ARMAX Modelling of International Tourism Demand

Transcription

1 ARMAX Modelling of Inernionl Tourism Demnd Lim, C. 1, Min, J.C.H. 2 nd McAleer, M. 3 1 Deprmen of Tourism nd Hospiliy Mngemen, Universiy of Wiko, New Zelnd 2 Deprmen of Tourism, Hsing Wu College, Tipei, Tiwn, R.O.C. 3 School of Economics nd Commerce, Universiy of Wesern Ausrli, Ausrli emil: clim@wiko.c.nz Keywords: Inernionl ourism demnd, ARMAX modelling, income elsiciies, New Zelnd, Tiwn EXTENDED ABSTRACT One of he bsic gols of ourism demnd modelling is o esime income nd/or price elsiciies, which cn hen be used in developing beer informed public nd prive policies. The focus of economeric sudies is o deermine he exen o which he d suppor priculr heory. In reviews of empiricl sudies on inernionl ourism demnd nd is deerminns, Lim (1999, 26) rgued h he mos prominen nd frequenly used vrible in hese sudies is income of ouris-genering counries, which ffecs he biliy of consumers in hese counries o py for heir overses rvel. More specificlly, he demnd for inernionl rvel is posiively reled o income in he origin mrke. Jpn hs been dominn economic power nd ourism superpower in he Asi-Pcific region. I hs been he lrges inbound mrke for mny counries in he region. Figure 1 shows he rel GDP nd oubound rvel of Jpn since 198. The purpose of his pper is o use he ARMAX model o invesige he dynmic relionship beween ourism demnd nd rel income of Jpn, nd o compre he findings wih he single-equion model. Exensive discussion of ARMAX modelling nd esimion cn be found in Frnses (1991) nd Greene (2). The ARMAX model is n exension of he Box-Jenkins uoregressivemoving verge (ARMA) model wih explnory exogenous vribles (X). Box-Jenkins (197) models re used o cpure he uoregressive moving verge of ps observions of ouris rrivls from Jpn o Tiwn nd New Zelnd. While i is possible o use he uoregressive (AR) nd moving verge (MA) processes o cpure he curren pern of ouris rrivls from priculr mrke bsed on is own ps rrivls nd he rndom error from previous periods, oher explnory vribles, such s rel income in he origin counry, hve lso ffeced he demnd for inernionl rvel. Rel G D P Rel GDP Residen Deprures 1992 Yer Figure 1. Rel GDP (billion JYP) nd residen deprures ( ) of Jpn, By including n income vrible wih finie lg srucure, he ARMAX model is used o esime he income elsiciy of ourism demnd by Jpn for New Zelnd nd Tiwn over he period 198 o 24. Before specifying he ARMAX model, ess nd dignosics re performed in he esimion of he Box-Jenkins models. By excluding insignificn AR nd MA lgs, he use of dignosics nd selecion crieri would help o deermine more prsimonious model. The ler is subsequenly used o underke ARMAX modelling nd esimion of he income elsiciy of rvel demnd. Afer discussing he ourism movemens from Jpn o New Zelnd nd Tiwn since 198 nd chrcerisics of inernionl ouriss, he mehodology nd uni roo ess for he ourism nd income ime series re discussed, he esimion of he single equion nd ARMAX models is presened, nd some concluding remrks re given. The EViews 5 economeric sofwre pckge is used for he d nlysis nd empiricl esimion Residen Deprures 1885

2 1. INTRODUCTION Jpnese oubound rvel rebounded srongly in 24 nd 25, fer wo yers of negive growh in 21 nd 23 (World Tourism Orgnision, 26). Fers of errorism nd diseses reled o he evens of Sepember 11, 21 in he USA, SARS nd bird flu oubreks in 23, hve cused negive growh of 9% nd 2% in 21 nd 23, respecively, in Jpnese inernionl rvel demnd (see Figure 2). 2,, 1,8, 1,6, 1,4, 1,2, 1,, 8, he Jpnese economy since he mid-199s, SARS nd he ppreciion of he New Zelnd dollr hve ll conribued significnly o he shrp decline in he Jpnese mrke (NZ Deprmen of Sisics ). n u m b e r o f o l v isio r rriv ls yer , 4, 2, Jn Feb Mr Apr My Jun Jul Aug Sep Oc Nov Dec Figure 2. Tol shor-erm residen deprures from Jpn, Afer some discussion of ourism movemens from Jpn o New Zelnd nd Tiwn since 198 nd cerin chrcerisics of he ouriss in Secion 2, he res of he pper is orgnised s follows. The mehodology nd uni roo ess for he ourism nd income ime series re discussed in Secions 3 nd 4, respecively. In Secion 5, he esimion of he single equion nd ARMAX models is presened. Some concluding remrks re given in Secion 6. The EViews 5 economeric sofwre pckge is used for he d nlysis nd empiricl esimion. 2. JAPANESE TOURISM DEMAND FOR NEW ZEALAND AND TAIWAN Jpn is New Zelnd s lrges Asin ouris source mrke. Touris rrivls from Jpn hd been incresing by more hn 14% per nnum from 198 o 1996, fer which New Zelnd sred o experience decline in he Jpnese mrke (see Figure 3). The 1997/1998 Asin economic nd finncil crises, coninuing economic slowdown in Figure 3. Inernionl ouris rrivls from Jpn o New Zelnd, Mos Jpnese ouriss regrd New Zelnd s holidy desinion, s shown in Figure 4. As long hul desinion, i seems h New Zelnd is populr desinion for older Jpnese ouriss, wih 37% of ll visiors ged 55 yers nd bove. According o he inernionl visior surveys conduced in 25, mos Jpnese visiors were pckge rvellers, nd very few were repe ouriss. Aucklnd (in he Norh Islnd), followed by Cnerbury nd Queensown (in he Souh Islnd), were he mos populr regions in New Zelnd for Jpnese ouriss. No surprisingly, hoels were he dominn ype of ccommodion used by hese visiors. Mrke surveys lso indiced h shopping nd eing ou were he mos populr civiies engged in by Jpnese ouriss (Tourism New Zelnd 26). Besides decline in Jpnese ouris rrivls, he increse in he srengh of he New Zelnd currency hs lso cused decrese in ouris spending. Averge Jpnese ouris expendiures in New Zelnd decresed by more hn 13% from 24 o 25. Hisoriclly, Tiwn ws colony of Jpn from 1895 o 1945 prior o he Kuominng (KMT) Pry s fligh o Tiwn (from Chin) o exercise is sovereigny. During h ime, only he Jpnese lnguge nd educion were llowed o be spoken 1886

3 nd lerned by he islnd residens. Thus, Tiwn s lifesyle hs been hevily influenced by he Jpnese culure. For insnce, Tiwnese nd Jpnese enjoy similr leisure civiies, such s shopping, dining, nd soking in ho springs ll yer round o survey conduced by he Tiwn Tourism Bureu (26), Troko, Tienhsing (one of he nionl prks loced on he esern side of Tiwn) nd he nigh mrkes were he mjor scenic spos for Jpnese ouriss. The sudy lso found h cuisine nd hisoricl relics were he mjor rcions for mos Jpnese ouriss. On verge, heir durion of sy ws 5.2 nighs, compred wih 7.1 nighs on verge for ll inbound visiors. 12 Holidy VFR Figure 4. Jpnese ouriss o New Zelnd by rip purpose, Business Jpn is significn inbound ourism mrke for Tiwn in erms of ouris rrivls nd ouris verge dily expendiure. Jpnese ouriss, which ccouned for over 3% of ll inernionl ouriss in Tiwn, hve been incresing by more hn 4% beween 1981 nd 25 (Tiwn Tourism Bureu, 26). Higher ourism or relive prices in Tiwn due o inflion in recen yers hve no slowed down he flows of ouriss from Jpn. In priculr, he number of Jpnese visiors o Tiwn hs reched new record of 1.1 million in 25, double-digi growh compred wih 24 (see Figure 5). However, he SARS oubrek in 23, which ws he firs pndemic of he 21s Cenury declred by he World Helh Orgnizion (23), hd fr-reching effec on Jpnese inbound rrivls o Tiwn o such levels he counry hd no experienced since Beween 2 nd 25, more hn one-hird of Jpnese ouriss o Tiwn were in he 5 nd older ge group. The shre of Jpnese mle ouriss ounumbered heir femle counerprs by he rio of pproximely 2:1. Abou 5% of Jpnese rvelled o Tiwn for plesure, followed by business (3%), nd visiing relives nd friends (3%), s shown in Figure 6. According number of ol visior rrivls yer Figure 5. Inernionl ouris rrivls from Jpn o Tiwn, Holidy Business VFR Figure 6. Jpnese ouriss o Tiwn by rip purpose,

4 The sesonl perns of ouris rrivls from Jpn o New Zelnd nd Tiwn re shown in Figure 7. Using he muliplicive rio-o-moving verge echnique o esime he monhly sesonl indices, i is no surprising h here is less sesonl vriion for shor-hul desinion such s Tiwn. The sesonl rnge is.34 nd.77 for Tiwn nd New Zelnd, respecively. Noneheless, he pek ourism monhs for he wo desinions re Februry (for New Zelnd) nd Mrch (for Tiwn). The desinions hve overlpping ourism sesons during he period 1979 o 25, h is, from November o Mrch. While he inr-yer movemens of Jpnese ouriss o New Zelnd my be reled o he climic condiions he desinion, he sme rgumen would no seem o pply o Tiwn. Sesonl Indices NZ Tiwn Jn Feb Mr Apr My Jun Jul Aug Sep Oc Nov Dec Figure 7. Esimed monhly sesonl indices for inbound ouris rrivls from Jpn o New Zelnd nd Tiwn, METHODOLOGY The focus of economeric sudies is o deermine he exen o which he d suppor priculr heory, nmely he demnd for inernionl rvel is posiively reled o income of he origin counry. We propose o use ime series economeric modelling of inbound ourism bsed on sesonlly undjused qurerly d for 198(1) o 24(2) o obin esimes of income elsiciies of rvel o New Zelnd nd Tiwn by Jpnese residens. nd ARMAX models by OLS o compre he esimes of he Jpnese income elsiciy of rvel demnd for he wo desinions. The sensiiviy of ouris rrivls from Jpn o chnges in is rel income will lso be evlued. As guide o model selecion, he Akike Informion Crierion (AIC) nd Schwrz Byesin Crierion (SBC) re useful, so h he model wih he smlles AIC nd SBC vlues is preferred We ssume liner model in he vribles in which he d on y1,..., y hve been genered by y = α + β x + ε, such h y depends linerly on α nd β. The oher key ssumpions of he clssicl liner regression model include: (1) Expeced vlue of disurbnce erm is zero: E( ε ) = ; (2) Homoskedsiciy, or consn vrince of he 2 disurbnces: Vr( ε ) = σ e for ll ; (3) No seril correlion of he disurbnces cross periods: E( ε ε s ) = ( s); (4) Explnory vribles re wekly exogenous, h is, here is zero covrince beween ε nd ech explnory vrible: E( x ε ) = for ll ; 2 (5) ε re normlly disribued: ε N(, σ ) e for ll ; (6) Prmeer consncy:α, β nd σ (> ) re fixed unknown numbers. 4. UNIT ROOT TESTS A grphicl nlysis of he sesonlly undjused qurerly d from 198(1)-24(2) suggess h he logrihm of ouris rrivls from Jpn o New Zelnd nd Tiwn re likely o be nonsionry (see Figure 8). This resul is suppored by he correlogrm, which displys he esimed uocorrelion nd pril uocorrelion funcions of he residuls. Ordinry les squres (OLS) esimion is used o esime he influence of rel income on ourism demnd by Jpn for New Zelnd nd Tiwn. More specificlly, we will esime single equion 1888

5 (A) o New Zelnd In order o es for uni roos, he hypohesis of ineres is: H : δ = Log Touris Arrivls Log Touris Arrivls (B) o Tiwn Yer Yer Figure 8. Logrihm of shor-erm ouris rrivls from Jpn, A ouris rrivl series is sid o be sionry if he men, vrince nd covrince of he series remin consn over ime. The uni roo es is forml mehod of esing he sionriy of series. Qurerly ouris rrivls (in logrihms) from Jpn o New Zelnd nd Tiwn re esed for uni roos using he Augmened Dickey- Fuller (ADF) es procedure, which is bsed on he following regression equion: Δ = α + β + δ + ψ Δ + ε 1 p j = 1 j j where is he logrihm of ouris rrivls o New Zelnd or Tiwn from Jpn ime, is deerminisic rend, ε is disurbnce erm of he regression which is independen nd normlly disribued wih zero men nd consn vrince. H 1 : δ < The null hypohesis of uni roo is bsed on he - sisic (which hs non-sndrd disribuion) using simuled criicl vlues. The deerminisic ime rend () is reined ( β ) in he es regression becuse he ADF -sisics wih nd wihou rend re subsnilly differen. As qurerly d re used, n iniil lg lengh of 4 is used in he ADF regression o ccommode possible seril correlion in he disurbnces. If he fourh lg is insignificn he 5% level, he lg lengh is reduced sequenilly unil significn lg lengh is obined. The hird lg is significn for boh series. The ADF es resuls indice h he ADF sisics for he ouris rrivl series from Jpn o New Zelnd nd Tiwn (-1.36 nd -2.67, respecively) re boh greer (h is, re less negive) hn he criicl vlue of he 5% significnce level. Therefore, he null hypohesis of uni roo cnno be rejeced, which implies h ouris rrivls from Jpn o New Zelnd nd Tiwn re nonsionry. Tking he firs differences of he logrihm of he ouris rrivls nd pplying he ADF es procedure o he rnsformed series, more negive es sisic (of -4.9 significn lg lengh of 4 for New Zelnd nd -1.2 lg lengh of 2 for Tiwn) hn he criicl vlue of re obined. This suggess h he firs difference series re sionry. Individul ADF ess show h he logrihm of ouris rrivls is inegred of order one, I(1), wheres he firs difference of he logrihm of he series follow n I() process, or is inegred of order zero. The ADF es procedures re pplied o he rel GDP of Jpn (in logrihms) for he presence of uni roos, nd he null hypohesis of uni roo cnno be rejeced, which implies h rel GDP series of Jpn re nonsionry. However, he differenced series is sionry nd follows n I() process, or is inegred of order zero, wheres he logrihm of rel GDP is inegred of order one, I(1). The firs difference series for ouris rrivls nd rel GDP will be used in he empiricl modelling in he nex secion. 1889

6 5. EMPIRICAL MODELLING OF JAPANESE TOURIST ARRIVALS TO NEW ZEALAND AND TAIWAN Using single equion model, he influence of rel income on ourism demnd by Jpn is given s follows: = + βy + φ 1 α + ε where y is he log of Jpnese rel GDP ime. Wih he inclusion of sesonl dummy vribles, D 2, D 3 nd D 4 in he model s well s SARS dummy vrible for Tiwn, he following esimes re obined by OLS (wih bsolue - rios in prenheses): (1) = yˆ.3 D (6.) (1.35) (4.8).8 D 3.1 D 4 (12.) (1.31) 2 ARIMA(4,1,4) for Tiwn s he opiml models. Inclusion of hree sesonl dummy vribles in hese models nd SARS dummy for Tiwn, he finl ARMAX models re obined s follows, wih he lowes AIC nd SBC vlues (wih bsolue -rios in prenheses): (3) (4) = yˆ.2D2 (9.81) (2.37) (3.36) 4.7D3 + (1 +.84L.49L ) ˆ ε (12.8) (8.7) (77.2) (New Zelnd Model 1) = ˆ y.81ˆ 1 (6.23) (4.14) (1.2).66ˆ 2.65ˆ 3.7D (7.78) (8.66) (6.1) (New Zelnd Model 2) 3 (2).3D (New Zelnd) =.1.39 yˆ.2d (2.35) (.27) (.38) 3.1D DSARS (4.92) (2.15) (5.43) (5) = yˆ (5.7) (4.76) (16.9) (13.).84ˆ 3.88ˆ.2D ˆ 4 + (1 +.95L ) ˆ ε (14.6) (5.55) (46.) (Tiwn) 2 (Tiwn) Deleion of he insignificn sesonl dummy vrible for New Zelnd does no yield significn income elsiciy of rvel demnd. The sme is lso rue for Tiwn wih he deleion of he insignificn sesonl nd SARS dummy vribles. The ARMAX model is n exension of he Box- Jenkins uoregressive-moving verge (ARMA) model wih explnory exogenous vribles X (Frnses 1991). Before he ARMAX model is used o esime he relionship beween income nd rvel demnd by Jpn, we need o deermine he opiml ARMA models. Using he firs difference of he log ouris rrivls from Jpn, vrious ARIMA hve been esimed using ordinry les squres. The models seleced yield significn -sisics he 5% level of significnce for he AR nd MA coefficiens, wih no seril correlion he 5% level, using he Lgrnge muliplier es for seril correlion. ARIMA(3,1,3) nd ARIMA(2,1,4) hve been idenified for New Zelnd, nd The Lgrnge muliplier ess, LM(SC), show h he models do no hve seril correlion he 5% level. 6. CONCLUDING REMARKS In his pper we hve esimed single equion nd ARMAX models o evlue he effec of chnges in income on Jpnese rvel demnd for New Zelnd nd Tiwn. The income vrible hs lso been esed nd ppropriely rnsformed o obin sionriy of he d series. Addiionl vribles, nmely sesonl nd SARS dummy vribles, were lso included in he esimion of he single equion nd ARMAX models. Unlike he single equion model, he ARMAX echnique is more pproprie for invesiging he dynmic relionship beween ourism demnd nd rel income of Jpn. The model is developed in wo sges, which iniilly requires h he Box- Jenkins ARIMA models be idenified nd seleced. The findings of he ARMAX model suppor he economic heory. In conrs o he single equion models, ll he ARMAX models show h he Jpnese income elsiciies of rvel demnd re 189

7 posiive nd significn. According o he single equion model for Tiwn, he effecs of SARS in 23 hd significn bu posiive effec on Jpnese inbound rvel. The ler is conrry o heory nd reliy. Only he sesonl effec in qurer 3 is negive nd significn in boh he single equion nd ARMAX models for New Zelnd nd Tiwn. World Tourism Orgnision (26). Tourism Highlighs 25 Ediion, Mdrid: World Tourism Orgnision. ACKNOWLEDGEMENTS The uhors re mos greful o he Wiko Mngemen School, Universiy of Wiko, New Zelnd, nd he Ausrlin Reserch Council for finncil suppor. 7. REFERENCES Box, G.E.P., nd G.M. Jenkins (197), Time Series Anlysis, Forecsing nd Conrol. Sn Frncisco: Holden Dy. Frnses, P. H. (1991), Primry demnd for beer in he Neherlnds: An pplicion of ARMAX model specificion. Journl of Mrkeing Reserch, 28(2), Greene, W.H. (2), Economeric Anlysis (3 rd ediion). New Jersey: Prenice Hll. Lim, C. (1999), A Me-Anlyic Review of Inernionl Tourism Demnd. Journl of Trvel Reserch, 37 (3), Lim, C. (26), A Survey of Tourism Demnd Modelling Prcice: Issues nd Implicions. In Dwyer L. nd Forsyh P. (eds.) Inernionl Hndbook On Tourism Economics, UK: Edwrd Elgr Publishing. New Zelnd Deprmen of Sisics (198-24), Monhly Touris Arrivls. Wellingon. Tiwn Tourism Bureu. (26), 25 survey repor on visiors expendiure nd rends in Tiwn. Tipei: Tourism Bureu. Tourism New Zelnd (26), Jpn. Rerieved 25 Ocober, 26 from: hp:// m_info/mrke-reserch/mrke-guides World Helh Orgnizion (23), World helh orgnizion issues emergency rvel dvisory. Rerieved Sepember 15, 26 from: hp:// 3_15/en/ 1891