Prediction of Tourist Arrivals to the Island of Bali with Holt Method of Winter and Seasonal Autoregressive Integrated Moving Average (SARIMA)

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1 4 h ICRIEM Proceedings Published by The Faculy Of Mahemaics And Naural ciences Yogyakara ae Universiy, IBN Predicion of Touris Arrivals o he Island of Bali wih Hol Mehod of Winer and easonal Auoregressive Inegraed Moving Average (ARIMA) Agus upriana 1,a), Elis Herini 2,b), Bey ubini 3,c), Dwi usani 4,d), udradja upian 5,e), 1,2,3,4,5 Dep. MaemaikaFMIPA Universias Padjadjaran Bandung, Indonesia a) asupriana55@ymail.com b) elisherini@unpad.ac.id c) bey.subarini@unpad.ac.id e) sudradja@unpad.ac.id Absrac. The ourism secor is one of he conribuors of foreign exchange is quie influenial in improving he economy of Indonesia. The developmen of his secor will have a posiive impac, including employmen opporuniies and opporuniies for enrepreneurship in various indusries such as advenure ourism, craf or hospialiy. The beauy and naural resources owned by Indonesia become a ouris aracion for domesic and foreign ouriss. One of he many ouris desinaion is he island of Bali. The island of Bali is no only famous for is naural, culural diversiy and ars bu here are also add he value of ourism. In 2015 he increase in he number of ouris arrivals amouned o 6.24% from he previous year. In improving he qualiy of services, facing a surge of visiors, or prepare a sraegy in aracing ouriss need a predicion of arrival so ha planning can be more efficien and effecive. This research used Hol Winer's mehod and easonal Auoregressive Inegraed Moving Average (ARIMA) mehod o predic ouris arrivals. Based on daa of foreign ouris arrivals who visied he Bali island in January 2007 unil June 2016, he resul of Hol Winer's mehod wih parameer values α=0.1,β=0.1,γ=0.3 has an error MAPE is 6, While he resul of ARIMA mehod wih (0,1,1) (1,0,0) 12 model has an error MAPE is 5, and i can be concluded ha ARIMA mehod is beer. Keywords: Foreign Touris, Predicion, Bali Island, Hol-Winer s, ARIMA. INTRODUCTION Indonesia has beauiful culure and naure which became inernaional and domesic ouris ineres. Growing number of ouriss visi elici posiive impac for Indonesia: increasing economic growh and provide vacancy for local communiy. One of he mos popular ouris desinaions in Indonesia is Bali. The number of inernaional ouris arrival is increasing annually. I is noed ha in 2015 here are 6.24% increase in ouris arrival compared o he previous year (Bali Governmen Tourism Office, 2015). To increase qualiy of service, anicipaing surge in ouris arrival or preparing sraegies o arac more ouriss, a predicion of ouris arrival should be made for more efficien and effecive planning. Forecasing is a mehod o predic fuure evens by reflecing pas evens. Forecasing mehods are classified ino wo mehods: causal and ime series mehod. Boh of hese mehods are he mos popular mehod and 60% of sudies conduced since year 2000 used ime series mehod. Forecasing ouris arrival was pioneered in he beginning of year [2] Proper forecasing mehod o predic ouris arrival is Hol Winer s mehod and easonal Auoregressive Inegraed Moving Average (ARIMA) mehod. Boh of hese mehods may be used on daa comprising seasonaliy and rend. Hol Winer s mehod uses hree smoohing parameers: level, rend and seasonaliy. ARIMA mehod is a ime series mehod developed by Box Jenkins which may be used in various daa paerns, eiher saionary or non-saionary. Hol Winer s and ARIMA mehod have been frequenly used as an alernaive soluion and have been used in various sudies conduced in implemening his problem, M-125

2 including sudies by aayman (2010) abou Forecasing Tourism Arrivals in ouh Africa and by Widiarsih [7] abou comparaive analysis of Hol Winer and ARIMA mehod in forecasing saisics of inernaional ouris arrival a Kraon Yogyakara. This paper is abou a sudy aimed o predic he number of inernaional ouris arrival in Bali using Hol Winer and easonal Auoregressive Inegraed Moving Average (ARIMA) also picking he bes mehod among he wo. Hol Winer s Mehod Hol Winer s mehod could be used on daa paern comprising rend and seasonaliy. This mehod uses hree smoohing parameers: α, β, γ locaed beween 0 and 1. The parameers value could be calculaed by rial and error. Hol Winer s Muliplicaive equaion is as follows: (Makridakis, 1999) Y L (1 )( L b ) (1) 1 1 Whereas: s is lengh of seasonaliy, s b ( L L ) (1 ) b (2) 1 1 Y (1 ) (3) s L F ( L b m) (4) m s m esimae for m in he nex period. Iniializing Process: L overall esimae value, b rend componen, Iniializing curren smoohing consan: Y Y Y... Y Iniializing rend: b Iniializing seasonaliy index : s 1 1 L s s... Ys 1 Y1 Ys 2 Y2 Ys s Ys s s s Y1 Y2 Ys 1, 2,..., s L L L s s s seasonal componen, F m Auoregressive Inegraed Moving Average (ARIMA) ARIMA is good for calculaing shor erm forecasing (Ekananda, 2014). Makridakis (1999) saed ha seps in ARIMA mehod are model idenificaion, parameer esimaion, diagnosic ess and forecasing. ARIMA model are represened as ( p, d, q) in general. ARIMA model wih order ( p, d, q ) (B)(1 B) X (B) e d p 0 q easonal Auoregressive Inegraed Moving Average (ARIMA) ( p, d, q) P, DQ, and is wrien as follows easonal ARIMA or ARIMA have a common form of e X : error is he (B) (1 B) d (1 B ) D X (B ) e (6) p p q Q : Observed value a ime of ( = 1,2,...,n) (1 B) d : Mahemaical operaion of non-seasonal differencing D (1 B ) : Mahemaical operaion of seasonal differencing (Β) 2 p : Auoregressive operaor = p (1 1 B 2B... p B ) (Β ) : easonal auoregressive operaor = 2 (1 B B... B P ) P 1 2 (Β) 2 q : Moving average operaor = (1+ q 1B+ 2B... qb ) (Β 2 Q Q ): easonal moving average operaor = (1+ 1B 2B... Q B ) (Ibrahim, 2016) P (5) M-126

3 DATA AND METHOD Based on he previous elaboraions, Bali was one of he op ouris desinaions for inernaional ouriss. Predicion of ouris arrival was imporan o undersand he dynamics of ourism secor in Bali. Table 1 showed daa of inernaional ouris arrival per January 2007-June Daa were used o calculae he predicion of inernaional ouris arrival during July 2016-December I could be seen clearly from Figure 1 ha here were rend and seasonaliy paern from he daa. Table 1. Daa of Inernaional Touris Arrival in Bali Island during January June 2016 Tahun Jan Feb Mar Apr Mei Jun Jul Agu ep Ok Nov Des Figure 1. Inernaional Touris Arrival in Bali Island (ource : Bali Governmen Tourism Office) Using he monhly arrival daa, calculaion of hree smoohing parameers by rial and error was done o deermine rend and seasonaliy smoohing using Hol Winer s mehod (Makridakis, 1999). Meanwhile, he iniial sep o forecas using ARIMA mehod was by idenifying model from daa saionary es in erms of mean and variance. hould daa were no saionary in he variance, hen variance sabiliy ransformaion was done, while non-saionary daa in he mean underwen differencing process. Afer he daa were saionary, a emporary model was made by idenifying Auocorrelaion Funcion (ACF) and Parial Auocorrelaion Funcion (PACF) plo o deermine he order of he model. The nex sep was esimaing parameers: AR, MA, seasonal and non-seasonal and conducing significance es of he parameers. Anoher assumpion which should be fulfilled was he exising error should undergo whie noise process, i.e. error was no auocorrelaed and normally disribued. The es which could be used o deermine auocorrelaion was Ljung-Box es and Kolmogorov-mirnov es o deermine normaliy. If here were some models which fulfilled all assumpions, selecion was done o selec he bes model based on residual (error) AIC (Akaike s Informaion Crierion), Roo Mean quare Error (RME) and Mean Absolue Percenage Error (MAPE). (Lesari and Wahyuningsih, 2012) REULT AND DICUION Hol Winer s Mehod In general, Hol Winer s mehod had hree smoohing consans (valued beween 0 o 1). Trial and error was done o achieve opimum parameer. Table 2 below showed process of finding values of, and, which was deermined by selecing he leas MAPE value. Hence, he parameers used in his sudy were M-127

4 Table 2 elecion Process from Parameer and Value No MAPE Calculaion process of Hol Winer s exponenial smoohing using parameers was as shown below: For forecasing he 13 h period: Y13 L 0.1 (1 0.1)( L b ) , b ( L L ) (1 ) b 2.444, M-128

5 Y L (1 ) 0, F ( L b m) , 3 Calculaion resul for oher periods could be seen from Table 3 below. Table 3. Forecasing Value using Hol Winer s Mehod alpha= 0.1 bea= 0.1 Gamma= 0.3 Monh Arrival Daa L B F Jan Feb Mar Apr May Jun Jul Aug ep Oc Nov Dec Jan Feb Mar Apr May Jun Jul Aug ep Oc Nov Dec Jan Feb Mar Apr May Jun Jul Aug M-129

6 alpha= 0.1 bea= 0.1 Gamma= 0.3 ep Oc Nov Dec Jan Feb Mar Apr May Jun Jul Aug ep Oc Nov Dec Jan Feb Mar Apr May Jun Jul Aug ep Oc Nov Dec Jan Feb Mar Apr May Jun Jul Aug ep Oc Nov Dec M-130

7 alpha= 0.1 bea= 0.1 Gamma= 0.3 Jan Feb Mar Apr May Jun Jul Aug ep Oc Nov Dec Jan Feb Mar Apr May Jun Jul Aug ep Oc Nov Dec Jan Feb Mar Apr May Jun Jul Aug ep Oc Nov Dec Jan Feb Mar Apr M-131

8 alpha= 0.1 bea= 0.1 Gamma= 0.3 May Jun Juli ,882 Aug ,302 ep ,722 Oc ,141 Nov ,561 Dec ,981 By using Hol Winer s mehod, i was obained ha he predicion for July 2016 was 438,882 arrivals, Augus 2016 was 443,302 arrivals, epember 2016 was 447,722 arrivals, Ocober 2016 was 452,141 arrivals, November 2016 was 456,561 arrivals, December 2016 was 460,981 arrivals and MAPE error was ARIMA Mehod Model Idenificaion On ime series analysis, he assumpions ha mus be fulfilled were daa saionary in mean and variance. aionary es in variance could be conduced by Box-Cox ransformaion and he lambda value obained was 0.337, hence ransformaion was done by changing he values ino logarihms. Time series analysis required he daa o be saionary; hence firs differencing was done o non-seasonal lag which could be seen on he ACF and PACF plo as follows. Figure 2. Daa plo resul from non-seasonal lag 1 differencing ince he daa was already saionary, he nex sep was finding he emporary model by looking a ACF and PACF plo. Figure 3 (a). ACF plo resul from non-seasonal lag 1 differencing Figure 3 (b). PACF plo resul from non-seasonal lag 1 differencing Based on Figure 3 (a) and (b), a emporary model was esablished as follows: Table 4. ARIMA model based on ACF and PACF M-132

9 No ARIMA Model Parameer Esimaion Parameers of models acquired from ACF and PACF plo were hen esimaed using MLE mehod wih help from R sofware. ignificance es was conduced aferwards and significan model was obained, i.e. ARIMA, ARIMA, ARIMA, ARIMA, ARIMA, ARIMA, ARIMA, ARIMA and ARIMA. Diagnosic Tes The nex assumpion o fulfill was ha error should undergo whie noise process. A sequence was noed whie noise if error was no auocorrelaed and normally disribued. Temporary models whose error underwen whie noise process were ARIMA,ARIMA,ARIMA,ARIMA,ARIMA,ARIMA. Forecasing Appropriae models were evaluaed by reviewing AIC, RME and MAPE errors. Table 5. AIC, RME and MAPE error AIC RME MAPE However, among all six models shown in Table 5, he model wih he smalles error was ARIMA 0,1,1 1,0,0 12 hence his model was used o predic arrivals for he nex six periods. The model could be wrien sysemaically as shown below 12 (1 B)(1 B) X (1 B ) e (1 B B B ) X (1 B ) e X X X + X = e e X = X X X e e ince, were significan, he equaion became: 1 1 M-133

10 X = X X X e e Hence, an arrival predicion was presened as shown below: Time Figure 4. Forecasing resul using ARIMA Table 6. Arrival predicion using ARIMA Arrival Predicion Based on Table 6, he predicion of inernaional ouris arrival using ARIMA mehod in July 2016 was 424,125 arrivals, Augus 2016 was 369,071 arrivals, epember 2016 was 428,565 arrivals, Ocober 2016 was 414,908 arrivals, November 2016 was 346,310 arrivals, December 2016 was 415,739 arrivals wih MAPE error of Time Arrival Predicion Jul Nov Aug Des ep Oc CONCLUION Resul from Hol Winer s mehod wih smoohing parameer value of gave MAPE error of Meanwhile predicion resul using ARIMA model produced MAPE error of , hence i could be concluded ha ARIMA mehod was beer since i has smaller error REFERENCE 1. Badan Pusa aisik Provinsi Bali, aisik Wisaawan Mancanegara ke Bali 2. Ekananda, M Analisis Time eries: Unuk Peneliian Ekonomi, Manajemen, dan Akuansi. Jakara: PT. Mira Wacana Media 3. Ibrahim, N, dkk The Fiing Of ARIMA Model On Peads Paiens Coming A Oupaiens Medical Laboraory (OPML), Mayo hospial, Lahore, hps:// (diakses 5 epember 2016). 4. Lesari, N., Wahyuningsih, N Peramalan Kunjungan Wisaawan dengan Pendekaan Model ARIMA (udi Kasus: Kusuma Argo Wisaa). Jurnal AIN dan eni IT Vol 1 No.1 5. Makridakis,., Wheelwrigh,. C., & McGee, V. E Meode dan Aplikasi Peramalan, Jilid 1. Jakara: Binapura Aksara 6. aayman, A., aayman,m Forcasing Touris Arrivals in ouh Africa. Aca commerce 2010: Widiarsih I.N, ubeki R Analisis Komparasi Hol Winer Dan arima Pada Peramalan aisik Wisaawan Asing Kraon Yogyakara. Makalah disajikan dalam eminar Nasional Maemaika dan Pendidikan Maemaika, Universias Negeri Yogyakara, Yogyakara, M-134