Abstract
Accurate wind power forecasts depend on reliable wind speed forecasts. Numerical weather predictions utilize huge amounts of computing time, but still have rather low spatial and temporal resolution. However, stochastic wind speed forecasts perform well in rather high temporal resolution settings. They consume comparably little computing resources and return reliable forecasts, if forecasting horizons are not too long. In the recent literature, spatial interdependence is increasingly taken into consideration. In this paper we propose a new and quite flexible multivariate model that accounts for neighbouring weather stations’ information and as such, exploits spatial data at a high resolution. The model is applied to forecasting horizons of up to 1 day and is capable of handling a high resolution temporal structure. We use a periodic vector autoregressive model with seasonal lags to account for the interaction of the explanatory variables. Periodicity is considered and is modelled by cubic B-splines. Due to the model’s flexibility, the number of explanatory variables becomes huge. Therefore, we utilize time-saving shrinkage methods like lasso and elastic net for estimation. Particularly, a relatively newly developed iteratively re-weighted lasso and elastic net is applied that also incorporates heteroscedasticity. We compare our model to several benchmarks. The out-of-sample forecasting results show that the exploitation of spatial information increases the forecasting accuracy tremendously, in comparison to models in use so far.
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Aguera-Perez A, Palomares-Salas JC, Gonzalez de la Rosa JJ, Moreno-Munoz A (2013) Spatial persistence in wind analysis. J Wind Eng Ind Aerodyn 119:48–52
Ambach D (2015) Short-term wind speed in germany. J Appl Statistics 1–19
Ambach D, Schmid W (2015) Periodic and long range dependent models for high frequency wind speed data. Energy 82:277–293
Bazilevs Y, Hsu M, Scott M (2012) Isogeometric fluid–structure interaction analysis with emphasis on non-matching discretizations, and with application to wind turbines. Comput Methods Appl Mech Eng 249–252:28–41
Burton T, Jenkins N, Sharpe D, Bossanyi E (2011) Wind energy handbook. Wiley, West Sussex
Croonenbroeck C, Dahl CM (2014) Accurate medium-term wind power forecasting in a censored classification framework. Energy 73:221–232
De Boor C (1978) A practical guide to splines. In: Mathematics of Computation, vol 27. pp 87–106
Ding Z, Granger CW, Engle RF (1993) A long memory property of stock market returns and a new model. J Empir Finance 1(1):83–106
Efron B, Hastie T, Johnstone I, Tibshirani R (2004) Least angle regression. Ann Stat 32(2):407–499
Eilers PH, Marx BD (1996) Flexible smoothing with b-splines and penalties. Stat Sci 11(2):89–102
Evans SC, Zhang Z, Iyengar S, Chen J, Hilton J, Gregg P, Eldridge D, Jonkhof M, McCulloch C, Shokoohi-Yekta M (2014) Towards wind farm performance optimization through empirical models. In: Aerospace conference, 2014 IEEE. IEEE, pp 1–12
Ewing BT, Kruse JB, Schroeder JL (2006) Time series analysis of wind speed with time-varying turbulence. Environmetrics 17(2):119–127
Friedman J, Hastie T, Tibshirani R (2009) The elements of statistical learning: data mining, inference, and prediction. Springer series in statistics
Giebel G, Brownsword R, Kariniotakis G, Denhard M, Draxl C (2011) The state-of-the-art in short-term prediction of wind power. Technical report, ANEMOS.plus, Ris DTU, Wind Energy Division
Glosten L, Jagannathan R, Runkle D (1993) On the relation between the expected value and the volatility of the nominal excess return on stocks. J Finance 48:1779–1801
Gneiting T, Larson K, Westrick K, Genton MG, Aldrich E (2006) Calibrated probabilistic forecasting at the stateline wind energy center: the regime-switching space-time method. J Am Stat Assoc 101(475):968–979
Gneiting T, Balabdaoui F, Raftery AE (2007) Probabilistic forecasts, calibration and sharpness. J R Stat Soc Ser B 69(2):243–268
Haslett J, Raftery AE (1989) Space-time modelling with long-memory dependence: assessing Ireland’s wind power resource. Appl Stat 30(1):1–50
Koopman SJ, Ooms M, Carnero MA (2007) Periodic seasonal Reg-ARFIMA–GARCH models for daily electricity spot prices. J Am Stat Assoc 102(477):16–27
Le Guyader C, Apprato D, Gout C (2014) Spline approximation of gradient fields: applications to wind velocity fields. Math Comput Simul 97:260–279
Lei M, Shiyan L, Chuanwen J, Hongling L, Zhang Y (2009) A review on the forecasting of wind speed and generated power. Renew Sustain Energy Rev 13:915–920
Mbamalu G, El-Hawary M (1993) Load forecasting via suboptimal seasonal autoregressive models and iteratively reweighted least squares estimation. IEEE Trans Power Syst 8(1):343–348
Nielsen TS, Joensen A, Madsen H, Landberg L, Giebel G (1998) A new reference for wind power forecasting. Wind Energy 1(1):29–34
Rajapakse JC, Mundra PA (2011) Stability of building gene regulatory networks with sparse autoregressive models. BMC Bioinformatics 12(Suppl 13):S17
Ren Y, Zhang X (2010) Subset selection for vector autoregressive processes via adaptive lasso. Stat Probab Lett 80(23):1705–1712
Šaltyte Benth J, Šaltyte L (2011) Spatial–temporal model for wind speed in Lithuania. J Appl Stat 38(6):1151–1168
Santos-Alamillos F, Pozo-Vázquez D, Ruiz-Arias JA, Lara-Fanego V (2014) A methodology for evaluating the spatial variability of wind energy resources: application to assess the potential contribution of wind energy to baseload power. Renew Energy 69:147–156
Soman SS, Zareipour H, Malik O, Mandal P (2010) A review of wind power and wind speed forecasting methods with different time horizons. In: North American power symposium (NAPS), 2010. IEEE, pp 1–8
Taylor JW, McSharry PE, Buizza R (2009) Wind power density forecasting using ensemble predictions and time series models. IEEE Trans Energy Convers 24(3):775–782
Thapar V, Agnihotri G, Sethi V (2011) Critical analysis of methods for mathematical modelling of wind turbines. Renew Energy 36:3166–3177
Tibshirani R (1996) Regression shrinkage and selection via the lasso. J R Stat Soc Ser B (Methodol) 58(1):267–288
Wu YK, Hong JS (2007) A literature review of wind forecasting technology in the world. In: Power technology, 2007 IEEE Lausanne. IEEE, pp 504–509
Yoon YJ, Park C, Lee T (2013) Penalized regression models with autoregressive error terms. J Stat Comput Simul 83(9):1756–1772
Zhu X, Genton MG, Gu Y, Xie L (2014) Space-time wind speed forecasting for improved power system dispatch. Test 23(1):1–25
Ziel F, Steinert R, Husmann S (2015) Efficient modeling and forecasting of electricity spot prices. Energy Econ 47:98–111
Zou H, Hastie T (2005) Regularization and variable selection via the elastic net. J R Stat Soc Ser B (Stat Methodol) 67(2):301–320
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Ambach, D., Croonenbroeck, C. Space-time short- to medium-term wind speed forecasting. Stat Methods Appl 25, 5–20 (2016). https://doi.org/10.1007/s10260-015-0343-6
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DOI: https://doi.org/10.1007/s10260-015-0343-6