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Periodic and long range dependent models for high frequency wind speed data

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  • Ambach, Daniel
  • Schmid, Wolfgang

Abstract

The production of wind power as one source of renewable energy has a huge potential to serve the increasing demand for energy. Therefore, it is necessary to improve the accuracy of wind energy forecasts to increase the energy output. We focus on short-term wind speed forecasts. This article considers a comparison study of two different periodic regression models with autoregressive fractionally integrated moving average errors in the mean part and asymmetric power generalized autoregressive conditional heteroscedasticity within the conditional variance (ARFIMA-APARCH) and two different estimation methods. The first one is a two-step approach where the regression parameters are estimated first with the least-squares method. Hereafter, an ARFIMA-APARCH process is fitted to the stationary residuals. In contrast to this, the second approach estimates the entire model with a QML (quasi-maximum likelihood) estimator in one step. Both models include periodic explanatory variables, but one model lets them vary over time. Moreover, we distinguish between two main distributional assumptions for the residuals. Each model is used to create suitable short-term forecasts up to 6 h. Eventually, we come up with a recommendation which model is preferred.

Suggested Citation

  • Ambach, Daniel & Schmid, Wolfgang, 2015. "Periodic and long range dependent models for high frequency wind speed data," Energy, Elsevier, vol. 82(C), pages 277-293.
    • Handle: RePEc:eee:energy:v:82:y:2015:i:c:p:277-293
    DOI: 10.1016/j.energy.2015.01.038
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    1. Yuan, Xiaohui & Tan, Qingxiong & Lei, Xiaohui & Yuan, Yanbin & Wu, Xiaotao, 2017. "Wind power prediction using hybrid autoregressive fractionally integrated moving average and least square support vector machine," Energy, Elsevier, vol. 129(C), pages 122-137.
    2. Abdelhakim Aknouche & Bader Almohaimeed & Stefanos Dimitrakopoulos, 2022. "Periodic autoregressive conditional duration," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(1), pages 5-29, January.
    3. Daniel Ambach & Robert Garthoff, 2016. "Vorhersagen der Windgeschwindigkeit und Windenergie in Deutschland," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 10(1), pages 15-36, February.
    4. Aknouche, Abdelhakim & Rabehi, Nadia, 2024. "Inspecting a seasonal ARIMA model with a random period," MPRA Paper 120758, University Library of Munich, Germany.
    5. Aknouche Abdelhakim & Demmouche Nacer & Dimitrakopoulos Stefanos & Touche Nassim, 2020. "Bayesian analysis of periodic asymmetric power GARCH models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 24(4), pages 1-24, September.
    6. Ziel, Florian & Croonenbroeck, Carsten & Ambach, Daniel, 2016. "Forecasting wind power – Modeling periodic and non-linear effects under conditional heteroscedasticity," Applied Energy, Elsevier, vol. 177(C), pages 285-297.
    7. Aknouche, Abdelhakim & Demmouche, Nacer & Touche, Nassim, 2018. "Bayesian MCMC analysis of periodic asymmetric power GARCH models," MPRA Paper 91136, University Library of Munich, Germany.
    8. Daniel Ambach & Carsten Croonenbroeck, 2016. "Space-time short- to medium-term wind speed forecasting," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(1), pages 5-20, March.
    9. Aknouche, Abdelhakim & Al-Eid, Eid & Demouche, Nacer, 2016. "Generalized quasi-maximum likelihood inference for periodic conditionally heteroskedastic models," MPRA Paper 75770, University Library of Munich, Germany, revised 19 Dec 2016.
    10. Aknouche, Abdelhakim & Almohaimeed, Bader & Dimitrakopoulos, Stefanos, 2020. "Periodic autoregressive conditional duration," MPRA Paper 101696, University Library of Munich, Germany, revised 08 Jul 2020.
    11. Daniel Ambach & Carsten Croonenbroeck, 2016. "Space-time short- to medium-term wind speed forecasting," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(1), pages 5-20, March.
    12. Daniel Ambach & Robert Garthoff, 2016. "Vorhersagen der Windgeschwindigkeit und Windenergie in Deutschland [Predictions of wind speed and wind energy in Germany]," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 10(1), pages 15-36, February.
    13. Ambach, Daniel & Schmid, Wolfgang, 2017. "A new high-dimensional time series approach for wind speed, wind direction and air pressure forecasting," Energy, Elsevier, vol. 135(C), pages 833-850.
    14. Abdelhakim Aknouche & Eid Al-Eid & Nacer Demouche, 2018. "Generalized quasi-maximum likelihood inference for periodic conditionally heteroskedastic models," Statistical Inference for Stochastic Processes, Springer, vol. 21(3), pages 485-511, October.

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