Skip to main content
SpringerLink
Log in

Introduction

  • Chapter
  • First Online:
Automatic trend estimation

Part of the book series: SpringerBriefs in Physics ((SpringerBriefs in Physics))

  • 895 Accesses

Abstract

A complete presentation of the theory of stochastic processes can be found in any treatise on the probability theory and time series theory. In this introductory chapter we briefly present some basic notions which are used in the rest of the book. The main methods to estimate trends from noisy time series are introduced in Sect. 1.2. In the last section we discuss the properties of the order one autoregressive stochastic process AR(1) which has the serial correlation described by a single parameter and which is a good first approximation for many noises encountered in real phenomena.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 49.99
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

Notes

  1. 1.

    We have changed the usual notation \(x_{s}\) in order to avoid the confusion with the terms of a time series.

References

  1. Alexandrov, T., Bianconcini, S., Dagum, E.B., Maass, P., McElroy, T. S.: A review of some modern approaches to the problem of trend extraction. Research Report Series US Census Bureau, Statistics 3. http://www.census.gov/srd/papers/pdf/rrs2008-03.pdf (2008)

  2. Blender, R.: Renormalisation group analysis of autoregressive processes and fractional noise. Phys. Rev. E 64, 067101 (2001)

    Article  ADS  Google Scholar 

  3. Brockwell, P.J., Davies, R.A.: Introduction to Time Series and Forecasting. Springer, New York (1996)

    MATH  Google Scholar 

  4. Brockwell, P.J., Davies, R.A.: Time Series:Theory and Methods. Springer, New York (1996)

    MATH  Google Scholar 

  5. Gao, J., Hu, J., Tung, W., Cao, Y., Sarshar, N., Roychowdhury, V.P.: Assessment of long range correlation in time series: How to avoid pitfalls. Phys. Rev. E 73, 016117 (2006)

    Article  ADS  Google Scholar 

  6. Guzman-Vargas, L., Angulo-Brown, F.: Simple model of the aging effect in heart interbeat time series. Phys. Rev. E 67, 052901 (2003)

    Article  ADS  Google Scholar 

  7. Hallerberg, S., Altmann, E.G., Holstein, D., Kantz, H.: Precursors of extreme increments. Phys. Rev. E 75, 016706 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  8. Király, A., Jánosi, I.M.: Stochastic modeling of daily temperature fluctuations. Phys. Rev. E 65, 051102 (2002)

    Article  ADS  Google Scholar 

  9. Kugiumtzis, D.: Statically transformed autoregressive process and surrogate data test for nonlinearity. Phys. Rev. E 66, 025201 (2002)

    Article  ADS  Google Scholar 

  10. Liley, D.T., Cadusch, P.J., Gray, M., Nathan, P.J.: Drug-induced modification of the system properties associated with spontaneous human electroencephalographic activity. Phys. Rev. E 68, 051906 (2003)

    Article  ADS  Google Scholar 

  11. Maraun, D., Rust, H.W., Timmer, J.: Tempting long-memory—on the interpretation of DFA results. Nonlinear Proc. Geoph. 11, 495–503 (2004)

    Article  ADS  Google Scholar 

  12. Palus, M., Novotna, D.: Sunspot cycle: a driven nonlinear oscillator? Phys. Rev. Lett. 83, 3406–3409 (1999)

    Article  ADS  Google Scholar 

  13. Stephen, D., Pollock, G.: Statistical signal extraction and filtering: a partial survey. In: Belsley, D.A., Kontoghiorghes, E. (eds.) Handbook of Computational Econometrics, pp. 321–376. Wiley, New York (2009).

    Google Scholar 

  14. Timmer, J., Schwarz, U., Voss, H.U., Wardinski, I., Belloni, T., Hasinger, G., van der Klis, M., Kurths, J.: Linear and nonlinear time series analysis of the black hole candidate Cygnus X-1. Phys. Rev. E 61, 1342–1352 (2000)

    Article  ADS  Google Scholar 

  15. Vamoş, C.: Automatic algorithm for monotone trend removal. Phys. Rev. E 75, 036705 (2007)

    Article  ADS  Google Scholar 

  16. Vamoş, C., Şoltuz, Ş.M., Crăciun, M.: Order 1 autoregressive process of finite length. Rev. Anal. Numer. Theor. 36, 199–214 (2007)

    Google Scholar 

  17. Wu, Z., Huang, N.E., Long, S.R., Peng, C.K.: On the trend, detrending, and variability of nonlinear and nonstationary time series. PNAS 18, 14889–14894 (2007)

    Article  ADS  Google Scholar 

  18. Wentzell, A.D.: A Course in the Theory of Stochastic Processes. McGraw-Hill, New York (1981)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, 400110, Cluj-Napoca, Romania

    Calin Vamos & Maria Craciun

Authors
  1. Calin Vamos
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Maria Craciun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Calin Vamos .

Rights and permissions

Reprints and permissions

Copyright information

© 2012 The Author(s)

About this chapter

Cite this chapter

Vamos, C., Craciun, M. (2012). Introduction. In: Automatic trend estimation. SpringerBriefs in Physics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4825-5_1

Download citation

  • DOI: https://doi.org/10.1007/978-94-007-4825-5_1

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-4824-8

  • Online ISBN: 978-94-007-4825-5

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation