IDEAS home Printed from
   My bibliography  Save this article

Modelling non-stationary time series using a peaks over threshold distribution with time varying covariates and threshold: An application to peak electricity demand


  • Sigauke, Caston
  • Bere, Alphonce


Long term peak electricity demand forecasting is a crucial step in the process of planning for power transmission and new generation capacity. This paper discusses an application of the Generalized Pareto Distribution to the modelling of daily peak electricity demand using South African data for the period 2000 to 2010. The main contribution of this paper is in the use of a cubic smoothing spline with a constant shift factor as a time varying threshold. An intervals estimator method is then used to decluster the observations above the threshold. We explore the influence of temperature by including it as a covariate in the Generalized Pareto Distribution parameters. A comparative analysis is done using the block maxima approach. The GPD model showed a better fit to the data compared to the GEVD model. Key findings from this study are that the Weibull class of distributions best fits the data which is bounded from above for both stationary and non-stationary models. Another key finding is that for different values of the temperature covariate the shape parameter is invariant and the scale parameter changes for different values of heating degree days.

Suggested Citation

  • Sigauke, Caston & Bere, Alphonce, 2017. "Modelling non-stationary time series using a peaks over threshold distribution with time varying covariates and threshold: An application to peak electricity demand," Energy, Elsevier, vol. 119(C), pages 152-166.
  • Handle: RePEc:eee:energy:v:119:y:2017:i:c:p:152-166
    DOI: 10.1016/

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. Sigauke, Caston & Verster, Andréhette & Chikobvu, Delson, 2013. "Extreme daily increases in peak electricity demand: Tail-quantile estimation," Energy Policy, Elsevier, vol. 53(C), pages 90-96.
    2. Hong, Tao & Pinson, Pierre & Fan, Shu & Zareipour, Hamidreza & Troccoli, Alberto & Hyndman, Rob J., 2016. "Probabilistic energy forecasting: Global Energy Forecasting Competition 2014 and beyond," International Journal of Forecasting, Elsevier, vol. 32(3), pages 896-913.
    3. Petra Friederichs & Thordis L. Thorarinsdottir, 2012. "Forecast verification for extreme value distributions with an application to probabilistic peak wind prediction," Environmetrics, John Wiley & Sons, Ltd., vol. 23(7), pages 579-594, November.
    4. Gaillard, Pierre & Goude, Yannig & Nedellec, Raphaël, 2016. "Additive models and robust aggregation for GEFCom2014 probabilistic electric load and electricity price forecasting," International Journal of Forecasting, Elsevier, vol. 32(3), pages 1038-1050.
    5. Christopher A. T. Ferro & Johan Segers, 2003. "Inference for clusters of extreme values," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 545-556, May.
    6. Emma F. Eastoe & Jonathan A. Tawn, 2009. "Modelling non‐stationary extremes with application to surface level ozone," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(1), pages 25-45, February.
    7. Mirlatifi, A.M. & Egelioglu, F. & Atikol, U., 2015. "An econometric model for annual peak demand for small utilities," Energy, Elsevier, vol. 89(C), pages 35-44.
    8. MacDonald, A. & Scarrott, C.J. & Lee, D. & Darlow, B. & Reale, M. & Russell, G., 2011. "A flexible extreme value mixture model," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2137-2157, June.
    9. Stephen Chan & Saralees Nadarajah, 2015. "Extreme value analysis of electricity demand in the UK," Applied Economics Letters, Taylor & Francis Journals, vol. 22(15), pages 1246-1251, October.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Tafakori, Laleh & Pourkhanali, Armin & Fard, Farzad Alavi, 2018. "Forecasting spikes in electricity return innovations," Energy, Elsevier, vol. 150(C), pages 508-526.


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:energy:v:119:y:2017:i:c:p:152-166. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.