Forecasting International Tourism Demand in Malaysia Using Box Jenkins Sarima Application

Transcription

1 Souh Asian Journal of Tourism and Heriage (2010), Vol. 3, Number 2 Forecasing Inernaional Tourism Demand in Malaysia Using Box Jenins Sarima Applicaion LOGANATHAN, NANTHAKUMAR* and YAHAYA IBRAHIM** *Loganahan, Nanhaumar, Deparmen of Economics, Faculy of Managemen and Economics Universii Malaysia Terengganu, Kuala Terengganu, Malaysia **Yahaya Ibrahim, School of Social, Developmen and Environmenal Sudies, Faculy of Social Sciences and Humaniies Universii Kebangsaan Malaysia, Bangi Selangor, Malaysia ABSTRACT The main aim of his paper is o generae one-period-ahead forecass of inernaional ourism demand for Malaysia. An appropriae ARIMA model or well nown as Box-Jenins model has been applied in his paper o generae he forecas of inernaional ourism demand. Before selecing an appropriae model, formal saionary ess has been applied in his paper and finds ha, he series are saionary a level. Secondly, in order o ge a good esimaion, his paper has idenified he auoregressive (AR) and moving average (MA) of he enire period of he daa. Therefore, he fuure demand of ourism is forecas based on he combinaion of AR and MA, which nown as ARMA model. In his paper, he compeing models have been horoughly invesigaed when he model adequacy has been checed before he bes combinaion of ARIMA model was seleced. Thus, he bes fied ARIMA (1,0,1) wih seasonal effecs or well nown as SARIMA approaches has been suggesed hrough his sudy and he forecasing process is based on his combinaion. The forecass generaed by he ARIMA model sugges ha Malaysia will face increasing ourism demand for he period of 2009:Q1-2009:Q4. Besides ha, his paper found he Box-Jenins model has offered valuable insighs and provide reliable forecass of ourism demand for Malaysia. KEYWORDS: Tourism Demand, Box-Jenins Mehod, ARIMA, SARIMA INTRODUCTION According o World Tourism Organizaion, inernaional ourism can be define as an aciviy of visiors who mae emporary visis across inernaional borders and remains for more han 24 hours. The purpose of visis can be visiing relaives and friends; leisure, business meeing or convenions, educaion, healhcare and spors. In 2008, inernaional ouris arrivals reached 924 million, up 16 million over 2007, represening a growh of 2%. As a resul of he exremely volaile world economy (financial crisis, commodiy and oil price rises, sharps exchange rae flucuaions), ourism demand slowed significanly hrough he year. The las six monhs of 2008, in paricular, showed an abrup shif in rends, wih inernaional ouris arrivals fla or showing negaive growh. Overall, he 5% growh beween January and June gave way o a 1% decline in he second half of he year. Afer he economic crisis and he swine flu pandemic produced "one of he mos difficul years" for he secor in 2009, global ourism is se o rebound in coming years. TOURISM DEMAND IN MALAYSIA Tourism is one of he major conribuing secors for Malaysia s economic growh for several years. Year by year, number of inernaional ouris arrivals o Malaysia showing an upward rend and his suppored wih he counry s poliical sabiliy, besides several program and pacage inroduce by he Malaysian governmen o encourage inernaional 2010 Souh Asian Journal of Tourism and Heriage

2 SMALL SIZED COMMERCIAL HOTELS IN INDIA 51 ouris visi Malaysia. Malaysia recorded million ouris arrivals las year in 2009, higher han he million arrivals in 2008 and he scaled-down arge of 19 million se for las year due o he global economic downurn. The op 10 ouris-generaing mares for Malaysia las year were Singapore, Indonesia, Thailand, Brunei, China, India, Ausralia, Philippines, Unied Kingdom and Japan. The Malaysian ourism indusry will coninue o grow rapidly in coming years on he bac of increasing promoional aciviies by he governmen and growing repuaion of he counry as a shopping hub. According o a research repor by RNCOS, "Opporuniies in Malaysian Tourism Indusry ( ), Malaysian ourism indusry coninues o grow rapidly, where: Singapore, Thailand and Indonesia are imporan sources of visiors for Malaysia. Beyond ASEAN, ouris arrivals from China and India will remain an imporan influence hroughou he forecas period ( ). The promoion of Educaion Tourism will coninue o be expanded o expedie he developmen of Malaysia as a preferred desinaion for inernaional sudens. The projeced foreign exchange earnings from his poenial source of growh are esimaed a RM 900 Million by I is expeced ha expendiure by inernaional ouriss in Malaysia will increase a a CAGR of 6.63% during he forecased period. Increasing disposable income in Malaysia will open he opporuniies for boh oubound and domesic ourism. Touris arrivals o Malaysia are poised o reach 24.6 million by 2010, wih he bul of ravelers comprising inra-regional ouriss. By he year 2010, he arge is o arac 24.6 million ouriss per annum especially youh ravelers from Middle-Eas and Eas-Asia. The projeced foreign exchange earnings from his poenial source of growh are esimaed a RM 900 Million by According o he new RNCOS repor Malaysian Tourism Indusry Forecas o 2012, inernaional ouris arrivals in Malaysia will grow a a CAGR of around 9% during , and ourism receips from overseas ouriss are expeced o rise a a CAGR of around 10% o RM 70 Billion (US$ 19.6 Billion) in he same period. Malaysia expeced o benefi from he greaer inra-asean ravel rade hrough inense regional co-operaion, culural and informaion exchanges, developmen of join our pacages and esablishmen of special arrangemens for youh ravelers from Asean. Apar from he ASEAN counries, ouris arrivals from China, India and he Middle Eas will srongly grow during he forecas period ( ). In he 9 h Malaysia plan, Malaysia argeed as a main inernaional ouris desinaion. The main programs ha implemened by he Governmen include enhancing access and faciliies for ouris arrivals, and improvising as well as mainaining ameniies and infrasrucure. An expendiure of RM1 billion has been allocaed for he purpose of mainenance. Wihin his plan, governmen s focus is on he developmen of rural ourism as based on research, foreign ouriss who came o Malaysia spen 15% of heir say in rural areas. In ne near fuure, MICE (Meeings, Incenives, Convenions and Exhibiions) indusry also expeced will be one of he major conribuors o he Malaysian ourism indusry LITERATURE REVIEWS Over he pas 3 decades, we have seen many sudies of inernaional ourism demand forecasing by boh ourism researchers and praciioners as well. Basically, he lieraure on modeling and forecasing ourism demand is huge wih various ype of empirical analysis. Some of he researchers apply cross-secional daa, bu mos of forecasing ourism demand used pure ime-series analyical models. One of he imporan ime-series modeling used in forecasing ourism forecasing is ARIMA modeling, which specified based on he sandard Box-Jenins mehod is a famous modeling approach o forecasing demand. Many sudies has applied his mehodology, such as Chu (2008a), Lee e al. (2008), Coshall (2008), Wong e al. (2007), Aal (2004), Preez and Wi (2003); and Kulendran and Wi (2001).

3 52 SAROJ KANT BISWAL and BIKASH KUMAR MISHRA Basically, his ARIMA model has been proved o be reliable in modeling and forecasing ourism demand wih monhly and quarerly ime-series. Wong (2007) has used four ypes of model, such as seasonal auo-regressive inegraed moving average model (SARIMA), auo-regressive disribued lag model (ADLM), error correcion model (ECM) and vecorauoregressive model (VAR) o forecas ourism demand for Hong Kong by residens from en major origin counries. The empirical resuls shows ha forecas combinaions do no always ouperform he bes single forecass. Therefore, combinaion of empirical models can reduce he ris of forecasing failure in pracical. Coshall (2008) meanwhile has used univariae analysis, combined he ARIMA-volailiy and smoohing model, which is a erm of finance o forecas Unied Kingdom demand for inernaional ourism. Generally, from his sudy we can find ha he ARIMA volailiy models end o overesimae demand, and he smoohing models are inclined underesimae he number of fuure ouris arrivals. Chu (2008a) has modified ARIMA modeling o fracionally inegraed auoregressive moving average (ARFIMA) in forecasing ourism demand. This ARFIMA model is ARMA based mehods. Three ypes of univariae models have applied in he sudy wih some modificaion in ARMA model become ARAR and ARFIMA model. The main purpose of he sudy is o invesigae he ARMA based models and is usefulness as a forecas generaing mechanism for ourism demand for nine major ouris desinaions in he Asia-Pacific region. This sudy is differen from various forecasing ourism sudy which been publish earlier, because we can idenify he ARMA based model behaviors and he ouperforming of he ARFIMA model wih oher ARMA based models. Again, Chu (2008b) has sudy he ARIMA based model using ARAR algorihm model in order o analyze and forecasing ourism demand for Asia-Pacific region using monhly and quarerly daa. The major findings of he sudies show he comparison beween forecass generaed by monhly and quarerly daa reveals ha he performance is broadly similar. Besides forecasing ouris arrivals, predicion of ourism revenue also can done using empirical modeling. Musafa (2004) has used auoregressive inegraed moving average cause-effec (ARMAX) modeling o forecas inernaional ourism demand for Turey. The ARMAX model is acually derived from he ARIMA approaches. The forecas esimaions are an imporan benchmar for Turey s governmen o srengh-ou he ourism secor becoming a major conribuing secor for economic developmen in fuure. Chong e al. (2003) has inroduce general-o-specific modeling approach o forecass inernaional ouris arrivals from 16 major counries o Hong Kong for he period The specificaion of economerics model is nown as auo-regressive disribued lag model (ADLM). The findings shows ha, he mos imporan facors ha deermine he demand for Hong Kong ourism are he cos of ourism in Hong Kong, he economic scenario in he origin counries, he coss of ourism in he compeing desinaions and he world of mouh effec. Again, ADLM measuremen of ourism forecasing is suiable for mulivariae modeling and by using his mehod, we able o deermine various facor causes on ouris arrivals in he fuure. Meanwhile, Greenidge (2001) has used srucural ime-series modeling (STM) o evaluae forecasing ourism demand in Barbados. STM modeling has is own capabiliy, which is can include ime-varying componens in he regression equaion and capure he movemen of ouris arrivals using explanaory variables. Besides using basic srucural modeling (BSM), STM model also able o include general srucural modeling (GSM) wih seasonal effec. Therefore, he findings offered valuable insighs ino he sylized facs of ourism behavior and provide reliable ou-of-sample forecass of ourism demand. On he oher hand, Ahanasopoulos and Hyndman (2008) have modeled Ausralian domesic ourism demand using regression model, exponenial smoohing via innovaions sae space model and innovaions sae space model wih exogenous variables. Crosssecional daa has been applied in his sudy, and he daa were colleced using compuerassised elephone inerview wih 120,000 Ausralians aged from 15 years onward. All he models been used in he sudies also highlighed he impac of world evens on Ausralian

4 SMALL SIZED COMMERCIAL HOTELS IN INDIA 53 domesic ourism such as he increase in business ravel immediaely afer he Sydney Olympic in he year 2000; and he significan increase in visiing relaives and friends afer he 2002 Bali bombings. One of he ineresing his we can find from his sudy is ha, all of hree saisical models used in his sudy ouperform he Tourism Forecas Commiee (TFC) resuls for shor-erm demand of Ausralian domesic ourism. Meanwhile, he longerm forecass resuls from his sudy also indicae ha he TFC forecass may be opimisic. Finally, from he forecass oupus, his sudy finds ha he Ausralian domesic ourism is on he decline sage. Unlie mos of he forecasing ourism sudies discussed earlier, forecasing expo demand involves boh qualiaive echnique and quaniaive forecasing models (Lee e al., 2008). The main reason using boh echniques is because of he limiaion of he available daa. Combining quaniaive echnique wih willingness-o-visi (WTV) surveys has prediced number of visiors o inernaional ourism expo which o be held in Korea in Preez and Wi (2003) have also compared wo ypes of mehods analyzing forecasing ourism. In heir sudy, univariae and mulivariae modeling has been used separaely o forecass ourism demand from four European counries o Seychelles. The findings of he sudy shows clearly he univariae forecasing models had ouperformed mulivariae models. Empirical resuls from he sudy shows an absence of srucural and ha ARIMA exhibis beer forecasing performance han univariae and mulivariae sae space modeling. According o Kim and Wong (2006), he volailiy in ourism demand daa can be influenced by he effecs of new shocs such as economic crises, naural disaser or war. In ourism lieraure, modeling he volailiy in ourism demand is imporan because i can capure he occurrence of unexpeced evens. Acually, volailiy of ourism demand is modeled using condiional volailiy models, and he models ha appears in ourism lieraure are univariae generalized auoregressive condiional heeroedasiciy (GARCH), univariae asymmeric GARCH, vecor auoregressive moving average GARCH (VARMA- GARCH); and VARMA asymmery GARCH (VARMA-AGARCH) models (Chan e al. (2005), Kim and Wong (2006), Shareef and McAleer (2005), Shareef and McAleer (2007). In middle of 1990s, dynamic specificaion such as vecor auoregressive model (VAR), error correcion model (ECM) and auoregressive disribued lag model (ADLM) began o appear in he ourism lieraure. VAR model able o apply various ype of independen variables o deermine ouris arrivals and from here we able o forecas fuure ouris arrivals. Besides ha, VAR model able o provide wih innovaive use of he impulse response analysis in ourism conex, besides provide resuls on co-inegraing analysis and forecasing. Song and Wi (2004) have used his VAR model o forecas inernaional ouris flows o Macau for he period The forecass generaed by he VAR models sugges ha Macau will face increasing ourism demand by residens from mainland China. Secondly, he ECM model also been used o measuring ourism forecasing bu laely his ECM model has modified become vecor error correcion model (VECM) which can es and impose wea exogeneiy resricion. Bonham e al. (2008) have used VECM echnique o idenify reasonable long-run equilibrium relaionship; and have ae ino accoun Diebold- Mariano ess for forecas accuracy demonsrae saisfacory forecasing performance for Hawaii. The main purpose of his sudy is o provide a much more comprehensive examinaion on ourism forecasing using seasonal ARIMA modeling. However, exising lieraure of forecasing inernaional ourism demand for Malaysia so far had no been adoped using seasonal auo-regressive inegraed moving average (SARIMA) modeling; herefore his paper will fill his gap. METHODOLOGY All daa for his sudy were colleced from Malaysia ourism arrivals daase provided by he Minisry of Tourism Malaysia. The ime-series daa used in his sudy are quarerly daa and i s covered from 1995:Q1-2008Q4. This sudy focuses on he demand for inernaional

5 54 SAROJ KANT BISWAL and BIKASH KUMAR MISHRA ourism for Malaysia and forecas 4 quarers ahead, which is 2009:Q1-2009:Q4. In his sudy, we used ARIMA and seasonal ARIMA (SARIMA) models o forecas one-period ahead of he series by applying Box-Jenins approach. An ARIMA model is a generalizaion of an ARMA model. These models are fied o ime-series daa eiher o beer undersand he daa or o predic fuure poins in he series (Chu, 2008a). The model is generally referred o as an ARIMA (p, d, q) model where p, d and q are inegers greaer han or equal o zero and refer o he order of he auoregressive, inegraed and moving average aspecs. In his sudy we applied Augmened Dicey-Fuller and Phillip-Perron saionary ess o idenify he level d in ime series of inernaional ouris arrivals o Malaysia. The resulan univariae ime series mode can be wrien as φ L y =θ L ε = p+1, p+2,..n (1) p Wih; φ L p q ( ) ( ), q p ( ) = 1 Φ1L... φ pl q ( L) = 1 Φ... φ L 1L φ (2) q Where, he las noaional convenional as chosen such ha he model in (1) amouns o he regression model y = φ1y φ p y p +ε +θ1ε θqε q Therefore, his model is called an auoregressive moving average model of order (p,q), or d briefly ARMA(p,q). When he y series replaced by, we say ha y is described by an auoregressive inegraed moving average model of order (p,d,q), or briefly ARIMA(p,d,q). This can express as Box-Jenins approach. The auocorrelaion funcions (ACF) of a ime series y can be define as ρ =γ /γ 0. Where γ is he order of auo-covariance of y, ha is γ = E y µ y µ, =..,-2,-1,0,1,2.,n (3) [( )( )] Given equaion (3), i is easily seen ha for he auocorrelaion i holds ha ρ 1, ρ = ρ and ha 1<ρ < 1. Therefore, his ACF can be useful o characerize ARIMA ime series models. Le say for example, a simple whie noise series ε for which E( ε ) = 0 and ρ = 0 for all 0. For he AR(1) model y µ=φ y µ + ε = 1,2,3..,n (4) 1 ( ), 1 Meanwhile, he ACF may no be paricularly useful o idenify wheher an AR of specific order is a suiable model. In fac, he ACF is more useful in case of MA(q) models. For he MA(1) process, i can be shown as follows wih PACF a lag h: h 2 2h α ( h) =φ hh = ( θ) /( 1+θ θ ) (5) Forecasing SARIMA processes is compleely analogous o he forecasing of ARIMA processes. This can be expressed as ARIMA(p,d,q)(P,D,Q) 12 [ARIMA(p,d,q) (P,D,Q)] 4 for quarerly daa. Which p and P are he orders of auoregressive operaor; d and D are he differences; and q and Q are he orders of moving average operaor of non-seasonal and seasonal componens respecively. The firs seps in idenifying SARIMA models for a daa se are o find d and D so as o mae he differenced observaions: y d s D ( 1 B) ( 1 B ) X y 1 = (6) In his sudy we used one-period-ahead forecasing using seasonal ARIMA modeling. In order o forecasing SARIMA model, he mean absolue percenage error (MAPE) is a useful measure for comparing he accuracy of forecass beween differen forecasing models since i measures relaive performance. If an error is divided by he corresponding observed value, we have a percenage error. In many empirical sudies i appears ha he models ha end 0 =

6 SMALL SIZED COMMERCIAL HOTELS IN INDIA 55 o do bes for wihin-sample daa do no necessarily forecas beer ou-of-he sample. There is no sric rule for ha, bu empirical experience suggess ha if may be beer o selec few models on he Aaie Informaion Crierion (AIC) and Schwarz Informaion Bayesian (SBC), and o evaluae hese on he forecas daa. The las evaluaion can be based on roo he mean square error (RMSE). The RMSE can be express as follow: m 2 RMSE = ( 1 m) ( ŷ n + h y n+ h) (7) h= 1 Meanwhile, in mos of previous lieraures, mean absolue percenage error (MAPE) has been used o deermine suiable models. I should be menioned ha, MAPE is no very useful for very small observaion (Franses, 1998). The MAPE can be express as follow: m MAPE = ( 1 m) ( ŷ n+ h y n+ h) / y (8) n+ h h= 1 Therefore, ARIMA-SARIMA model selecion in his sudy is based on AIC, SIC and forecas evoluion resuls, especially referring on he minimum value of RMSE and MAPE. EMPIRICAL RESULTS The daa of inernaional ouris arrivals o Malaysia for he period 1995:Q1-2008:Q4 wih seasonal effecs is shown clearly in Figure 1. Basically, figure 2 has shown clearly he demand of inernaional ouris arrivals o Malaysia is no depending on seasonal effecs; because he flow of ouris arrivals o Malaysia for he four quarers is exis same paerns for he pas 1 decade. The daa of inernaional ouris arrivals wih seasonal effecs are ploed o examine he paern of inernaional ouris arrivals in Malaysia. I was found ha he plo exhibied a permanen deerminisic paern of long erm upward rend. Figure 1 : Seasonal Saced Line of Log Toal Inernaional Touris Arrival o Malaysia Q1 Q2 Q3 Q4 LNTOUR Means by Season Table 1 summarizes he oucome of he Augmened Dicey-Fuller and Phillip-Perron ess on 1995:Q1-2008:Q4 quarerly ouris arrivals o Malaysia. The null hypohesis esed is ha he variable under invesigaion has a uni roo agains he alernaive ha i does no. The lag-lengh is chosen using he Aaie Informaion Crierion (AIC) afer esing for firs and higher order serial correlaion in he residuals. In he firs half of Table 1, he null hypohesis has a uni roo canno be rejeced by boh ADF and PP ess. However, afer applying he firs difference, boh ADF and PP ess rejec he null hypohesis. Since he daa appear o be saionary by applying he ADF and PP ess in firs differences, herefore we never perform furher ess. In his sudy we apply saionary ess wih rend effecs. Therefore, he null hypohesis has a roo has been rejeced in boh ADF and PP ess a levels I(0). Hence, all

7 56 SAROJ KANT BISWAL and BIKASH KUMAR MISHRA series are saionary wih rend effecs analysis and acceps I (0). Once saionary has been esablished, examinaion of he auocorrelaion funcion plo (ACF) and parial auocorrelaion plo (PACF) over several quarerly lags suggess which auoregressive and moving average erms should be included in he ARIMA model (Coshall, 2008). Figure 3 shows clearly he sage of ACF and PACF for ouris arrivals o Malaysia, and from he diagrams, we choose combinaion of ARIMA (p,d,q) o obain he mos suiable SARIMA model for his sudy. The sandard procedure for idenificaion, esimaion, diagnosic checing and over fiing in a Box-Jenins analysis of ime series was performed. Table 1 : Saionary Tess Wihou Trend Wih Trend Variables Level Firs Difference Level Firs Difference ADF Tes ( ) τ (0) (0)* (8)** (0)* PP Tes ( Z ) τ [11] [11]* [4]** [19]* Noe: Lag lengh in () and Newey-Wes value using Barle ernel in [], Aseriss (*) and (**) denoe saisically significan a 1% and 5% significance levels The esimaion mehod involved maximum lielihood parameer esimaion o obain iniial esimaes and hen uncondiional leas-squares esimaions o obain final esimaes. I is a fairly common occurrence ha differencing a ime series inroduces moving average erms ino he resulan ARIMA model. Two ofen applied crieria o selec beween ime series models are he Aaie Informaion Crierion (AIC) and Schwarz Bayesian Crierion (SBC). Boh crieria evaluae he fi versus he number of parameers. Table 2 clearly indicaes diagnosic correlogram wih auocorrelaion (ACF) and parial auocorrelaion (PACF) for ARMA(1,1). The flow of ACF and PACF shows clearly he effecs of auoregressive effecs wih firs differen of hisorical daa. Figure 2 : ARMA(1,1) Diagnosic Correlogram wih Auocorrelaion (ACF) and Parial Auocorrelaion (PACF) 1.2 Auocorrelaion Acual Theoreical Parial auocorrelaion Acual Theoreical

8 SMALL SIZED COMMERCIAL HOTELS IN INDIA 57 Table 2 : Regression Resuls and Diagnosic Tess for Seasonal ARIMA Models ARCH-LM H Models Coefficien o: No serial H Tes (a) correlaion o: Normaliy (b) (c) ARIMA(1,0,1) Season (1) Season (2) Season (3) AR(1) MA(1) AIC value SBC value ARIMA(1,0,2) Season (1) Season (2) Season (3) AR(1) MA(1) MA(2) AIC value SBC value ARIMA(2,0,2) Season (1) Season (2) Season (3) AR(1) AR(2) MA(1) MA(2) AIC value SBC value (1.040) (-0.011) (0.723) (19.48) (-1.447) (1.137) (0.237) (0.803) (23.51) (-1.621) (-0.882) (1.017) (0.332) (1.033) (5.857) (-1.777) (-2.748) (-0.609) [0.259] [0.569] [1.166] [0.28] [0.364] [0.469] [0.00] [0.000] [0.000] Noe: (a), (b) and (c) indicaes Auoregressive condiional heerocedasiciy (ARCH) LM es, Breusch-Godfrey (BG); serial correlaion es and Jarque-Bera (JB) normaliy es. Figures in ( ) and [ ] indicaes -saisics and probabiliy values Table 2 clearly indicaes he AIC and SBC s values and he decision of selecing mos suiable model is by comparing he value of AIC and SBC according o he ARIMA models used in his sudy. Smaller he value of AIC and SBC, is beer and fi he ARIMA model used. Therefore ARIMA(1,0,1) is relevan because he value of AIC and SBC is smaller han oher ARIMA models. Besides ha, diagnosics ess have been applied in his sudy o deermine he esimaed models deviae from he assumpions of he sandard linear regression model. Therefore, we esed he auoregressive condiional heeroscedasiciy (ARCH), serial correlaion using Breusch-Godfrey (BG) es; and normaliy es using Jarque-Bera (JB) es. Since correlogram of squared residuals from ARMA(1,1) shows auocorrelaion paern in square residuals which could be aribued o volailiy clusering, herefore, o es he presence of ARCH effec, we compue ARCH LM es. The resuls in Table 2 do no indicae any ARCH effecs in all models esimaed in his. The Breusch-Godfrey (BG) es of serial correlaion indicaes ha serial correlaion hypohesis canno be rejeced in all hree ARIMA models. Meanwhile, normaliy es using Jarque-Bera (JB) es indicaes ha normaliy in he errors has be rejeced in all here ARIMA models. This indicaes ha, all here models are no normal disribued because of some seasonal effecs. One ineresing resuls can be derived from Table 2 is ha, alhough seasonal effecs

9 58 SAROJ KANT BISWAL and BIKASH KUMAR MISHRA have been ae ino accoun in every ARIMA models, bu he resuls does no exiss any significan seasonal effecs, eiher posiively or negaively. To choose suiable ARIMA model for his sudy, we used he inequaliy coefficiens. The inequaliy coefficien of he ARIMA(1,0,1) model are marginally smaller han hose of he ARIMA(1,0,2) and ARIMA(2,0,2). Therefore ARIMA (1,0,1) is he bes ARIMA seleced in his sudy. Keep in mind ha ARIMA models are very hard o bea, especially when i comes o dealing shorerm forecasing. For one-sep ahead forecasing which been applied in his sudy, he MA(1) model is he bes because he value of RMSE and MAPE are he lowes. The resuls illusraed in Table 3 is in he line of AIC and SIC values which been discussed hrough Table 2 earlier. As a conclusion, we used ARIMA(1,0,1) o forecas one-period ahead ouris arrivals o Malaysia. Table 3 Summary of Forecas Evoluions of ARIMA Models ARIMA Models ARIMA (1,0,1) ARIMA (1,0,2) ARIMA (2,0,2) Inequaliy Coefficien RMSE MAE MAPE Theil Coefficien The ARIMA(1,0,1) model ha has been esimaed for he sample period can be describe as shown in equaion (9) wih -values of he coefficiens are in parenheses. Esimaed AR(1) and MA(1) were found significan a 1 percen. I is clear ha he AR(1) and MA(1) componens are significan wihou any seasonal dummies. Therefore, our selecion of ARIMA(1,0,1) model is a righ choice: ln( Tour) = In( Tou) ε 1 (9) ( 9 ) ( 21 ) ( ) I needs o be noed ha, once we acceped ARIMA(1,0,1) as a suiable model for his sudy, herefore we used he model o forecasing purpose. We applied ARIMA(1,0,1) o forecas one-period ahead using hisorical daa 1995Q1-2008Q4 and predic for shor-erm period 2009:Q1-2009:Q4 of ouris arrivals o Malaysia. Figure 3 shows clearly he forecased inernaional ouris arrivals o Malaysia using ARIMA(1,0,1) wih one-period ahead forecasing mehod. In erm of using quarerly daa wih shor erm forecasing, oneperiod-ahead procedure slighly beer forecas for Malaysia; while seasonal ARIMA generaes relaively no accurae in his sudy because seasonaliy does no exiss in his sudy. Figure 3 : Forecased Inernaional Touris Arrivals o Malaysia wih ± 2 x S.E from he ARIMA(1,0,1) Model in Logarihm Form Prediced Touris Arrivals Touris Arrivals 2 x S.E

10 SMALL SIZED COMMERCIAL HOTELS IN INDIA 59 Table 4 displays an ex-pos forecas of he inernaional ouris arrivals in Malaysia from 2009:Q1 o 2010:Q4. The forecased value is according o ARIMA(1,0,1) esimaion which minimize mean absolue percenage errors. The rend of forecased inernaional ouris arrivals for 8 period-ahead indicaes an upward rend in lower and upper limis. Table 4 Acual and Fied Value of Forecased Inernaional Tourism Demand Year/Quarer Lower 90% Forecased Tourism Demand Upper 90% 2009:Q :Q :Q :Q CONCLUSION For he firs ime, his sudy demonsraes ha seasonaliy exiss in he ARMA of ouris arrivals o Malaysia. To capure he seasonal effecs, seasonal dummy variables were included in he condiional ARIMA models. Furhermore, given he seasonal ARIMA models have been widely employed in forecasing ouris arrivals o Malaysia. Overall, his paper concludes ha ARIMA model (1,0,1) canno perform seasonal effecs in predicing ouris arrivals o Malaysia because seasonaliy no affeced on he numbers of ouris arrivals o Malaysia. The findings of his sudy is also in line wih previous sudies conduc by Chu (2008), Chan and McAleer (2005); and Song e al. (2003) using univariae daa wih ARMA- ARIMA forecasing echniques. The empirical forecasing mehod used in his sudy perform bes fi ARIMA model and from a planning perspecive, his should be a major research heme in he sudy of inernaional ourism demand, since incorporaion of forecass ino decision maing processes would assis developmen and invesmen sraegies in ourism indusry in he fuure. As a conclusion, more forecasing mehod should be included in fuure sudies in Malaysia. For example, here was some inconclusive evidence suggesing ha smoohing echnique performs beer han he Box-Jenins mehodology. ACKNOWLEDGEMENTS We would lie o express our hans o Malaysia Tourism Developmen Cooperaion (MTDC) for providing laes available daa; and Universiy Malaysia Terengganu (UMT) for providing faciliies and financial suppors. REFERENCES Aal, M. (2004). Forecasing Turey s ourism revenues by ARMAX model. Tourism Managemen, 25, Ahanasopoulos, G. & Hyndman, R. J. (2008) Modeling and forecasing Ausralian domesic ourism. Tourism Managemen, 29, Bonham, C., Gangnes, B. & Zhau, T. (2008). Modelling ourism: a fully idenified VECM approach. Inernaional Journal of Forecasing (in press) Chan, F., Lim, C. & McAleer, M. (2005). Modelling mulivariae inernaional ourism demand and volailiy. Tourism Managemen, 26(3), Chu, F.L. (2008a). Forecasing ourism demand wih ARMA-based mehods. Tourism Managemen, x, Chong, C.L. (2003). Chu, F.L. (2008b). Analyzing and forecasing ourism demand wih ARAR algorihm. Tourism Managemen, 29(6), Coshall, J. T. (2008). Combining volailiy and smoohing forecas of UK demand for inernaional ourism. Tourism Managemen (in press)

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