PERFORMANCE COMPARISON OF SOME TYPES OF WAVELET TRANSFORMS FOR TOURISM DATA PATTERN APPROXIMATION

Abstract

Tourism is an economic sector that significantly supports the country's foreign exchange, including in West Nusa Tenggara Province (NTB). Data on tourist visits to an area, including to NTB, is a representation of time series data. The wavelet method is one of the tools that is quite reliable for modeling time series data. This study aims to model the number of tourist visits to NTB Province using discrete wavelet transformation decomposition to estimate data. Several Wavelet functions such as Haar wavelet, Symlet, Coiflet, Daubechies, Best-localized Daubechies, Fejér-Korovkin, and Bi-orthogonal Splines at various orders and levels of decomposition became the basis for simulation in modeling data. Based on the Root of Mean of Square Error (RMSE) indicator, this study compares the performance of each wavelet function against the modeling performance at various orders and levels of decomposition. Numerically, for the data on the total number of tourists visiting NTB Province, the best approximation was given by the Fejér-Korovkin wavelet order 4-th (fk4) and the best-localized Daubechies wavelet order 7-th (bl7) at the 2-nd level with an RMSE value of 2.2993 × 10-11. Partially, the best approximation of the data on the number of foreign tourist visits was given by the Bi-orthogonal Splines wavelet type order 2.6 (bior2.6) at the 2nd decomposition level with an RMSE value of 1.1718 × 10-11 and for the data on domestic tourist visits was given by the Fejér-Korovkin wavelet type order 4-th (fk4) and the best-localized Daubechies wavelet order 7-th (bl7) at the 2nd level with an RMSE value of 1.3352 × 10-11.