Intervention Model of Sinabung Eruption to Occupancy of the Hotel in Brastagi, Indonesia

This paper presents an analysis of intervention of Sinabung eruption to the rate of hotel reservation in Brastagi, North Sumatera, Indonesia. The weekly data of this study was collected from four hotels in Brastagi for the period of January 2012 – May 2015. The method that be used is an analysis of the intervention with ARIMA (Autoregressive Integrated Moving Average) process by Box – Jenkins. To see the stationary of data is used the plot of ACF (Autocorrelation Function). For identification of model is used the plot of PACF (Partial Autocorrelation Function), and to choose the best of model is used AIC (Akaike Information Criterion). Meanwhile to see the suitability of data to model is used Q-Statistics Ljung-Box. The result shows that decline the rate of hotel reservation only until the 30th period after the intervention. After that, the rate of hotel reservation will be as normal as before the eruption. The results of this study are limited, valid only on the subject of research, not generally applicable, to be generalizable needed further research.


INTRODUCTION:
The eruption of Mount Sinabung in Karo district, province of North Sumatera, Indonesia on September 15, 2013 had a negative impact on the tourism sector in Brastagi city which is approximately 11 km from Mount Sinabung, especially in term of hotel reservation in the surrounding areas impacting the city's income. Intervention in time series is an event or events that may affect the data pattern of the time series. Intervention model in time series analysis was introduced by Box and Tiao in 1975 that discussed the effect of the enactment of legislation engine design to the level of pollution oxidant in Los Angles (Box & Tiao, 1975). Others the paper related to this research are (Montgomery & Weatherby, 1980) investigated the influence of the Arab oil embargo against the level of electricity consumption in the United State. (Suhartono & Huriroh, 2003) investigated the influence of New York WTC bombing against fluctuations in the price of the world. (Chung, Ip, & Chan, 2009) using ARIMA intervention model in research, investigated the effects of the financial crisis on manufacturing industry in China, while (Jarrett & Kyper, 2011) also uses the ARIMA intervention model to predict and analyze the Chinese stock prices. This paper focuses on the determination of the intervention model of Sinabung eruption to the rate of hotel reservation in Brastagi city.

MATERIAL AND METHODS:
The data used in this study is the rate of hotel reservation in Brastagi based on the number of rooms booked by visitors. Data collected weekly from four hotels in Brastagi, two hotels located alongside Sumatera highway, namely Grand Mutiara hotel and The Hill Sibolangit, while two more hotels are located alongside the road to Gundaling, namely Sibayak International Hotel, and Brastagi Cottage. All four hotels are seen to represent all hotels in Brastagi. This study does not consider the peak time, because the data is weekly and the peak time occurs on weekens. Sampling strategy using cluster sampling for determining the location, then the selection of hotels is done randomly. The number of time series data the hotel reservation rate there are 178 of data, starting on the first week in January 2012 as the 1 st data until the fourth week of May 2015 as the 178 th data. Based on the data used, the first Sinabung eruption at second week of September 2013 viewed as the intervention on the 89 th data. The method used is the analysis of intervention with ARIMA process.

RESULTS:
The data ploting when eruption ocucured at t = 89, as Figure 1 below:

Figure 1: Plot of time series data and Intervention Analisys before Intervention:
Based on the Sinabung eruption on the second week of September 2013 viewed as the intervention on the 89 th data, therefore there are 88 datas before the intervention on the 1 st data through to 88 th data and are denoted as x1. The data plotong, ACF, and PACF consecutive for x1 presented in Figure 2, 3, and 4 below: ACF plot in Figure 3 in the form damped sine wave, this indicates that the time series data for x1 is stationary. ACF plot in Figure 3 is disconnected after first lag and PACF plot in Figure 4 is also disconnected after first lag, this indicates that the model is appropriate for x1 series is ARIMA (1,0,0), ARIMA (0,0,1) and ARIMA (1,0,1). Furthermore, the calculation with the software "R", obtained the value of parameters and the value of AIC as Table 1 below: To conclude whether the model of equation (1)  Testing with Q-statistic Ljung-Box: Chi-squared = 0.0069, df = 1, p-value = 0.9337. Value statistics count < value of Statistics Tables, so it can be concluded that the model is fit data.

Analisys of Intervention:
Identification of intervention response which has been done by observing the data pattern before, during, and after the intervention. Observations were made on the data pattern around the 89 th data, ie from the 70 th data until the 108 th data, presented in Figure 6  In Figure 6 can be seen that the effect of interventions at the 2 nd week of September 2013 (89 th data). Although not decline dramatically, however, after the eruption seen a decline until some lag time in the future, so that the function of intervention for this case is: model is appropriate for series x2 is ARIMA (1,0,0), ARIMA (0,0,1), ARIMA (1,0,1), ARIMA (0,0,2), ARIMA (2,0,0), ARMA (1,0,2), ARMA (2,0,1) and ARMA (2.0, 2). Furthermore, the calculation with the software "R", obtained the value of parameters and the value of AIC as Table 2 below: (3) To conclude whether the model of equation (3) fits to the data, used the autocorrelation test for residuals by Q-Statistic Ljung-Box, to test whether the residuals   t a is a sequence of random variables with mean is zero and constant variance, as Figure 10 below: Testing with Q-statistic Ljung-Box: chi-squared = 0.0283, df = 1, p-value = 0.8665. Value of statistics count < value of Statistics

CONCLUSION:
Plot of the time series data in figure 11 shows that after the Sinabung eruption on 15 September or the 3 rd week of September 2013 as the 89 th data, the data pattern changes that inflict decrease of hotel reservation until the 119 th data. After the 119 th data, the pattern back into its previous form before the intervention, this indicates that the imfact of intervention on the hotel reservation only until the 119 th data or for 30 weeks after the eruption, after that, the rate of hotel reservation will be as normal as before the eruption. Figure 11: Limit the impact of intervention