding the past. Addison-Wesley, Reading

    Google Scholar 

  • Wickham H, Chang W (2017) devtools: Tools to Make Developing R Packages Easier. URL http://CRAN.R-project.org/package=devtools, R package version 1.13.2

  • Wu C, Chau K (2011) Rainfall–runoff modeling using artificial neural network coupled with singular spectrum analysis. J Hydrol 399(3):394–409

    Article  Google Scholar 

  • Xiao Y, Liu JJ, Hu Y, Wang Y, Lai KK, Wang S (2014) A neuro-fuzzy combination model based on singular spectrum analysis for air transport demand forecasting. J Air Transp Manag 39:1–11

    Article  Google Scholar 

  • Xin W, Chao L, Weiren X, Ying L (2015) A failure time series prediction method based on UML model. In: 2015 4th international conference on computer science and network technology (ICCSNT), vol 01, pp 62–70

    Google Scholar 

  • Yang Z, Bingham C, Ling WK, Zhang Y, Gallimore M, Stewart J (2012) Unit operational pattern analysis and forecasting using EMD and SSA for industrial systems. Springer, Berlin, Heidelberg, pp 416–423

    Google Scholar 

  • Zabalza J, Ren J, Wang Z, Marshall S, Wang J (2014) Singular spectrum analysis for effective feature extraction in hyperspectral imaging. IEEE Geosci Remote Sens Lett 11(11):1886–1890

    Article  Google Scholar 

  • Zabalza J, Ren J, Zheng J, Han J, Zhao H, Li S, Marshall S (2015) Novel two-dimensional singular spectrum analysis for effective feature extraction and data classification in hyperspectral imaging. IEEE Trans Geosci Remote Sens 53(8):4418–4433

    Article  Google Scholar 

  • Zhang Q, Wang BD, He B, Peng Y, Ren ML (2011) Singular spectrum analysis and ARIMA hybrid model for annual runoff forecasting. Water Resour Manag 25(11):2683–2703

    Article  Google Scholar 

  • Zhigljavsky A (2010) Singular spectrum analysis for time series: Introduction to this special issue. Stat Interface 3(3):255–258

    Article  MathSciNet  Google Scholar 

  • Zhigljavsky A, Golyandina N, Gillard J (2016a) Analysis and design in the problem of vector deconvolution. In: Kunert J, Müller HC, Atkinson CA (eds) mODa 11 - Advances in model-oriented design and analysis. Springer International Publishing, pp 243–251

    Google Scholar 

  • Zvonarev N, Golyandina N (2017) Iterative algorithms for weighted and unweighted finite-rank time-series approximations. Stat Interface 10(1):5–18

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mathematics and Mechanics, Saint Petersburg State University, Saint Petersburg, Russia

    Nina Golyandina & Anton Korobeynikov

  2. School of Mathematics, Cardiff University, Cardiff, UK

    Anatoly Zhigljavsky

Authors
  1. Nina Golyandina
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anton Korobeynikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Anatoly Zhigljavsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer-Verlag GmbH Germany, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Golyandina, N., Korobeynikov, A., Zhigljavsky, A. (2018). Introduction: Overview. In: Singular Spectrum Analysis with R. Use R!. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-57380-8_1

Download citation

Publish with us

Policies and ethics

Search

Navigation