FORECASTING THE NUMBER OF FOREIGN TOURISM IN BALI USING THE HYBRID HOLT-WINTERS-ARTIFICIAL NEURAL NETWORK METHOD

Article History: Bali is one of the destinations frequently visited by tourists because it has natural beauty, especially in the tourism sector. The number of foreign tourists coming to Bali until 2019 had increased, but there was a significant decrease in 2020. Forecasting the number of tourists coming to Bali in the future is needed to provide input or recommendations to the government and business people in anticipating decisions taken in developing the tourism sector in Bali. One of the forecasting methods that can be used is the Holt-Winters method. The Holt-Winters method is a part of Exponential Smoothing, which is based on smoothing stationary, trend, and seasonal elements. However, the Holt-Winters method can only capture linear patterns, so a method is needed to capture non-linear patterns. The Artificial Neural Network method is proposed to overcome the shortcomings of the Holt-Winters Method. This research was focused on the number of foreign tourists visiting Bali using the Hybrid Holt Winters-Artificial Neural Network method. The results show that the data on foreign tourists fluctuated monthly. The best method for predicting the number of foreign tourists is the Hybrid Holt-Winters (α = 0.987, β = 0.000001, and γ = 1)-Artificial Neural Network (12-15-1) because it has the best accuracy as indicated by the MAD value of 0.036684, MSE 0.01098698 and MAPE 6.30417%.


INTRODUCTION
Indonesia, with its abundance of natural resources, is a special attraction for foreign tourists. The wealth of natural resources owned by Indonesia can be an opportunity for developing the tourism sector. Tourism cannot be separated from foreign tourists [1]- [4]. Bali Island is one of the tourist places that domestic and foreign tourists often visit [1], [4]. The number of foreign tourist arrivals to Bali Province in 2015-2019 has increased yearly from 4,001,835 people in 2015 to 6,275,210 people in 2019. However, this condition has changed since the announcement of the COVID-19 outbreak as a pandemic in Indonesia in 2020 [5], [6]. The number of foreign tourists coming to Indonesia, especially in Bali, has decreased significantly, namely 1,069,473 tourists. The fall in the number of foreign tourist visits to Bali was due to the closure of access to Indonesia due to the COVID-19 pandemic and the establishment of a travel restriction policy issued by the Ministry of Law and Human Rights, which took effect on April 2, 2020, and the issuance of a travel advisory by the Ministry of Foreign Affairs to reduce the rate of spread of COVID-19 [6].
Predicting the number of foreign tourists coming to Bali in the future is needed to provide input or recommendations to the government and business people in anticipating decisions to develop the tourism sector in Bali [1], [7], [8]. One of the forecasting methods that can be used to make predictions is the Holt-Winters method. The Holt-Winters method is part of Exponential Smoothing, which involves three smoothing equations: stationary, trend, and seasonal [3], [4]. However, the Holt-Winters method can only capture linear patterns, so a method that can capture non-linear patterns is needed, one of which is the Artificial Neural Network [9]. Several researchers have done the combined (hybrid) model because it is proven to be able to significantly improve the accuracy of prediction when compared to using a single model [9], [10]. Therefore, a hybrid approach between the Holt-Winters method and Artificial Neural Network is proposed in this study. The existence of linear and non-linear components in time series data is also a complex problem in data analysis, so hybrid models are an effective alternative solution to improve forecasting accuracy [11].
Previous research related to this research has been conducted by Aryati

Data Source
The research data was on the number of foreign tourists visiting Bali by the entrance. The data was obtained from the official publication of the Bali Provincial Statistics Agency. The observation data were collected monthly from January 2009 to April 2022, totaling 160 [6].

Research Steps
The research steps taken were as follows: e. Train the Artificial Neural Network with the backpropagation algorithm on the training data; f. Test the network using testing data. 5. Perform data unstandardization; 6. Find the forecasting accuracy of the best model.

Data Standardization
The technique of changing the scale to make the range of values 'standard' based on the initial data's standard deviation and average values is known as data standardization. Data standardization in this study was carried out before further testing because there was some data with a value of 0 in several months in 2021. Data standardization can be calculated with the following equation: is the actual data, μ is the mean, and σ is the standard deviation of the actual data [5], [12].

Holt-Winters Method
The Holt-Winters method applies a prediction equation ( ) and three smoothing components, which include equations for level ( ), trend ( ), and seasonal components ( ) with smoothing parameters of α, β, and γ [3], [9], [13]. The Holt-Winters method was divided into two parts based on the type of seasonality: multiplicative and additive. If the seasonal component is constant, the additive approach can be used. Meanwhile, the multiplicative method was used when the seasonal element was proportional to the trend level. The Holt-Winters equation with multiplicative seasonal elements was formulated in the following equation [3]: = Smoothing parameter whose value is in the interval 0 to 1; = number of prediction periods ahead; = Seasonal length; = Observation data at time t. The values of level, trend, and seasonal components can be initiated with the following equation: The calculation of the seasonal additive type Holt-Winters method was done with the following equation:

Artificial Neural Network (ANN)
ANN is an algorithm miming how the human nervous system works to study a phenomenon. ANN consists of interconnected input, hidden, and output layer components. The connectivity of the input, hidden, and output layers are represented by weights whose values will always be updated until they reach the desired target. The input layer connects the observation data to the processing algorithm. The hidden layer connects the input layer with the output layer, which is the expected value [14]. Neural networks can provide high accuracy because they accommodate non-linear components in relatively complex data patterns [11], [15].

Backpropagation Neural Network
The backpropagation algorithm is also called backpropagation because in the processing of input data forwarded to the output layer if it has not met the desired target, it will be forwarded back to the hidden layer and forwarded to the input layer [16]. The Backpropagation algorithm has the advantage of adjusting to observational data and a small error rate. The Backpropagation algorithm is widely used on complex data because it adjusts network conditions to the data given in the learning stage [17]. The backpropagation learning algorithm is as follows [14]: 1. Assign weights to each network; 2. Each unit in the input layer ( , = 1,2,3, … , ) receives the input signal and passes it on to all units in the hidden layer; 3. Each unit in the hidden layer ( , = 1,2,3, … , ) sums the weights of the input signals with the following formula: and apply the activation function to calculate the signal at the following output layer: 4. Each output unit ( , = 1,2,3, … , ) sums the weights of the incoming signals with the following equation: and apply the activation function to calculate the output signal as follows: 5. Each output unit ( , = 1,2,3, … , ) receives a pattern that matches the input training pattern and calculates the error value with the following equation: 6. Calculate the weight correction with the following equation: 7. Calculating bias correction to update with the following equation: and send to the unit at its below layer. 8. Each unit in the hidden layer ( , = 1,2,3, … , ) sums the input deltas and multiplies by the derivative of the activation function to calculate the error with the following equation: 9. Calculate the input layer weight correction with the following equation: 10. Each output unit ( , = 1,2,3, … , ) updates the weights and bias ( = 0, … , ) with the following equation: 11. Each hidden unit ( , = 1,2,3, … , ) updates the weights and bias ( = 0, … , ): 12. Stop the process if it meets the desired parameters.

Hybrid Holt Winters-Artificial Neural Network
The hybrid Holt-Winters Artificial Neural Network method is performed by applying the Holt-Winters method to predict the observation data. The Artificial Neural Network method is applied to forecast the residuals generated from the Holt-Winters method Description: = number of observations. = observation of the t-th period. ̂ = Predicted Value at t-th period.

RESULTS AND DISCUSSION
Descriptive analysis was conducted to determine the general data description of the number of foreign tourists visiting Bali. An overview of the data on the number of tourists coming to Bali is presented in Table  1 and Figure 1.  Based on Figure 1 and Table 1, it can be seen that every month the number of tourists coming to Bali fluctuates and tends to increase from 2009 to 2019. However, in 2020, there began a decline in the number of foreign tourists due to the closure of access from outside the country. From January 2009 to April 2022, the number of foreign tourists coming to Bali reached the highest number in July 2018; namely, 624336 tourists, and the lowest number in July, August, September, and December 2021 was 0 tourists.

Data Standardization
The data on the number of foreign tourists visiting Bali was standardized first before other modeling using the Equation (1). The calculation of standardization for the first data is January 2009 as follows: The standardization calculation process was carried out similarly until the last observation in April 2022.

Holt-Winters Method
The smoothing parameter values for level (α), trend (β), and seasonality (γ) are sought by trial and error to maximize forecasting accuracy. The results of the Holt-Winters method of estimating the smoothing parameter values on the data of the number of foreign tourists visiting Bali are presented in Table 2. Based on Table 2  After obtaining the predicted data value on the number of foreign tourists coming to Bali with the Holt-Winters method (α = 0.987; β = 0.000001 and γ = 1), the next process was to calculate the leftover data by subtracting the actual data from the predicted data. The residual value obtained was processed by the Artificial Neural Network (ANN) method using the backpropagation algorithm to find the best architecture for forecasting the number of foreign tourists coming to Bali in the next period. The value of the leftover data with the Holt-Winters method (α = 0.987; β = 0.000001 and γ = 1) is presented in Table 3. The initial stage in applying the Hybrid Holt Winters-Artificial Neural Network method was by dividing the Holt-Winters method data into 2 parts, namely training data and testing data. This research applied 3 compositions of data division, namely 70% training data-30% testing data, 80% training data-20% testing data, and 85% training-15% testing data. It was intended to see the consistency of ANN architecture accuracy in forecasting. The next step was to define the network input and target. The input data used amounted to 12, the residual of the first month to the 12th month in the first year. Meanwhile, the target data amounted to one, namely the 13th month data or the first month in the second year. The use of 12 input data was because it was monthly data, and with 12 months, it was expected to represent the diversity of annual data. The input and target data for building the ANN network are presented in Table 4. The formation of ANN network architecture based on the Backpropagation algorithm was carried out by setting the target error parameter 0.001; the maximum number of iterations is 1000 with a learning rate of 0.1 and a momentum constant of 0.95. The architecture formed was selected by paying attention to the smallest MSE, MAD, and MAPE values in the architecture testing process. Based on three experiments on the composition of 70% training -30% testing, 80% training -20% testing, and 85% training-15% testing, the best architecture is found in the hidden layer with 15 neurons. A comparison of forecasting accuracy on training and testing data is presented in Table 5. Based on Table 5, the 12-15-1 architecture is the best in the 3 training and testing compositions. The three architectures were then selected by considering the smallest MSE, MAD, and MAPE values in the network testing process to avoid overfitting. Therefore, the 12-15-1 network architecture with a training composition of 70% training-30% testing was determined as the best architecture with a MAD value of 0.2109, MSE value of 2.9064, and MAPE value of 11.8%. An overview of the ANN architecture based on the best Backpropagation algorithm with 85% training and 15% testing data composition is presented in Figure 3.

Data Unstandardization
Data unstandardization was done to convert the output results into the actual data scale. The formula used is as follows: Calculation of data unstandardization on the first forecast results, namely data for May 2022, as follows: = −1.2710543 × 167465.6 + 286872 = 74014.129 The same process was carried out to calculate data unstandardization on the results of forecasting data on the number of foreign tourists visiting Bali.

Comparison of Forecasting Results
After obtaining forecasting results on data that has been standardized with the Holt-Winters (α = 0.987; β = 0.000001 and γ = 1) and Hybrid Holt-Winters (α = 0.987; β = 0.000001 and γ = 1)-Artificial Neural Network (12-15-1) methods, then a comparison was made to see the best method for equalizing data on the number of foreign tourists visiting Bali based on the forecasting accuracy value presented in Table 6.  Based on Table 6 above, it can be seen that the forecasting accuracy value of the Holt-Winters Hybrid method (α = 0.987; β = 0.000001 and γ = 1)-Artificial Neural Network (12-15-1) is better than the Holt-Winters method (α = 0.987; β = 0.000001 and γ = 1) to forecast the number of foreign tourists coming to Bali because it has a low prediction error value; namely the MAD value of 0.036684; MSE value of 0.01098698 and MAPE value of 6.30417%. A comparison graph of the forecasting results between the Holt-Winters method and the Hybrid Holt-Winters-Artificial Neural Network method against actual data is presented in Figure 4.

CONCLUSIONS
The hybrid Holt-Winters-Artificial Neural Network method effectively equalizes the number of foreign tourists visiting Bali because it produces a much better forecast than the Holt-Winters method. Based on data analysis, the best method to equalize the number of foreign tourists visiting Bali is the Hybrid Holt-Winters (α = 0.987; β = 0.000001 and γ = 1)-Artificial Neural Network (12-15-1) method because it produces the best accuracy shown by the MAD value of 0.036684, MSE 0.01098698 and MAPE 6.30417%.