Estimation of Wind Speed Data with Setar Model

Year 2022, Volume: 7 Issue: 2, 115 - 124, 31.08.2022

Ümran Münire Kahraman , İsmail Arsel , Aşır Genç , Galip Oturanç

https://doi.org/10.30931/jetas.1099407

Abstract

The threshold model allows expression with different Autoregressive Moving Average (ARMA) models sorted according to the threshold value of the observations. In this study, nineteen years of observed wind speed data have been modeled with the Self Exciting Threshold Autoregressive (SETAR) model. Two different Autoregressive (AR(3)) models have been obtained for the situation where the wind speed was below and above 2.5 m / s of the previous observation in the time series. In addition, in the SETAR (1,3,3) model, it has been determined that the residual terms have the effect of GARCH (1,1) and a range has been estimated for model predictions.

Keywords

Threshold autoregressive Model, GARCH, wind speed, SETAR prediction, weibull distribution

References

• [1] Narayana M., Sunderland K. M., Putrus G., Conlon M. F., "Adaptive linear prediction for optimal control of wind turbines", Renewable Energy 113 (2017) : 895-906.
• [2] Kamjoo A., Maheri A., and Putrus G., "Wind speed and solar irradiance variation simulation using ARMA models in design of hybrid wind-PVBattery system", Journal of Clean Energy Technologies 1(1) (2013).
• [3] Zhang M., Wei Yu w., Xu J., "Aerodynamic physics of smart load control for wind turbine due to extreme wind shear", Renewable Energy 70 (2014) : 204-210.
• [4] Kose R., Ozgur M.A., Erbas O., Tugcu A., "The analysis of wind data and wind energy potential in Kutahya, Turkey", Renewable and Sustainable Energy Reviews 8(3) (2004) : 277-288.
• [5] Mathew S., Pandey K.P., Kumar A.V., "Analysis of wind regimes for energy estimation", Renewable Energy 25(3) (2002) : 381-399.
• [6] Ahmed, N.B., "A comparative analysis of forecast performance between SARIMA and SETAR models using macroeconomic variables in Ghana", Master Thesis, Unıversıty of Ghana, (2018).
• [7] Albuquerquemello, V.P., Medeiros R.K., Besarria, C.N., Maia, S.F., "Forecasting crude oil price: Does exist an optimal econometric model? ", Energy 155 (2018) : 578-591.
• [8] Campenhout B.V., "Modelling trends in food market integration: Method and an application to Tanzanian maize markets", Food Policy 32(1) (2006).
• [9] Chen, J., "Crisis, capital controls and covered interest parity: evidence from China in transformation", Paris-Jourdan Sciences Economiques, CNRS : UMR8545, (2012).
• [10] Clements, M., Smith, J., "Evaluating forecasts from SETAR models of exchange rates", Journal of International Money and Finance 20 (2001) : 133-148.
• [11] Cleveland, W.S., "Robust locally weighted regression and smoothing scatterplots", Journal of the American Statistical Association 74(368) (1979) : 829-836.
• [12] Engle, R.F., "Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation", Econometrica 50(4) (1982) : 987-1008.
• [13] Feng, H., Liu, J., "A SETAR model for Canadian GDP: non-linearities and forecast comparisons", Applied Economics 35(18) (2003).
• [14] Genc, A., Erisoglu, M., Pekgor, A., Oturanc, G., Hepbasli, A., Ulgen, K., "Estimation of Wind Power Potential Using Weibull Distribution", Energy Sources 27(9), (2005) : 809-822.
• [15] Hasan, H., Nordin, M. A. B. C., & Salleh, N. H. M., "Modeling daily maximum temperature for thermal comfort in northern Malaysia". Advances in Environmental Biology, 9(26 SI) (2015) : 12+.
• [16] Hsu, B., Sherina, V., McCall, M.N., "Auto-regressive modeling and diagnostics for qPCR amplification", bioRxiv (2019).
• [17] Huang, B.N., Hwang, M.J., Peng, H.P., "The asymmetry of the impact of oil price shocks on economic activities: An application of the multivariate threshold model", Energy Economics 27(3) (2005).
• [18] Hutchison, M., Kendall, J., Pasricha, G., Singh, N., "Indian capital control liberalization: evidence from NDF markets", Munich Personal RePEc Archive (2010).
• [19] Khadaroo, A.J., "A Threshold in inflation dynamics: Evidence from emerging countries", Applied Economics, 37(6) (2005).
• [20] Pinson, P., Christensen, L.E.A., Madsen, H., Sørensen, P.E., Donovan, M.H., Jensen, L.E., "Regime-switching modeling of the fluctuations of offshore wind generation", Journal of Wind Engineering and Industrial Aerodynamics 96(12) (2008)
• [21] Singh, T., "Testing nonlinearities in economic growth in the OECD countries: An evidence from SETAR and STAR models", Applied Economics 44 (2012) : 3887–3908 .
• [22] Tsay, R., "Testing and modelling threshold autogressive processes", Journal of the American Statistical Association 84 (1989) : 231-240.
• [23] Tong, H., "On a threshold model", In Pattern Recognition and Signal Processing (C. H. Chen, ed.), 101-141. Sijthoff and Noordhoff, Amsterdam, (1978).
• [24] Tong, H. and Lim, K.S., "Threshold autoregression, Limit cycles and cyclial data", Journal of the Royal Statistical Society Ser. B 42 (1980) : 245-292.
• [25] Tong, H., Yeung, I., "On tests for self-exciting threshold autoregressive-type non-linearity in partially observed time series", Applied Statistics 40 (1991) : 43-62.
• [26] Tsay, R.S., "Analysis of financial time series", Johns Wiley & Sons, Inc., Publication, Third Edition, Canada, (2010).
• [27] Tsay, R.S., Chen, R., "Nonlinear time series analysis", Wiley Series in Probability and Statistics (2019).
• [28] Watier, L., Richardson, S., "Modelling of an epidemiological time series by a threshold autoregressive model", The Statistician 44(3) (1999) : 353-364.
• [29] Yadav, P.K., Pope, P.F., Paudyal, K., "Threshold autoregressive modelling in finance: the price difference of equivalent assets", Mathematical Finance 4 (1994) : 205-221.
• [30] Yang, X.H., Li, Y.Q., "DNA optimization threshold autoregressive prediction model and its application in ice condition time series", Hindawi Publishing Corporation Mathematical Problems in Engineering 2012 (2012), Article ID 191902, 10 pages.
• [31] Zhao, Z., Wang, X., Qiao, Y., Sun, H., "Wind speed prediction based on improved self excitation threshold auto regressive model", 37th Chinese Control Conference (CCC), Wuhan 2018 (2018) : 1498-1503.
• [32] Zhang, J. J., Shao, C. F., Wang, F., "Research on short-term traffic flow prediction model based on threshold autoregression", Special Issue 3 (2018) : 79-84.
• [33] Chan, W., Wong, A., Tong H., "some nonlinear threshold autoregressive time series models for actuarial use", North American Actuarial Journal 8(4) (2004) : 37-61.