Modelling and Prediction of Time Series Arising on a Graph

  • Matthew A. NunesEmail author
  • Marina I. Knight
  • Guy P. Nason
Conference paper
Part of the Lecture Notes in Statistics book series (LNS, volume 217)


Time series that arise on a graph or network arises in many scientific fields. In this paper we discuss a method for modelling and prediction of such time series with potentially complex characteristics. The method is based on the lifting scheme first proposed by Sweldens, a multiscale transformation suitable for irregular data with desirable properties. By repeated application of this algorithm we can transform the original network time series data into a simpler, lower dimensional time series object which is easier to forecast. The technique is illustrated with a data set arising from an energy time series application.



We would like to thank the organisers of the “2nd Workshop on Industry Practices for Forecasting” (WIPFOR13) for an instructive and stimulating meeting. The authors would like to gratefully acknowledge the UK Met Office and British Atmospheric Data Centre (BADC) for access to the wind speed data.


  1. 1.
    Anderson, O. D. (1976). Time series analysis and forecasting: The Box-Jenkins approach. London: Butterworths.Google Scholar
  2. 2.
    Gardner, E. S. (1985). Exponential smoothing: The state of the art. Journal of Forecasting, 4(1), 1–28.CrossRefGoogle Scholar
  3. 3.
    Jansen, M., Nason, G. P., & Silverman, B. W. (2001). Scattered data smoothing by empirical Bayesian shrinkage of second generation wavelet coefficients. In M. Unser & A. Aldroubi (Eds.), Wavelet applications in signal and image processing IX (Vol. 4478, pp. 87–97). SPIE.Google Scholar
  4. 4.
    Jansen, M., Nason, G. P., & Silverman, B. W. (2009). Multiscale methods for data on graphs and irregular multidimensional situations. Journal of the Royal Statistical Society: Series B, 71(1), 97–125.zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Krzanowski, W. J., & Marriott, F. H. C. (1995). Multivariate analysis part 2: Classification, covariance structures and repeated measurements (Kendall’s library of statistics, Vol. 2). London: Edward Arnold.Google Scholar
  6. 6.
    Mahadevan, N., Nason, G., & Munro, A. (2008). Multi-dimensional network function estimation. In IEEE international conference on communications, Beijing.Google Scholar
  7. 7.
    Sweldens, W. (1996). The lifting scheme: A custom-design construction of biorthogonal wavelets. Applied and Computational Harmonic Analysis, 3(2), 186–200.zbMATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Sweldens, W. (1998). The lifting scheme: A construction of second generation wavelets. SIAM Journal on Mathematical Analysis, 29(2), 511–546.zbMATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    UK Meteorological Office. (2013). Met Office integrated data archive system (MIDAS) land and marine surface stations data (1853-current). Harwell/Oxford: British Atmospheric Data Centre.Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Matthew A. Nunes
    • 1
    Email author
  • Marina I. Knight
    • 2
  • Guy P. Nason
    • 3
  1. 1.Department of Mathematics and StatisticsLancaster UniversityLancasterUK
  2. 2.Department of MathematicsUniversity of YorkYorkUK
  3. 3.School of MathematicsUniversity of BristolBristolUK

Personalised recommendations