Skip to main content

Modelling Circular Time Series with Applications

  • Chapter
  • First Online:
Directional Statistics for Innovative Applications

Abstract

Circular time series modelling has posed a big challenge to many researchers due to the nature of observations. This article traces different circular time series models and the methods adopted in the development. It goes further to illustrate the use of these methods and the resultant circular time series models of wind direction data. The application involved hourly data on wind direction for the two major seasons (wet and dry seasons) in Nigeria. Training and development of the models are done using R codes and SPSS version 24. The results shows that score-driven models based on von Misses distribution is the best model using some error statistics and goodness of fit tests.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover 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

  1. Ailliot, P., Monbet, V.: Markov-switching autoregressive models for wind time series. Environ. Modelling Softw. 30, 92–101 (2012)

    Article  Google Scholar 

  2. Artes, R., Toloi, M.C.: An autoregressive model for time series of circular data. Commun. Statist.-Theor. Methods 39, 186–194 (2010)

    Article  MathSciNet  Google Scholar 

  3. Box, G.E.P., Jenkins, G.M., Reinsel, G.C., et al.: Time Series Analysis: Forecasting and Control, 5th edn. John Wiley & Sons Inc, Hoboken, New Jersey (2016)

    MATH  Google Scholar 

  4. Breckling, J.: Analysis of Directional Time Series: Application to Wind Speed and Direction. Lecture Notes in Statistics, vol. 61. Springer, Berlin (1989)

    Google Scholar 

  5. Bulla, J., Lagona, F., Maruotti, A., et al.: A multivariate hidden Markov model for the identification of sea regimes from incomplete skewed and circular time Series. J. Agric. Biol. Environ. Statist. 17(4), 544–567 (2012)

    Article  MathSciNet  Google Scholar 

  6. Coles, S.G.: Inference for circular distributions and processes. Statist. Comput. 8, 105–113 (1998)

    Article  Google Scholar 

  7. Craig, P.S.: Time Series Analysis for Directional Data. Unpublished Ph.D. thesis, Trinity College Dublin (1988)

    Google Scholar 

  8. Créal, D., Koopman, S.J., Lucas, A.: A dynamic multivariate heavy-tailed model for time-varying volatilities and correlations. J. Bus. Econ. Statist. 29, 552–563 (2011)

    Article  MathSciNet  Google Scholar 

  9. Creal, D., Koopman, S.J., Lucas, A.: Generalized autoregressive score models with applications. J. Appl. Econometrics 28, 777–795 (2013)

    Google Scholar 

  10. Fisher, N.I.: Statistical Analysis of Circular Data. Cambridge University Press, Cambridge (1993)

    Book  Google Scholar 

  11. Fisher, N.I., Lee, A.J.: Regression models for an angular response. Biometrics 48, 665–677 (1992)

    Article  MathSciNet  Google Scholar 

  12. Fisher, N.I., Lee, A.J.: Time series analysis of circular data. J. Roy. Statist. Soc. 56, 327–639 (1994)

    MathSciNet  MATH  Google Scholar 

  13. Hamilton, L.: Characterising spectral sea wave conditions with statistical clustering of actual spectra. Appl. Ocean Res. 32, 332–342 (2010)

    Article  Google Scholar 

  14. Harvey, A.C.: Dynamic Models for Volatility and Heavy Tails with Applications to Financial Time Series, Chapter 1. Cambridge University Press, Cambridge (2012)

    Google Scholar 

  15. Harvey, A.C.: Dynamic Models for Volatility and Heavy Tails: With Applications to Financial and Economic Time Series. Cambridge University Press, Econometric Society Monograph, New York (2013)

    Google Scholar 

  16. Harvey, A.C., Luati, A.: Filtering with heavy tail. J. Am. Statist. Assoc. 109(507), 1112–1122 (2014)

    Article  MathSciNet  Google Scholar 

  17. Harvey, A.C., Hurn, S., Thiele, S.: Modeling directional (circular) time series. In: Cambridge Working Papers in Economics: 1971 (2019)

    Google Scholar 

  18. Holzmann, H., Münk, A., Suster, M., et al.: Hidden Markov models for circular and linear circular time series. Environ. Ecol. Statist. 13, 325–347 (2006)

    Article  MathSciNet  Google Scholar 

  19. Jammalamadaka, S.R., SenGupta, A.: Topics in Circular Statistics. World Scientific Publishers, Singapore (2001)

    Book  Google Scholar 

  20. Jones, M.C., Pewsey, A.: A family of symmetric distributions on the circle. J. Am. Statist. Assoc. 100(472), 1422–1428 (2005)

    Article  MathSciNet  Google Scholar 

  21. Kato, S.: A Markov process for circular data. J. Roy. Statist. Soc. B (Statistical Methodology) 72(5), 655–672 (2010)

    Google Scholar 

  22. Ljung, G.M., Box, G.E.P.: On a measure of lack of fit in time series models. Biometrika 65, 297–303 (1978)

    Article  Google Scholar 

  23. Mardia, K.V., Jupp, P.E.: Directional Statistics. Wiley, Chichester (2000)

    MATH  Google Scholar 

  24. Monbet, V., Ailliot, P., Prevosto, M.: Survey of stochastic models for wind series. Prob. Eng. Mech. 22, 113–126 (2007)

    Article  Google Scholar 

  25. Pewsey, A., Neuhäuser, M., Ruxton, G.D.: Circular Statistics in R. Oxford University Press, Oxford (2013)

    Google Scholar 

  26. Reikard, G., Rogers, W.E.: Forecasting ocean waves: comparing physics-based statistical models. Coastal Eng. 58, 409–416 (2011)

    Article  Google Scholar 

  27. Taniguchi, M., Katob, S., Ogata, H., et al.: Models for circular data from time series spectra. J. Time Ser. Anal. (2020). https://doi.org/10.1111/jtsa.12549

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Fidelis Ifeanyi Ugwuowo .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Ugwuowo, F.I., Udokang, A.E. (2022). Modelling Circular Time Series with Applications. In: SenGupta, A., Arnold, B.C. (eds) Directional Statistics for Innovative Applications. Forum for Interdisciplinary Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-19-1044-9_22

Download citation

Publish with us

Policies and ethics