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Developing grey prediction with Fourier series using genetic algorithms for tourism demand forecasting

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Abstract

Predicting the number of foreign tourists is significant for governments in devising development policies for tourism demand. Time series related to tourism often feature significant temporal fluctuation. Therefore, grey prediction in conjunction with the Fourier series for oscillating sequences is appropriate to foreign tourists forecasting. Grey prediction traditionally uses the ordinary least squares (OLS) to derive relevant parameters. However, as the conformance to statistical assumption is not guaranteed, estimators derived by using OLS may not be reliable. This study proposes an OLS-free grey model with the Fourier series by using soft computing techniques to determine the optimal parameters to maximize prediction accuracy. The experimental results demonstrate that the proposed grey prediction model performs well compared with other prediction models considered.

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References

  • Askari, M., Fetanat, A.: Long-term forecasting in power system: grey system prediction-based models. J. Appl. Sci. 11(16), 3034–3038 (2011)

    Google Scholar 

  • Chang, C.J., Yu, L., Jin, P.: A mega-trend-diffusion grey forecasting model for short-term manufacturing demand. J. Oper. Res. Soc. 67(12), 1439–1445 (2016)

    Google Scholar 

  • Chen, C.I.: Application of the novel nonlinear grey Bernoulli model for forecasting unemployment rate. Chaos Solitons Fractals 37(1), 278–287 (2008)

    Google Scholar 

  • Chen, C.I., Chen, H.L., Chen, S.P.: Forecasting of foreign exchange rates of Taiwan’s major trading partners by novel nonlinear grey Bernoulli model NGBM(1,1). Commun. Nonlinear Sci. Numer. Simul. 13(6), 1194–1204 (2008)

    Google Scholar 

  • Demšar, J.: Statistical comparisons of classifiers over multiple data sets. J. Mach. Learn. Res. 7, 1–30 (2006)

    Google Scholar 

  • Ene, S., Öztürk, N.: Grey modelling based forecasting system for return flow of end-of-life vehicles. Technol. Forecast. Soc. Change 115, 155–166 (2017)

    Google Scholar 

  • Feng, S.J., Ma, Y.D., Song, Z.L., Ying, J.: Forecasting the energy consumption of China by the grey prediction model. Energy Sources Part B 7, 376–389 (2012)

    Google Scholar 

  • Friedman, M.: A comparison of alternative tests of significance for the problem of m rankings. Ann. Math. Stat. 11, 86–92 (1940)

    Google Scholar 

  • Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading (1989)

    Google Scholar 

  • Habibi, F., Rahim, K.A., Ramchandran, S., Chin, L.: Dynamic model for international tourism demand for Malaysia: panel data evidence. Int. Res. J. Finance Econ. 33, 207–217 (2009)

    Google Scholar 

  • Hsu, L.C.: A genetic algorithm based nonlinear grey Bernoulli model for output forecasting in integrated circuit industry. Expert Syst. Appl. 37(6), 4318–4323 (2010)

    Google Scholar 

  • Hsu, Y.T., Liu, M.C., Yeh, J., Hung, H.F.: Forecasting the turning time of stock market based on Markov–Fourier grey model. Expert Syst. Appl. 36(4), 8597–8603 (2009)

    Google Scholar 

  • Hu, Y.C.: Functional-link nets with genetic-algorithm-based learning for robust nonlinear interval regression analysis. Neurocomputing 72(7-9), 1808–1816 (2009)

    Google Scholar 

  • Hu, Y.C.: Nonadditive similarity-based single-layer perceptron for multi-criteria collaborative filtering. Neurocomputing 129, 306–314 (2014)

    Google Scholar 

  • Hu, Y.C.: Electricity consumption forecasting using a neural-network-based grey prediction approach. J. Oper. Res. Soc. 68(10), 1259–1264 (2017a)

    Google Scholar 

  • Hu, Y.C.: Grey prediction with residual modification using functional-link net and its application to energy demand forecasting. Kybernetes 46(2), 349–363 (2017b)

    Google Scholar 

  • Hu, Y.C., Jiang, P.: Forecasting energy demand using neural-network-based grey residual modification models. J. Oper. Res. Soc. 68(5), 556–565 (2017)

    Google Scholar 

  • Huang, Y.L., Lee, Y.H.: Accurately forecasting model for the stochastic volatility data in tourism demand. Mod. Econ. 2(5), 823–829 (2011)

    Google Scholar 

  • Iman, R.L., Davenport, J.M.: Approximations of the critical region of the Friedman statistic. Commun. Stat. 9(6), 571–595 (1980)

    Google Scholar 

  • Ishibuchi, H., Nakashima, T., Nii, M.: Classification and modeling with linguistic information granules: advanced approaches to linguistic data mining. Springer, Heidelberg (2004)

    Google Scholar 

  • Jang, J.S.R., Sun, C.T., Mizutani, E.: Neuro-fuzzy and soft computing: a computational approach to learning and machine intelligence. Prentice-Hall, Englewood Cliffs (1997)

    Google Scholar 

  • Lee, S.C., Shih, L.H.: Forecasting of electricity costs based on an enhanced gray-based learning model: a case study of renewable energy in Taiwan. Technol. Forecast. Soc. Change 78, 1242–1253 (2011)

    Google Scholar 

  • Lee, Y.S., Tong, L.I.: Forecasting energy consumption using a grey model improved by incorporating genetic programming. Energy Convers. Manag. 52, 147–152 (2011)

    Google Scholar 

  • Li, D.C., Chang, C.J., Chen, C.C., Chen, W.C.: Forecasting short-term electricity consumption using the adaptive grey-based approach—an Asian case. Omega 40, 767–773 (2012)

    Google Scholar 

  • Lin, C.J., Chen, H.F., Lee, T.S.: Forecasting tourism demand using time series, artificial neural networks and multivariate adaptive regression splines: evidence from Taiwan. Int. J. Bus. Adm. 2(2), 14–24 (2011)

    Google Scholar 

  • Liu, S., Lin, Y.: Grey information: theory and practical applications. Springer, Berlin (2010)

    Google Scholar 

  • Liu, S., Yang, Y., Forrest, J.: Grey data analysis: methods, models and applications. Springer, Berlin (2017)

    Google Scholar 

  • Lu, J., Xie, W., Zhou, H., Zhang, A.: An optimized nonlinear grey Bernoulli model and its applications. Neurocomputing 177, 206–214 (2016)

    Google Scholar 

  • Makridakis, S.: Accuracy measures: theoretical and practical concerns. Int. J. Forecast. 9(4), 527–529 (1993)

    Google Scholar 

  • Mao, M.Z., Chirwa, E.C.: Application of grey model GM(1,1) to vehicle fatality risk estimation. Technol. Forecast. Soc. Change 73, 588–605 (2006)

    Google Scholar 

  • Murata, T., Ishibuchi, H., Tanaka, H.: Multi-objective genetic algorithm and its applications to flowshop scheduling. Comput. Ind. Eng. 30(4), 957–968 (1996)

    Google Scholar 

  • Nguyen, T.L., Huang, J.C., Chiu, C.C., Shu, M.H., Tsai, W.R.: Forecasting model for the international tourism demand in Taiwan. In: Proceedings of 2013 International Conference on Technology Innovation and Industrial Management, Phuket, Thailand, pp. 61–70 (S5) (2013)

  • Osyczka, A.: Evolutionary algorithms for single and multicriteria design optimization. Physica-Verlag, Heidelberg (2003)

    Google Scholar 

  • Ouerfelli, C.: Co-integration analysis of quarterly European tourism demand in Tunisia. Tour. Manag. 29, 127–137 (2008)

    Google Scholar 

  • Pao, Y.H.: Adaptive pattern recognition and neural networks. Addison-Wesley, Reading (1989)

    Google Scholar 

  • Pao, Y.H.: Functional-link net computing: theory, system architecture, and functionalities. Computer 25(5), 76–79 (1992)

    Google Scholar 

  • Pao, H.T., Fu, H.C., Tseng, C.L.: Forecasting of CO2 emissions, energy consumption and economic growth in China using an improved grey model. Energy 40(1), 400–409 (2012)

    Google Scholar 

  • Park, G.H., Pao, Y.H.: Unconstrained word-based approach for off-line script recognition using density-based random-vector functional-link net. Neurocomputing 31(1–4), 45–65 (2000)

    Google Scholar 

  • Song, H., Li, G.: Tourism demand modelling and forecasting: a review of recent research. Tour. Manag. 29(2), 203–220 (2008)

    Google Scholar 

  • Suganthi, L., Samuel, A.A.: Energy models for demand forecasting—a review. Renew. Sustain. Energy Rev. 16, 1223–1240 (2012)

    Google Scholar 

  • Sun, X., Sun, W., Wang, J., Gao, Y.: Using a Grey–Markov model optimized by Cuckoo search algorithm to forecast the annual foreign tourist arrivals to China. Tour. Manag. 52, 369–379 (2016)

    Google Scholar 

  • Tsaur, R.C., Liao, Y.C.: Forecasting LCD TV demand using the fuzzy grey model GM(1,1). Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 15, 753–767 (2007)

    Google Scholar 

  • Wang, Z.X.: Grey forecasting method for small sample oscillating sequences based on Fourier series. Control Decis. 29(2), 270–274 (2014)

    Google Scholar 

  • Wang, Z.Z., Dang, Y.G., Liu, S.F., Zhao, J.J.: Solution of GM (1, 1) power model and its properties. Syst. Eng. Electron. 31(10), 2380–2383 (2009)

    Google Scholar 

  • Wang, Z.X., Hao, P.: An improved grey multivariable model for predicting industrial energy consumption in China. Appl. Math. Model. 40(11-12), 5745–5758 (2016)

    Google Scholar 

  • Wang, Z.X., Hipel, K.W., Wang, Q., He, S.W.: An optimized NGBM(1,1) model for forecasting the qualified discharge rate of industrial wastewater in China. Appl. Math. Model. 35(12), 5524–5532 (2011)

    Google Scholar 

  • Wang, C.N., Phan, V.T.: An improved nonlinear grey Bernoulli model combined with Fourier series. Math. Probl. Eng. Vol. 2015, Article ID 740272 (2015)

  • Wei, J., Zhou, L., Wang, F., Wu, D.: Work safety evaluation in Mainland China using grey theory. Appl. Math. Model. 39(2), 924–933 (2015)

    Google Scholar 

  • Wen, K.L.: Grey systems modeling and prediction. Yang’s Scientific Research Institute, Tucson (2004)

    Google Scholar 

  • Wu, D.C., Song, H., Shen, S.: New developments in tourism and hotel demand modeling and forecasting. Int. J. Contemp. Hosp. Manag. 29(1), 507–529 (2017)

    Google Scholar 

  • Yang, Y.N.: Financial econometric with Gretl. Compass Publishing, Taipei (2010)

    Google Scholar 

  • Zhou, J., Fang, R., Li, Y., Zhang, Y., Peng, B.: Parameter optimization of nonlinear grey Bernoulli model using particle swarm optimization. Appl. Math. Comput. 207(2), 292–299 (2009)

    Google Scholar 

Download references

Acknowledgements

The author would like to thank the anonymous referees for their valuable comments. This research is supported by the Ministry of Science and Technology, Taiwan under Grant MOST 108-2410-H-033-038-MY2.

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Correspondence to Yi-Chung Hu.

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Hu, YC. Developing grey prediction with Fourier series using genetic algorithms for tourism demand forecasting. Qual Quant 55, 315–331 (2021). https://doi.org/10.1007/s11135-020-01006-5

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