Forecasting Tourist Arrivals to Sangiran Using Fuzzy with Calendar Variations

Abstract

Fuzzy method has been widely used in time series forecasting. However, the current fuzzy time models have not accommodated the holiday effects so that the forecasting error becomes large at certain moments. Regarding the problem, this study proposes two algorithms, extended of Chen’s and seasonal fuzzy time series method (FTS), to consider the holiday effect in forecasting the monthly tourist arrivals to ancient human Sangiran Museum. Both algorithms consider the relationship between Eid holidays as the effect of calendar variations. The forecasting results obtained from the two proposed algorithms are then compared with those obtained from the Chen’s and the seasonal FTS. Based on the experimental results, the proposed method can reduce mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE) obtained from Chen’s method up to 61%, 61%, and 58%, respectively. Moreover, compared to that obtained from the seasonal FTS, the proposed method can reduce the MAE, RMSE, and MAPE values up to 35%, 36%, and 29%, respectively. The method proposed in this paper can be implemented to other time series with seasonal pattern and calendar variation effects.

Keywords

• Fuzzy Time Series
• Seasonal
• Calendar Variations
• Tourist Arrivals
• Sangiran

References

1. Aladag, S., Aladag, C. H., Mentes, T., & Egrioglu, E. (2012). A new seasonal fuzzy time series method based on the multiplicative neuron model and SARIMA. Hacettepe Journal of Mathematics and Statistics, 41(3), 337–345.
2. Alpaslan, F., Cagcag, O., Aladag, C. H., Yolcu, U., & Egrioglu, E. (2012). A novel seasonal fuzzy time series method. Hacettepe Journal of Mathematics and Statistics, 41(3), 375–385.
3. Anggraeni, W., Vinarti, R. A., & Kurniawati, Y. D. (2015). Performance comparisons between arima and arimax method in moslem kids clothes demand forecasting: Case study. Procedia Computer Science, 72, 630–637.
4. Bas, E., Yolcu, U., & Egrioglu, E. (2021). Intuitionistic fuzzy time series functions approach for time series forecasting. Granular Computing, 6(3), 619-629.
5. Cagcag, O., Yolcu, U., Egrioglu, E., & Aladag, C. H. (2013). A novel seasonal fuzzy time series method to the forecasting of air pollution data in Ankara. American Journal of Intelligent Systems, 3(1), 13–19.
6. Chang, Y. W., & Liao, M. Y. (2010). A seasonal ARIMA model of tourism forecasting: The case of Taiwan. Asia Pacific Journal of Tourism Research, 15(2), 215–221.
7. Chen, K. 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. Chen, R. J., Bloomfield, P., & Cubbage, F. W. (2008). Comparing forecasting models in tourism. Journal of Hospitality & Tourism Research, 32(1), 3–21.

9. Chen, S. M. (1996). Forecasting enrollments based on fuzzy time series. Fuzzy Sets and Systems, 81(3), 311–319.
10. Cheng, C. H., Chen, T. L., Teoh, H. J., & Chiang, C. H. (2008). Fuzzy time-series based on adaptive expectation model for TAIEX forecasting. Expert Systems with Applications, 34(2), 1126–1132.
11. Egrioglu, E., Bas, E., Yolcu, U., & Chen, M. Y. (2020). Picture fuzzy time series: Defining, modeling and creating a new forecasting method. Engineering Applications of Artificial Intelligence, 88, 103367.
12. Gao, R., & Duru, O. (2020). Parsimonious fuzzy time series modelling. Expert Systems with Applications, 156, 113447.
13. Hanke, E.J., Wichern, W. D., & Reitsch, G. A. (2005). Business Forecasting (8th ed.). Pearson, Prentice Hall.
14. Hyndman, R. J., & Koehler, A. B. (2006). Another look at measures of forecast accuracy. International Journal of Forecasting, 22(4), 679–688. https://doi.org/10.1016/j.ijforecast.2006.03.001
15. Koo, J. W., Wong, S. W., Selvachandran, G., & Long, H. V. (2020). Prediction of Air Pollution Index in Kuala Lumpur using fuzzy time series and statistical models. Air Quality, Atmosphere & Health, 13(1), 77–88.
16. Lee, M. H., & Hamzah, N. (2010). Calendar variation model based on ARIMAX for forecasting sales data with Ramadhan effect. Proceedings of the Regional Conference on Statistical Sciences, 10, 30–41.
17. Lee, M. H., & Javedani, H. (2011). A weighted fuzzy integrated time series for forecasting tourist arrivals. International Conference on Informatics Engineering and Information Science, 206–217.
18. Lee, M. H., Nor, M. E., Suhartono, Sadaei, H. J., Rahman, N. H. A., & Kamisan, N. A. B. (2012). Fuzzy Time Series: An Application to Tourism Demand Forecasting. American Journal of Applied Sciences, 9(1), 132–140. https://doi.org/10.3844/ajassp.2012.132.140
19. Lee, M. H., & Suhartono. (2010). A novel weighted fuzzy time series model for forecasting seasonal data. Proceeding the 2nd International Conference on Mathematical Sciences, 332–340.
20. Ling, A. S. C., Darmesah, G., Chong, K. P., & Ho, C. M. (2019). Application of ARIMAX Model to Forecast Weekly Cocoa Black Pod Disease Incidence. Mathematics and Statistics, 7(4A), 29–40. https://doi.org/10.13189/ms.2019.070705
21. Liu, H. T., & Wei, M. L. (2010). An improved fuzzy forecasting method for seasonal time series. Expert Systems with Applications, 37(9), 6310–6318.
22. Makridakis, S., & Hibon, M. (2000). The M3-Competition: Results, conclusions and implications. International Journal of Forecasting, 16(4), 451–476. https://doi.org/10.1016/S0169-2070(00)00057-1
23. Sarı, I. U. (2012). Forecasting energy demand using fuzzy seasonal time series. In Computational Intelligence Systems in Industrial Engineering (pp. 251–269). Springer.
24. Singh, H., Gupta, M. M., Meitzler, T., Hou, Z. G., Garg, K. K., Solo, A. M. G., & Zadeh, L. A. (2013). Real-Life Applications of Fuzzy Logic. Advances in Fuzzy Systems, 2013, e581879. https://doi.org/10.1155/2013/581879
25. Song, Q. (1999). Seasonal forecasting in fuzzy time series. Fuzzy Sets and Systems, 107(2), 235–236.
26. Song, Q., & Chissom, B. S. (1993). Forecasting enrollments with fuzzy time series—Part I. Fuzzy Sets and Systems, 54(1), 1–9.
27. Song, Q., & Chissom, B. S. (1993). Fuzzy time series and its models. Fuzzy Sets and Systems, 54(3), 269–277.
28. Song, Q., & Chissom, B. S. (1994). Forecasting enrollments with fuzzy time series—Part II. Fuzzy Sets and Systems, 62(1), 1–8.
29. Suhartono, Lee, M. H., & Prastyo, D. D. (2015). Two levels ARIMAX and regression models for forecasting time series data with calendar variation effects. AIP Conference Proceedings, 1691(1), 050026.
30. Suhartono, S. (2006). Calendar variation model for forecasting time series data with islamic calendar effect. Jurnal Matematika Sains Dan Teknologi, 7(2), 85–94.
31. Suhartono, S., Dana, I. M. G. M., & Rahayu, S. P. (2019). Hybrid model for forecasting space-time data with calendar variation effects. Telkomnika, 17(1), 118–130. https://doi.org/10.12928/TELKOMNIKA.v17i1.10096
32. Sulandari, W., Subanar, S., Lee, M. H., & Rodrigues, P. C. (2020). Time series forecasting using singular spectrum analysis, fuzzy systems and neural networks. MethodsX, 7, 101015. https://doi.org/10.1016/j.mex.2020.101015
33. Sulandari, W., Subanar, S., Suhartono, S., Utami, H., Lee, M. H., & Rodrigues, P. C. (2020). SSA-based hybrid forecasting models and applications. Bulletin of Electrical Engineering and Informatics, 9(5), 2178–2188. https://doi.org/10.11591/eei.v10i1.1950
34. Sulandari, W., Subanti, S., Slamet, I., Sugiyanto, Zukhronah, E., & Susanto, I. (2021). Application of linear and nonlinear seasonal autoregressive based methods for forecasting Grojogan Sewu tourism demand. AIP Conference Proceedings, 2329(1), 060008.
35. Sumarminingsih, E., Matoha, S., Suharsono, A., & Ruchjana, B. N. (2018). Spatial Vector Autoregressive Model with Calendar Variation for East Java Inflation and Money Supply. Appl. Math. Inf. Sci, 12(6), 1157–1163.
36. Sun, S., Wei, Y., Tsui, K.-L., & Wang, S. (2019). Forecasting tourist arrivals with machine learning and internet search index. Tourism Management, 70, 1–10. https://doi.org/10.1016/j.tourman.2018.07.010
37. Tayyaba, S., Ashraf, M. W., Alquthami, T., Ahmad, Z., & Manzoor, S. (2020). Fuzzy-Based Approach Using IoT Devices for Smart Home to Assist Blind People for Navigation. Sensors (Basel, Switzerland), 20(13), 3674. https://doi.org/10.3390/s20133674
38. Vlamou, E., & Papadopoulos, B. (2019). Fuzzy logic systems and medical applications. AIMS Neuroscience, 6(4), 266–272. https://doi.org/10.3934/Neuroscience.2019.4.266
39. Wong, K. K., Song, H., Witt, S. F., & Wu, D. C. (2007). Tourism forecasting: To combine or not to combine? Tourism Management, 28(4), 1068–1078.
40. Yu, H. K. (2005). Weighted fuzzy time series models for TAIEX forecasting. Physica A: Statistical Mechanics and Its Applications, 349(3–4), 609–624.