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Year 2022, Volume: 51 Issue: 1, 308 - 326, 14.02.2022

Zafer Öztürk , Halis Bilgil , Ümmügülsüm Erdinç

https://doi.org/10.15672/hujms.939543
Cited By: 5

Abstract

References

  • [1] A. Altan, S. Karasu and E. Zio, A new hybrid model for wind speed forecasting combining long short-term memory neural network, decomposition methods and grey wolf optimizer, Appl. Soft Comput. 100, 1-20, 2021.
  • [2] S. Balochian and H. Baloochian, Improving grey prediction model and its application in predicting the number of users of a public road transportation system, Int. J. Intell. Syst. 30 (1), 104–114, 2021.
  • [3] H. Bilgi, New grey forecasting model with its application and computer code, AIMS Mathematics 6 (2), 1497–1514, 2021.
  • [4] P.Y. Chen and H.M. Yu, Foundation settlement prediction based on a novel NGM model, Math. Probl. Eng., Doi:10.1155/2014/242809, 2014.
  • [5] J. Cui, S. Liu, B. Zeng and N. Xie, A novel grey forecasting model and its optimization, Appl. Math. Model 37 (6), 4399–4406, 2013.
  • [6] J.L. Deng, Control problems of grey systems, Syst. Control. Lett. 1 (5), 288–294, 1982.
  • [7] S. Ene and N. Öztürk, Grey modelling based forecasting system for return flow of end-of-life vehicles, Technol. Forecast. Soc. Change 115, 155–166, 2017.
  • [8] Y. Hu, X. Ma, W. Li, W. Wu and D. Tu, Forecasting manufacturing industrial natural gas consumption of china using a novel time-delayed fractional grey model with multiple fractional order, Comp. Appl. Math. 39 (4), 1–30, 2020.
  • [9] A.K. Jain, J. Mao and KM. Mohiuddin, Artificial neural networks: A tutorial, Computer 29 (3), 31–44, 1996.
  • [10] S.A. Javed and S. Liu, Predicting the research output/growth of selected countries: application of even GM (1,1) and NDGM models, Scientometrics 115 (1), 395–413, 2018.
  • [11] J. Jiang, T. Feng and C. Liu, An improved nonlinear grey Bernoulli model based on the whale optimization algorithm and its application, mathematical problems in engineering, Math. Probl. Eng., Doi:10.1155/2021/66917242021, 2021.
  • [12] R. Khalil, M. Al Horani, Y. Abdelrahman and S. Mohammad, A new definition of fractional derivative, J. Comput. Appl. Math. 264, 65–70, 2014.
  • [13] S. Li, X. Ma and C. Yang, A novel structure-adaptive intelligent grey forecasting model with full-order time power terms and its application, Comput Ind Eng 120, 53–67, 2018.
  • [14] L. Liu, Y. Chen and L. Wu, The damping accumulated grey model and its application, Commun. Nonlinear Sci. Numer. Simul. 95, 1-14, 2021.
  • [15] L. Liu and L. Wu, Forecasting the renewable energy consumption of the European countries by an adjacent non-homogeneous grey model, Appl. Math. Model. 89 (2), 1932–1948, 2021.
  • [16] X. Ma, Research on a novel kernel based grey prediction model and its applications, Math. Probl. Eng., Doi:10.1155/2016/5471748, 2016.
  • [17] X. Ma and Z. Liu, Application of a novel time-delayed polynomial grey model to predict the natural gas consumption in China, J. Comput. Appl. Math. 324, 17–24, 2017.
  • [18] X. Ma, Z. Liu and Y. Wang, Application of a novel nonlinear multivariate grey Bernoulli model to predict the tourist income of China, J. Comput. Appl. Math. 347, 84–94, 2019.
  • [19] X. Ma, W. Wu, B. Zeng, Y. Wang and X. Wu, The conformable fractional grey system model, ISA Transactions 96, 255–271, 2020.
  • [20] S. Mao, M. Gao, X. Xiao and M. Zhu, A novel fractional grey system model and its application, Appl. Math. Model. 40 (7-8), 5063–5076, 2016.
  • [21] E. Masry, Multivariate local polynomial regression for time series: uniform strong consistency and rates, J. Time Series Anal. 17 (6), 571–599, 1996.
  • [22] W. Meng, Q. Li and B. Zeng, Study on fractional order grey reducing generation operator, Grey Syst. Theory Appl. 6 (1), 80–95, 2016.
  • [23] X. Meng and L. Wu, Prediction of per capita water consumption for 31 regions in China, Environ. Sci. Pollut. Res. 28, 29253–29264, 2021.
  • [24] X. Ping, F. Yang, H. Zhang, J. Zhang, W. Zhang and G. Song, Introducing machine learning and hybrid algorithm for prediction and optimization of multistage centrifugal pump in an orc system, Energy 222, 1-13, 2021.
  • [25] U. Sahin and T. Sahin, Forecasting the cumulative number of confirmed cases of covid- 19 in Italy, UK and USA using fractional nonlinear grey Bernoulli model, Chaos Solitons Fractals 138, 1-7, 2020.
  • [26] Y. Shen, B. He and P. Qing, Fractional-order grey prediction method for nonequidistant sequences, Entropy 18 (6), 1–16, 2016.
  • [27] A.J. Smola and B. Schölkopf, A tutorial on support vector regression, Stat. Comput. 14 (3), 199-222, 2004.
  • [28] Z.X. Wang, Q. Li and L.L. Pei, A seasonal GM (1,1) model for forecasting the electricity consumption of the primary economic sectors, Energy 154, 522–534, 2018.
  • [29] B. Wei, N. Xie and A. Hu, Optimal solution for novel grey polynomial prediction model, Appl. Math. Model. 62, 717–727, 2018.
  • [30] L. Wu, S. Liu, D. Chen, L. Yao and W. Cui, Using gray model with fractional order accumulation to predict gas emission, Nat. Hazards 71 (3), 2231–2236, 2014.
  • [31] L. Wu, S. Liu, L. Yao and S. Yan, The effect of sample size on the grey system model, Appl. Math. Model. 37, 6577–6583, 2013.
  • [32] L. Wu, S. Liu, L. Yao, S. Yan and D. Liu, Grey system model with the fractional order accumulation, Commun. Nonlinear Sci. Numer. Simul. 18 (7), 1775–1785, 2013.
  • [33] L.Z. Wu, S.H. Li, R.Q. Huang and Q. Xi, A new grey prediction model and its application to predicting landslide displacement, Appl. Soft Comput. 95, 1-11, 2020.
  • [34] W. Wu, X. Ma, Y. Wang, W. Cai and B. Zeng, Predicting Chinas energy consumption using a novel grey Riccati model, Appl. Soft Comput. 95, 1-11, 2020.
  • [35] W. Wu, X. Ma, B. Zeng, Y. Wang and W. Cai, Application of the novel fractional grey model FAGMO (1,1,k) to predict China’s nuclear energy consumption, Energy 165, 223–234, 2018.
  • [36] W. Wu, X. Ma, Y. Zhang, W. Li and Y. Wang, A novel conformable fractional nonhomogeneous grey model for forecasting carbon dioxide emissions of brics countries, Sci. Total Environ. 707, 1-24, 2020.
  • [37] W. Xie, L. Caixia, W. Wu, L. Weidong and L. Chong, Continuous grey model with conformable fractional derivative, Chaos Solitons Fractals 139, 1-9, 2020.
  • [38] W. Xie, W.Z. Wu, C. Liu and J. Zhao, Forecasting annual electricity consumption in China by employing a conformable fractional grey model in opposite direction, Energy 202, 1-13, 2020.
  • [39] W. Xie, W.Z. Wu, T. Zhang, and Q. Li, An optimized conformable fractional nonhomogeneous gray model and its application, Comm. Statist. Simulation Comput., Doi:10.1080/03610918.2020.1788588, 2020.
  • [40] K. Yuxiao, M. Shuhua, Z. Yonghong and Z. Huimin, Fractional derivative multivariable grey model for nonstationary sequence and its application, J. Syst. Eng 31 (5), 1009–1018, 2020.
  • [41] B. Zeng, Y. Tan, H. Xu, J. Quan, L. Wang and X. Zhou, Forecasting the electricity consumption of commercial sector in Hong Kong using a novel grey dynamic prediction model, J. Grey Syst. 30 (1), 157–172, 2018.
  • [42] P. Zhang, X. Ma and K. She, A novel power-driven fractional accumulated grey model and its application in forecasting wind energy consumption of China, Plos one 14, 1-33, 2019.
  • [43] Y.G. Zhang, Y. Xu and Z.P.Wang, GM (1,1) grey prediction of lorenz chaotic system, Chaos Solitons Fractals 42, 1003–1009, 2009.
  • [44] W. Zhou and J. M. He, Generalized GM (1,1) model and its application in forecasting of fuel production, Appl. Math. Model. 37 (9), 6234–6243, 2013.

An optimized continuous fractional grey model for forecasting of the time dependent real world cases

Year 2022, Volume: 51 Issue: 1, 308 - 326, 14.02.2022

Zafer Öztürk , Halis Bilgil , Ümmügülsüm Erdinç

https://doi.org/10.15672/hujms.939543
Cited By: 5

Abstract

The new priority in the grey modelling is to build new models that have more accurate forecasting power than the previous ones. This paper aims to develop the prediction performance of the existing continuous grey models. Therefore, a novel continuous grey model (OCCFGM(1,1)) is proposed with conformable fractional derivative. The numerical results of three case studies show that the novel model's prediction accuracy is higher than other competitive models, and the proposed model is more reasonable for practical cases.

Keywords

Grey Systems Conformable fractional derivative Fractional grey model OCCFGM model

References

  • [1] A. Altan, S. Karasu and E. Zio, A new hybrid model for wind speed forecasting combining long short-term memory neural network, decomposition methods and grey wolf optimizer, Appl. Soft Comput. 100, 1-20, 2021.
  • [2] S. Balochian and H. Baloochian, Improving grey prediction model and its application in predicting the number of users of a public road transportation system, Int. J. Intell. Syst. 30 (1), 104–114, 2021.
  • [3] H. Bilgi, New grey forecasting model with its application and computer code, AIMS Mathematics 6 (2), 1497–1514, 2021.
  • [4] P.Y. Chen and H.M. Yu, Foundation settlement prediction based on a novel NGM model, Math. Probl. Eng., Doi:10.1155/2014/242809, 2014.
  • [5] J. Cui, S. Liu, B. Zeng and N. Xie, A novel grey forecasting model and its optimization, Appl. Math. Model 37 (6), 4399–4406, 2013.
  • [6] J.L. Deng, Control problems of grey systems, Syst. Control. Lett. 1 (5), 288–294, 1982.
  • [7] S. Ene and N. Öztürk, Grey modelling based forecasting system for return flow of end-of-life vehicles, Technol. Forecast. Soc. Change 115, 155–166, 2017.
  • [8] Y. Hu, X. Ma, W. Li, W. Wu and D. Tu, Forecasting manufacturing industrial natural gas consumption of china using a novel time-delayed fractional grey model with multiple fractional order, Comp. Appl. Math. 39 (4), 1–30, 2020.
  • [9] A.K. Jain, J. Mao and KM. Mohiuddin, Artificial neural networks: A tutorial, Computer 29 (3), 31–44, 1996.
  • [10] S.A. Javed and S. Liu, Predicting the research output/growth of selected countries: application of even GM (1,1) and NDGM models, Scientometrics 115 (1), 395–413, 2018.
  • [11] J. Jiang, T. Feng and C. Liu, An improved nonlinear grey Bernoulli model based on the whale optimization algorithm and its application, mathematical problems in engineering, Math. Probl. Eng., Doi:10.1155/2021/66917242021, 2021.
  • [12] R. Khalil, M. Al Horani, Y. Abdelrahman and S. Mohammad, A new definition of fractional derivative, J. Comput. Appl. Math. 264, 65–70, 2014.
  • [13] S. Li, X. Ma and C. Yang, A novel structure-adaptive intelligent grey forecasting model with full-order time power terms and its application, Comput Ind Eng 120, 53–67, 2018.
  • [14] L. Liu, Y. Chen and L. Wu, The damping accumulated grey model and its application, Commun. Nonlinear Sci. Numer. Simul. 95, 1-14, 2021.
  • [15] L. Liu and L. Wu, Forecasting the renewable energy consumption of the European countries by an adjacent non-homogeneous grey model, Appl. Math. Model. 89 (2), 1932–1948, 2021.
  • [16] X. Ma, Research on a novel kernel based grey prediction model and its applications, Math. Probl. Eng., Doi:10.1155/2016/5471748, 2016.
  • [17] X. Ma and Z. Liu, Application of a novel time-delayed polynomial grey model to predict the natural gas consumption in China, J. Comput. Appl. Math. 324, 17–24, 2017.
  • [18] X. Ma, Z. Liu and Y. Wang, Application of a novel nonlinear multivariate grey Bernoulli model to predict the tourist income of China, J. Comput. Appl. Math. 347, 84–94, 2019.
  • [19] X. Ma, W. Wu, B. Zeng, Y. Wang and X. Wu, The conformable fractional grey system model, ISA Transactions 96, 255–271, 2020.
  • [20] S. Mao, M. Gao, X. Xiao and M. Zhu, A novel fractional grey system model and its application, Appl. Math. Model. 40 (7-8), 5063–5076, 2016.
  • [21] E. Masry, Multivariate local polynomial regression for time series: uniform strong consistency and rates, J. Time Series Anal. 17 (6), 571–599, 1996.
  • [22] W. Meng, Q. Li and B. Zeng, Study on fractional order grey reducing generation operator, Grey Syst. Theory Appl. 6 (1), 80–95, 2016.
  • [23] X. Meng and L. Wu, Prediction of per capita water consumption for 31 regions in China, Environ. Sci. Pollut. Res. 28, 29253–29264, 2021.
  • [24] X. Ping, F. Yang, H. Zhang, J. Zhang, W. Zhang and G. Song, Introducing machine learning and hybrid algorithm for prediction and optimization of multistage centrifugal pump in an orc system, Energy 222, 1-13, 2021.
  • [25] U. Sahin and T. Sahin, Forecasting the cumulative number of confirmed cases of covid- 19 in Italy, UK and USA using fractional nonlinear grey Bernoulli model, Chaos Solitons Fractals 138, 1-7, 2020.
  • [26] Y. Shen, B. He and P. Qing, Fractional-order grey prediction method for nonequidistant sequences, Entropy 18 (6), 1–16, 2016.
  • [27] A.J. Smola and B. Schölkopf, A tutorial on support vector regression, Stat. Comput. 14 (3), 199-222, 2004.
  • [28] Z.X. Wang, Q. Li and L.L. Pei, A seasonal GM (1,1) model for forecasting the electricity consumption of the primary economic sectors, Energy 154, 522–534, 2018.
  • [29] B. Wei, N. Xie and A. Hu, Optimal solution for novel grey polynomial prediction model, Appl. Math. Model. 62, 717–727, 2018.
  • [30] L. Wu, S. Liu, D. Chen, L. Yao and W. Cui, Using gray model with fractional order accumulation to predict gas emission, Nat. Hazards 71 (3), 2231–2236, 2014.
  • [31] L. Wu, S. Liu, L. Yao and S. Yan, The effect of sample size on the grey system model, Appl. Math. Model. 37, 6577–6583, 2013.
  • [32] L. Wu, S. Liu, L. Yao, S. Yan and D. Liu, Grey system model with the fractional order accumulation, Commun. Nonlinear Sci. Numer. Simul. 18 (7), 1775–1785, 2013.
  • [33] L.Z. Wu, S.H. Li, R.Q. Huang and Q. Xi, A new grey prediction model and its application to predicting landslide displacement, Appl. Soft Comput. 95, 1-11, 2020.
  • [34] W. Wu, X. Ma, Y. Wang, W. Cai and B. Zeng, Predicting Chinas energy consumption using a novel grey Riccati model, Appl. Soft Comput. 95, 1-11, 2020.
  • [35] W. Wu, X. Ma, B. Zeng, Y. Wang and W. Cai, Application of the novel fractional grey model FAGMO (1,1,k) to predict China’s nuclear energy consumption, Energy 165, 223–234, 2018.
  • [36] W. Wu, X. Ma, Y. Zhang, W. Li and Y. Wang, A novel conformable fractional nonhomogeneous grey model for forecasting carbon dioxide emissions of brics countries, Sci. Total Environ. 707, 1-24, 2020.
  • [37] W. Xie, L. Caixia, W. Wu, L. Weidong and L. Chong, Continuous grey model with conformable fractional derivative, Chaos Solitons Fractals 139, 1-9, 2020.
  • [38] W. Xie, W.Z. Wu, C. Liu and J. Zhao, Forecasting annual electricity consumption in China by employing a conformable fractional grey model in opposite direction, Energy 202, 1-13, 2020.
  • [39] W. Xie, W.Z. Wu, T. Zhang, and Q. Li, An optimized conformable fractional nonhomogeneous gray model and its application, Comm. Statist. Simulation Comput., Doi:10.1080/03610918.2020.1788588, 2020.
  • [40] K. Yuxiao, M. Shuhua, Z. Yonghong and Z. Huimin, Fractional derivative multivariable grey model for nonstationary sequence and its application, J. Syst. Eng 31 (5), 1009–1018, 2020.
  • [41] B. Zeng, Y. Tan, H. Xu, J. Quan, L. Wang and X. Zhou, Forecasting the electricity consumption of commercial sector in Hong Kong using a novel grey dynamic prediction model, J. Grey Syst. 30 (1), 157–172, 2018.
  • [42] P. Zhang, X. Ma and K. She, A novel power-driven fractional accumulated grey model and its application in forecasting wind energy consumption of China, Plos one 14, 1-33, 2019.
  • [43] Y.G. Zhang, Y. Xu and Z.P.Wang, GM (1,1) grey prediction of lorenz chaotic system, Chaos Solitons Fractals 42, 1003–1009, 2009.
  • [44] W. Zhou and J. M. He, Generalized GM (1,1) model and its application in forecasting of fuel production, Appl. Math. Model. 37 (9), 6234–6243, 2013.
There are 44 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Statistics
Authors

Zafer Öztürk 0000-0001-5662-4670

Halis Bilgil 0000-0002-8329-5806

Ümmügülsüm Erdinç This is me 0000-0002-4504-3675

Publication Date February 14, 2022
Published in Issue Year 2022 Volume: 51 Issue: 1

Cite

APA Öztürk, Z., Bilgil, H., & Erdinç, Ü. (2022). An optimized continuous fractional grey model for forecasting of the time dependent real world cases. Hacettepe Journal of Mathematics and Statistics, 51(1), 308-326. https://doi.org/10.15672/hujms.939543
AMA Öztürk Z, Bilgil H, Erdinç Ü. An optimized continuous fractional grey model for forecasting of the time dependent real world cases. Hacettepe Journal of Mathematics and Statistics. February 2022;51(1):308-326. doi:10.15672/hujms.939543
Chicago Öztürk, Zafer, Halis Bilgil, and Ümmügülsüm Erdinç. “An Optimized Continuous Fractional Grey Model for Forecasting of the Time Dependent Real World Cases”. Hacettepe Journal of Mathematics and Statistics 51, no. 1 (February 2022): 308-26. https://doi.org/10.15672/hujms.939543.
EndNote Öztürk Z, Bilgil H, Erdinç Ü (February 1, 2022) An optimized continuous fractional grey model for forecasting of the time dependent real world cases. Hacettepe Journal of Mathematics and Statistics 51 1 308–326.
IEEE Z. Öztürk, H. Bilgil, and Ü. Erdinç, “An optimized continuous fractional grey model for forecasting of the time dependent real world cases”, Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 1, pp. 308–326, 2022, doi: 10.15672/hujms.939543.
ISNAD Öztürk, Zafer et al. “An Optimized Continuous Fractional Grey Model for Forecasting of the Time Dependent Real World Cases”. Hacettepe Journal of Mathematics and Statistics 51/1 (February 2022), 308-326. https://doi.org/10.15672/hujms.939543.
JAMA Öztürk Z, Bilgil H, Erdinç Ü. An optimized continuous fractional grey model for forecasting of the time dependent real world cases. Hacettepe Journal of Mathematics and Statistics. 2022;51:308–326.
MLA Öztürk, Zafer et al. “An Optimized Continuous Fractional Grey Model for Forecasting of the Time Dependent Real World Cases”. Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 1, 2022, pp. 308-26, doi:10.15672/hujms.939543.
Vancouver Öztürk Z, Bilgil H, Erdinç Ü. An optimized continuous fractional grey model for forecasting of the time dependent real world cases. Hacettepe Journal of Mathematics and Statistics. 2022;51(1):308-26.

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