Accurately forecasting the demand for tourism can help governments formulate industrial policies and guide the business sector in investment planning. Combining forecasts can improve the accuracy of forecasting the demand for tourism, but limited work has been devoted to developing such combinations. This article addresses two significant issues in this context. First, the linear combination is the commonly used method of combining tourism forecasts. However, additive techniques unreasonably ignore interactions among the inputs. Second, the available data often do not adhere to specific statistical assumptions. Grey prediction has thus drawn attention because it does not require that the data follow any statistical distribution. This study proposes a nonadditive combination method by using the fuzzy integral to integrate single-model forecasts obtained from individual grey prediction models. Using China and Taiwan tourism demand as empirical cases, the results show that the proposed method outperforms the other combined methods considered here.
AndrawisR. R.AtiyaA. F.El-ShishinyH. (2011). Combination of long-term and short-term forecasts, with application to tourism demand forecasting. International Journal of Forecasting, 27(3), 870-886. https://doi.org/10.1016/j.ijforecast.2010.05.019
2.
CangS. (2014). A comparative analysis of three types of tourism demand forecasting models: Individual, linear combination and non-linear combination, International Journal of Tourism Research, 16(6), 596-607. https://doi.org/10.1002/jtr.1953
3.
ChenC. F.LaiM. C.YehC. C. (2012). Forecasting tourism demand based on empirical mode decomposition and neural network. Knowledge-Based Systems, 26(February), 281-287. https://doi.org/10.1016/j.knosys.2011.09.002
4.
ChenC. I. (2008). Application of the novel nonlinear grey Bernoulli model for forecasting unemployment rate. Chaos, Solitons & Fractals, 37(1), 278-287. https://doi.org/10.1016/j.chaos.2006.08.024
5.
ChenC. I.ChenH. L.ChenS. P. (2008). Forecasting of foreign exchange rates of Taiwan’s major trading partners by novel nonlinear grey Bernoulli model NGBM(1,1). Communications in Nonlinear Science and Numerical Simulations, 13(6), 1194-1204. https://doi.org/10.1016/j.cnsns.2006.08.008
6.
ChenC. Y.HuangJ. J. (2019). Forming a hierarchical Choquet integral with a GA-based heuristic least square method. Mathematics, 7(12), 1155. https://doi.org/10.3390/math7121155
7.
ChenK. Y. (2011). Combining linear and nonlinear model in forecasting tourism demand. Expert Systems With Applications, 38(8), 10368-10376. https://doi.org/10.1016/j.eswa.2011.02.049
8.
ChenY. Y.LiuH. T.HsiehH. L. (2019). Time series interval forecast using GM(1,1) and NGBM(1,1) models. Soft Computing, 23(5), 1541-1555. https://doi.org/10.1007/s00500-017-2876-0
ClaveriaO.MonteE.TorraS. (2015). Tourism demand forecasting with neural network models: Different ways of treating information. International Journal of Tourism Research, 17(5), 492-500. https://doi.org/10.1002/jtr.2016
ClementsM.HendryD. (2009). Forecasting economic time series. Cambridge University Press.
13.
CoshallJ. T.CharlesworthR. (2011). A management orientated approach to combination forecasting of tourism demand. Tourism Management, 32(4), 759-769. https://doi.org/10.1016/j.tourman.2010.06.011
14.
DeMiccoF.CetronM.DaviesO.GuzmanJ. (2021). COVID-19 impact on the future of hospitality and travel. Journal of Hospitality & Tourism Research, 45(5), 911-914. https://doi.org/10.1177/10963480211000822
GoodfellowI.BengioY.CourvilleA. (2016). Deep learning. MIT Press.
18.
HarveyD.LeybourneS.NewboldP. (1997). Testing the equality of prediction mean squared errors. International Journal of Forecasting, 13(2), 281-291. https://doi.org/10.1016/S0169-2070(96)00719-4
19.
HeatonJ. (2015). Artificial intelligence for humans: Deep learning and neural networks. St. Heaton Research.
20.
HuM.QiuR. T. R.WuD. C.SongH. (2021). Hierarchical pattern recognition for tourism demand forecasting. Tourism Management, 84(June), 104263. https://doi.org/10.1016/j.tourman.2020.104263
21.
HuY. C. (2014). Non-additive similarity-based single-layer perceptron for multi-criteria collaborative filtering. Neurocomputing, 129(April), 306-314. https://doi.org/10.1016/j.neucom.2013.09.027
22.
HuY. C. (2020). A multivariate grey prediction model with grey relational analysis for bankruptcy prediction problems. Soft Computing, 24(6), 4259-4268. https://doi.org/10.1007/s00500-019-04191-0
23.
HuY. C. (2021). Forecasting tourism demand using fractional grey prediction models with Fourier series. Annals of Operations Research, 300(2), 467-491. https://doi.org/10.1007/s10479-020-03670-0
24.
HuY. C.JiangP.LeeP. C. (2019). Forecasting tourism demand by incorporating neural networks into grey-Markov models. Journal of the Operational Research Society, 70(1), 12-20. https://doi.org/10.1080/01605682.2017.1418150
25.
HuangY. L.LeeY. H. (2011). Accurately forecasting model for the stochastic volatility data in tourism demand. Modern Economy, 2(5), 823-829. https://doi.org/10.4236/me.2011.25091
26.
IshibuchiH.NakashimaT.NiiM. (2004). Classification and modeling with linguistic information granules: Advanced approaches to linguistic data mining. Springer-Verlag.
27.
JiangP.WangW. B.HuY. C.ChiuY. J.TsaoS. R. (2020). Pattern classification using tolerance rough sets based on non-additive grey relational analysis and DEMATEL. Grey Systems: Theory and Application, 11(1), 166-182. https://doi.org/10.1108/GS-05-2020-0062
LawR.LiG.FongD. K. C.HanX. (2019). Tourism demand forecasting: A deep learning approach. Annals of Tourism Research, 75(March), 410-423. https://doi.org/10.1016/j.annals.2019.01.014
LiaoZ.LiaoH.TangM.Al-BarakatiA.Llopis-AlbertC. (2020). A Choquet integral-based hesitant fuzzy gained and lost dominance score method for multi-criteria group decision making considering the risk preferences of experts: Case study of higher business education evaluation. Information Fusion, 62(October), 121-133. https://doi.org/10.1016/j.inffus.2020.05.003
33.
LinC. J.ChenH. F.LeeT. S. (2011). Forecasting tourism demand using time series, artificial neural networks and multivariate adaptive regression splines: Evidence from Taiwan. International Journal of Business Administration, 2(2), 14-24. https://doi.org/10.5430/ijba.v2n2p14
34.
LiouJ. J. H. (2013). New concepts and trends of MCDM for tomorrow: In honor of Professor Gwo-Hshiung Tzeng on the occasion of his 70th birthday. Technological and Economic Development of Economy, 19(2), 367-375. https://doi.org/10.3846/20294913.2013.811037
35.
LiouJ. J. H.ChuangY. C.TzengG. H. (2014). A fuzzy integral-based model for supplier evaluation and improvement. Information Sciences, 266(May), 199-217. https://doi.org/10.1016/j.ins.2013.09.025
36.
LiouJ. J. H.TzengG. H. (2012). Comments on “Multiple criteria decision making (MCDM) methods in economics: An overview.”Technological and Economic Development of Economy, 18(4), 672-695. https://doi.org/10.3846/20294913.2012.753489
37.
LiuH.LiuW.WangY. (2020). A study on the influencing factors of tourism demand from Mainland China to Hong Kong. Journal of Hospitality & Tourism Research, 45(1), 171-191. https://doi.org/10.1177/1096348020944435
38.
LiuS.LinY. (2010). Grey information: Theory and practical applications. Springer.
39.
LiuS.XieN. (2013). Grey system theory and its applications. Scientific Press.
LiuX.PengH.BaiY.ZhuY.LiaoL. (2014). Tourism flows prediction based on an improved grey GM(1,1) model. Procedia: Social and Behavioral Sciences, 138(July), 767-775. https://doi.org/10.1016/j.sbspro.2014.07.256
42.
MaX.LiuZ.WangY. (2019). Application of a novel nonlinear multivariate grey Bernoulli model to predict the tourist income of China. Journal of Computational and Applied Mathematics, 347(February), 84-94. https://doi.org/10.1016/j.cam.2018.07.044
OhC. O.MorzuchB. J. (2005). Evaluating time-series models to forecast the demand for tourism in Singapore: Comparing within-sample and post sample results. Journal of Travel Research, 43(4), 404-413. https://doi.org/10.1177/0047287505274653
45.
OnafoworaO. A.OwoyeO. (2012). Modelling international tourism demand for the Caribbean. Tourism Economics, 18(1), 159-180. https://doi.org/10.5367/te.2012.0102
46.
OnisawaT.SugenoM.NishiwakiM. Y.KawaiH.HarimaY. (1986). Fuzzy measure analysis of public attitude towards the use of nuclear energy. Fuzzy Sets and Systems, 20(3), 259-289. https://doi.org/10.1016/S0165-0114(86)90040-0
47.
OsyczkaA. (2002). Evolutionary algorithms for single and multicriteria design optimization. Physica-Verlag.
48.
PengK. H.TzengG. H. (2013). A hybrid dynamic MADM model for problems-improvement in economics and business. Technological and Economic Development of Economy, 19(4), 638-660. https://doi.org/10.3846/20294913.2013.837114
49.
QiuR. T. R.WuD. C.DropsyV.PetitS.PrattS.OheY. (2021). Visitor arrivals forecasts amid COVID-19: A perspective from the Asia and Pacific team. Annals of Tourism Research, 88(May), 103155. https://doi.org/10.1016/j.annals.2021.103155
50.
ShenS. J.LiG.SongH. (2008). An assessment of combining tourism demand forecasts over different time horizons. Journal of Travel Research, 47(2), 197-207. https://doi.org/10.1177/0047287508321199
SongH.QiuR. T. R.ParkJ. (2019). A review of research on tourism demand forecasting: Launching the Annals of Tourism Research Curated Collection on tourism demand forecasting. Annals of Tourism Research, 75(March), 338-362. https://doi.org/10.1016/j.annals.2018.12.001
54.
SongH.WittS. F.WongK. F.WuD. C. (2009). An empirical study of forecast combination in tourism. Journal of Hospitality & Tourism Research, 33(1), 3-29. https://doi.org/10.1177/1096348008321366
55.
SuganthiL.SamuelA. A. (2012). Energy models for demand forecasting: A review. Renewable and Sustainable Energy Reviews, 16(2), 1223-1240. https://doi.org/10.1016/j.rser.2011.08.014
56.
SugenoM.NarukawaY.MurofushiY. (1998). Choquet integral and fuzzy measures on locally compact space. Fuzzy Sets and Systems, 99(2), 205-211. https://doi.org/10.1016/S0165-0114(97)00028-6
57.
SunX.SunW.WangJ.GaoY. (2016). Using a grey–Markov model optimized by Cuckoo search algorithm to forecast the annual foreign tourist arrivals to China. Tourism Management, 52(February), 369-379. https://doi.org/10.1016/j.tourman.2015.07.005
TorralejaF. A. G.VazquezA. M.FrancoM. J. B. (2009). Flows into tourist areas: An econometric approach. International Journal of Tourism Research, 11(1), 1-15. https://doi.org/10.1002/jtr.657
60.
TsuiW. H. K.BalliH. O.GilbeyA.GowH. (2014). Forecasting of Hong Kong airport’s passenger throughput. Tourism Management, 42(June), 62-76. https://doi.org/10.1016/j.tourman.2013.10.008
61.
TzengG. H.HuangJ. J. (2011). Multiple attribute decision making: Methods and applications. CRC Press. https://doi.org/10.1201/b11032
WangJ.LuoY.TangL.GeP. (2018). Modeling a combined forecast algorithm based on sequence patterns and near characteristics: An application for tourism demand forecasting. Chaos, Solitons & Fractals, 108(March), 136-147. https://doi.org/10.1016/j.chaos.2018.01.028
66.
WangX. Z.HeY. L.DongL. C.ZhaoH. Y. (2011). Particle swarm optimization for determining fuzzy measures from data. Information Sciences, 181(19), 4230-4252. https://doi.org/10.1016/j.ins.2011.06.002
WeiB.XieN. (2021). Parameter estimation for grey system models: A nonlinear least squares perspective. Communications in Nonlinear Science and Numerical Simulation, 95(April), 105653. https://doi.org/10.1016/j.cnsns.2020.105653
World Travel and Tourism Council. (2020). The economic impact of travel of travel and tourism. Author.
71.
WuD. C.CaoZ.WenL.SongH. (2020). Scenario forecasting for global tourism. Journal of Hospitality & Tourism Research, 45(1), 28-51. https://doi.org/10.1177/1096348020919990
72.
WuD. C.JiL.HeK.TsoK. F. G. (2020). Forecasting tourist daily arrivals with a hybrid SARIMA–LSTM approach. Journal of Hospitality & Tourism Research, 45(1), 52-67. https://doi.org/10.1177/1096348020934046
73.
WuD. C.SongH.ShenS. (2017). New developments in tourism and hotel demand modeling and forecasting. International Journal of Contemporary Hospitality Management, 29(1), 507-529. https://doi.org/10.1108/IJCHM-05-2015-0249
74.
WuL.GaoX.XiaoY.YangY.ChenX. (2018). Using a novel multi-variable grey model to forecast the electricity consumption of Shandong Province in China. Energy, 157(August), 327-335. https://doi.org/10.1016/j.energy.2018.05.147
75.
WuL.LiuS.FangZ.XuH. (2015). Properties of the GM(1,1) with fractional order accumulation. Applied Mathematics and Computation, 252(February), 287-293. https://doi.org/10.1016/j.amc.2014.12.014
76.
WuL.LiuS.YaoL.YanS. (2013). The effect of sample size on the grey system model. Applied Mathematical Modelling, 37(9), 6577-6583. https://doi.org/10.1016/j.apm.2013.01.018
77.
XieM.WuL.LiB.LiZ. (2020). A novel hybrid multivariate nonlinear grey model for forecasting the traffic-related emissions. Applied Mathematical Modelling, 77(January), 1242-1254. https://doi.org/10.1016/j.apm.2019.09.013
78.
XuN.DangY.GongY. (2017). Novel grey prediction model with nonlinear optimized time response method for forecasting of electricity consumption in China. Energy, 118(January), 473-480. https://doi.org/10.1016/j.energy.2016.10.003
79.
YaoY.CaoY. (2020). A neural network enhanced hidden Markov model for tourism demand forecasting. Applied Soft Computing, 94(September), 106465. https://doi.org/10.1016/j.asoc.2020.106465
80.
ZengB.MengW. (2015). Research on fractional accumulating generation operators and grey prediction models. Scientific Press.
81.
ZhangY.LiG.MuskatB.LawR. (2020). Tourism demand forecasting: A decomposed deep learning approach. Journal of Travel Research, 60(5), 981-997. https://doi.org/10.1177/0047287520919522
Supplementary Material
Please find the following supplemental material available below.
For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.
For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.
