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Forecasting and Effectiveness Analysis of Domestic Airplane PROC. INTERNAT. CONF. SCI. ENGIN. ISSN 2597-5250 Volume 3, April 2020 | Pages: 365-369 E-ISSN 2598-232X Forecasting and Effectiveness Analysis of Domestic Airplane Passengers in Yogyakarta Adisutjipto Airport with Autoregressive Integrated Moving Average with Exogeneous (ARIMAX) Model Sarah Khairunnisa1, Nusyrotus Sa’dah2, Isnani1, Rohmah Artika1, Prihantini1 1Mathematics, 2Statistics, Faculty of Mathematics and Natural Science, Yogyakarta State University Jl. Colombo No.1, Karang Malang, Caturtunggal, Kec. Depok, Kabupaten Sleman, Daerah Istimewa Yogyakarta 55281 Abstract. Airplane is one of the public transportations options that many people choose when traveling long distance. Nowadays, it is notes that the number of passengers domestic flight has increased from the previous months. This increase, especially occurs on the holidays, such as year-end holidays, Eid, and others. The increase of airplane passengers is inversely proportional to the number of available airplane. Forecasting the number of airplane passangers is necessary to prepare additional facilities when there is increasing passengers. This research focused on forecasting domestic airplane passengers at Adisucipto Airport, Yogyakarta using ARIMAX method to forecast the number of domestic airplane passengers and the effectiveness of domestic passengers at the international airport. The purpose of this research is to determine the best ARIMAX model and forecast airplane passengers in Adisucipto airport. The results will show the effectiveness of ARIMAX model with the effect of calendar variance on domestic airplane passenger forecasting at international airport. Based on the result of AIC and RMSE values, it shows that the ARIMAX(1,0,1) model with calendar variation is better than ARIMA(1,0,1) in predicting the number of airplane passengers at Yogyakarta Adisutjipto airport. Keywords: ARIMAX Model, Effectiveness Analysis, Forecasting Abbreviations: ARIMAX (Autoregressive Integrated Moving Average with Exogeneous) INTRODUCTION International Airport, 2019). The effect of the Eid day also had an effect on increasing the number of airplane The increasing number of population causes the passengers at Yogyakarta Adisutjipto Airport. increasing use of transportation services. One of the Passengers number data is time series data that is transportations that many people choose is airplane. That collected, recorded, and observed every year to is because, if you are travelling by airplane, the time determine the increase number of passengers at needed to get to the destination becomes faster. Airplane Yogyakarta Adisutjipto Airport. Therefore, it is is also one of the transportation that many people choose necessary to model and forecast the number of airplane when traveling long distances. The increase in airplane passengers at Yogyakarta Adisutjipto Airport. This study passengers mainly occurs during holidays, such as year- aims to determine the forecasting of the number of end holidays, Eid and others. Badan Pusat Statistika domestic airplane passengers at PT. Angkasa Pura I (BPS) recorded the number of airplane passengers for (Persero) Yogyakarta Adisutjipto International Airport domestic flights in October 2018 increased 6,85% to using the Autoregressive Integrated Moving Average 8,11 million people and also grew 7,85% compared to with Exogeneous (ARIMAX) method with calendar October of the previous year. Likewise, cumulatively in variations. The data used are secondary data obtained January-October period this year grew 6,98% to 78,63 from the Transportation Department of Special Region million people compared to the same period in 2017 of Yogyakarta in January 2013 to August 2018. (Databoks, 2018). The increasing number of airplane Research related to forecasting the number of passengers must be followed by the availability of the passengers was also carried out by Juniar Iqbalullah and airplant fleet, so there is no long queues. Wiwiek Setya Winahju in 2014 with forecasting the Yogyakarta Adisutjipto Airport is one of the number of airplane passengers at the arrival gate of the international airports that has an important role in the Lombok International Airport by the Arima Box- development of transportation and tourism in Indonesia. Jenkins, Arimax, and time series regression methods. In The number of passengers at the Adisutjipto Airport has addition, Yoan Sofyana Noer, Gumgum Darmawan, increased every year, especially during the holidays and Resa Septiani Pontoh in 2016 forecasted the number of the end of the year. PT Angkasa Pura I (Persero) passengers in Fajar Utama Train of Yogyakarta - Pasar Yogyakarta Adisutjipto International Airport recorded Senen using variations in the ARIMAX calendar (Case passenger growth during 2018 is 8.417.089, up 7,65% Study at PT. Kereta Api Indonesia). Based on previous compared to 2017 as 7.818.871 passengers (Adisutjipto studies, the ARIMAX method with calendar variations is 366 PROC. INTERNAT. CONF. SCI. ENGIN. 3: 365-369, April 2020 suitable to forecast the number of airplane passengers at The general model for a mixture of pure 퐴푅 (1) Yogyakarta Adisutjipto Airport with time series data and 푀퐴 (1) processes, for example ARIMA patterns that are affected by calendar variations. (1,0,1) as follows : ′ 푋푡 = 휇 + ∅1푋푡−1 + 푒푡 − ∅1푒푡−1 푎푡푎푢 METHODS ′ (1 − ∅1퐵)푋푡 = 휇 + (1 − ∅1)푒푡 ii. ARIMA process The data used in this study are secondary data obtained If non-stationarity is added to the ARMA process from the Transportation Department of Special Region mixture, then the general ARIMA model (푝, 푑, 푞) of Yogyakarta in January 2013 to August 2018. The is fulfilled. The equation for the simple case of Transportation Department of Special Region of ARIMA (1,1,1) is as follows: Yogyakarta located at Babarsari Street No.30, Janti, (1 − ∅ 퐵)푋 = 휇′ + (1 − ∅ )푒 Caturtunggal, Depok, Sleman Regency, Special Region 1 푡 1 푡 d. Autocorelation Function (ACF) of Yogyakarta 55281. ACF is the correlation between data in time period t with the previous time period 푡 − 1. The mean and Auto Regressive Integrated Moving Average range of periodic data may not be useful if the series (ARIMA) is not stationary, but the maximum and minimum ARIMA is one of the forecasting methods that have been values can be used for plotting purposes. How the introduced by G.E.P. Box and G. Jenkins. ARIMA key statistics in the periodical analysis are models are a class of linear models that is capable of autocorrelation coefficients. The ACF equation can representing stationary as well as non-stationary time be seen in the following formula: series (E. Hanke & W. Wichern, 2006). There are several models that have been produced using the ∑푛 (푥 − 푥̅) (푥 − 푥̅) method Box-Jenkins is a moving average (MA), 푡=푏 푡 푡+푘 푟푘 = 푛 2 autoregressive (AR) model, one class model useful for ∑푡=푏(푥푡 − 푥̅) time series which is a combination of MA and AR processes called ARMA. These models are linear and e. Partial Autocorelation Function (PACF) stationary models of the Box-Jenkins method. While the Partial autocorrelation is used to measure the level of model for non-standard data is the ARIMA model. There intelligence between 푥푡 and 푥푡−푘, if the effects of lag are four groups of ARIMA classification, are: time are considered separately. The only objective in Autoregressive (AR), Moving Average (MA) and mixed periodic series analysis is to help determine the right model Autoregressive Integrated Moving Average ARIMA model. Sample value the ordered PACF can (ARIMA) which has characteristics from the first two be seen in the formula: models as well as the Seasonal Autoregressive Integrated Moving Average (SARIMA) which is a derivative of 푟푘푘 = 푟1 푖푓 푘 = 1 푟푘−∑푘−1 푟 푟 ARIMA to get seasonal data predictions. 푟푘푘 = 푗−1 푘−1.푗 푘−푗 푖푓 푘 = 2,3 푘−1 a. Autoregressive (AR) 푘−1 The general form of the autoregressive model with 푟푘푘 = 1 − ∑푗−1 푟푘−1,푗푟−푗 the order 푝 (퐴푅 (푃)) or the ARIMA model (푝, 0.0) say as follows : Auto Regressive Integrated Moving Average with ′ Exogeneous (ARIMAX) 푥푡 = 휇 + ∅1푋푡−1 + ∅2푋푡−2 + ⋯ + ∅푝푋푡−푝 + 푒푡[0] Where: ARIMAX model is a modification of seasonal ARIMA. This modification is done by add predictor variables. 휇′= a constant Variations calender effects is one of the variables that ∅ = p-autoregressive parameter 푝 are often used in the modeling. (wiwik, Vinarti, & 푒푡= error value-t Kurniati, 2015). There are two kind of additional b. Moving average Model (MA) variables, I.e. the dummy variable(s) for calendar The order model 푞 (푀퐴 (푞)) or ARIMA (0.0, 푞) as variation effects only, and dummy variable(s) for follows : calendar variation effects and deterministic trend. The ′ 푋푡 = 휇 + 푒푡 − ∅1푒푡−2 − ⋯ − ∅푞푒푡−푘 first model is known as ARIMAX with stichastic trend Where: by implementing a difference non seasonal or seasonal 휇′= a constant and the second with deterministic trend (without ∅1 − ∅푞= parameter moving average differencing order). (Lee, Suhartono, & Hamzah, 2010) 푒푡−푘= error value-푡 − 푘 ARIMAX model with stochastic trend is c. Mixed Model i. ARMA process 푦푡 = 훽1푉1,푡 + 훽2푉2,푡 + ⋯ + 훽푝푉푝,푡 푆 휃푞(퐵)훩푄(퐵 ) + 푆 푑 푆 퐷 휀푡 ∅푃(퐵)훷푃(퐵 )(1 − 퐵) (1 − 퐵 ) KHAIRUNNISA et al. – Forecasting and Effectiveness Analysis of Domestic Airplane Passengers … 367 ARIMAX model with deterministic trend is Time Series Plot of penumpang 700000 푆 휃푞(퐵)훩푄(퐵 ) 푦푡 = 훾푡 + 훽1푉1,푡 + 훽2푉2,푡 + ⋯ + 훽푝푉푝,푡 + 푆 퐷 휀푡 ∅푃(퐵)훷푃(퐵 ) 600000 g n a p 500000 The proposed ARIMAX model building procedure, m u n e in the presence of calendar variation effects in the time p series data is described as follows: 400000 . Step 1: determination of dummy variable for calender variation priode 300000 Month Jan Jul Jan Jul Jan Jul Jan Jul Jan Jul Jan Jul . Step 2: remove the calendar variation effect from the Year 2013 2014 2015 2016 2017 2018 response by fitting Eq. (2) for model with stochastic trend, or fitting Eq.
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