Modelling International Tourist Arrivals to the Five Major Spanish Destinations

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1 Modellng Inernaonal Tours Arrvals o he Fve Major Spansh Desnaons Álvares, G., S. Ho and M. McAleer Research Deparmen, Bank of Span Deparmen of Treasury and Fnance, Wesern Ausrala School of Economcs and Commerce, Unversy of Wesern Ausrala Emal: suhejla.ho@df.wa.gov.au Keywords: Inernaonal ours arrvals, Span, regons, seasonaly, condonal varance, uncerany EXTENDED ABSTRACT Inernaonal oursm s an mporan source of foregn ncome for Span and s regons. Span s a counry ha consss of 7 auonomous communes, namely Andalusa, Aragon, Asuras, Balearc Islands, Basque Counry, Canary Islands, Canabra, Casle-La Mancha, Casle-Leon, Caalona, Ceua and Mellla, Communy of Madrd, Communy of Valenca, Exremadura, Galca, Murca, and Navarra, wh hsorcal ses and unque culural feaures ha have always made he counry aracve o foregn vsors (Fgure ). Accordng o he World Toursm Organzaon (WTO (6)), Span was he world s second mos vsed counry n 5, wh a oal of 55.6 mllon nernaonal ours arrvals, exceeded only by France, wh 76 mllon arrvals. Span was also he world s second hghes ours earner (USD47.9 bllons), afer he USA, wh USD8.7 bllons. Global oursm grew a a hgher han expeced rae n he frs four monhs of 7 due o several posve facors, he connung world prospery n parcular. Wh ncreasng dsposable ncome n boh developed and developng counres and facors such as he connued developmen of low cos arlnes makng ravel avalable for larger shares of populaon, nernaonal oursm s expeced o reman srong. Toursm s conrbuon o economc growh and job creaon s ncreasngly drawng he aenon of naonal governmens, especally hose n developng regons. Hgher nvesmen n nfrasrucure, markeng and promoon, developmen of domesc markes, lberalzaon of ar ranspor, growng nra-regonal cooperaon, and a growng number of publc-prvae parnershps are key o he srong growh of he global oursm ndusry (WTO, 7). Ths paper examnes he me seres properes of oursm demand o he op 5 auonomous communy desnaons n Span, namely Andalusa, he Balearc Islands, he Canary Islands, Caalona and he Communy of Madrd, from January 994 o February 6. Of he 7 regons n Span, he op 5 desnaons represen almos 84% of he oal ours arrvals n Span. The log-dfferenced monhly ours arrvals and her assocaed uncerany are modelled and esmaed for he 5 seres usng unvarae and mulvarae condonal volaly models. Unvarae esmaes sugges ha condonal volaly models provde an accurae measure of uncerany n monhly ours arrvals for he 5 seres. The esmaed condonal correlaon coeffcens (CCC) ndcae wheher Span should specalze or dversfy s oursm promoon effors on hose auonomous communes ha receve he larges numbers and growh n oursm arrvals. These esmaes sugges ha he monhly ours arrvals shocks o alernave ours communes are n general ndependen or weakly relaed, excep for he par of Andalusa and Caalona. Fgure. Regonal Map of Span (Source: hp:// 9

2 . DATA As dscussed n Alvarez e al. (7), he World Toursm Organzaon (WTO) defnes nernaonal ourss as ndvduals ha ravel o and say n places ousde her counry for more han 4 hours for lesure, busness and oher purposes. The mos common un of measure used o quanfy he volume of nernaonal oursm for sascal purposes s he number of nernaonal ours arrvals (a froners or arpors) and overngh ourss (WTO (5)). Inernaonal oursm arrvals daa o he op 5 auonomous communy desnaons n Span are suppled by he Spansh Naonal Insue of Sascs (Insuo Naconal de Esadsca (INE)) webse. The op 5 desnaons receve 84% of he oal nernaonal ourss o Span, wh a sample sze for each of he 5 desnaons from January 994 o February 6. Table gves he descrpve sascs for monhly nernaonal ours arrvals o he op 5 auonomous communy desnaons n Span. The mean ours arrvals vary subsanally across he 5 communes, rangng from 94,56 for he Communy of Madrd o 47,84 for he Balearc Islands. Of he 5 communes, he Canary Islands and he Communy of Madrd have means ha are less han 5, ourss, whle Andalusa has a mean of 6,4. The means of he Balearc Islands and Caalona monhly ours arrvals, whch are he wo major oursm regons, are boh well above 4, ourss. By comparson o he mean, he medan ours arrval measure does no vary as much across he 5 communes. Moreover, for he medan case, he rank from he mos o he leas vsed regon changes. Caalona s ranked frs wh 6,8 monhly nernaonal ours arrvals, followed by Andalusa wh 49,7 and he Balearc Islands wh 4,968 (whch are ranked frs n erms of he mean). The Canary Islands and he Communy of Madrd have he lowes medan n he sample, recevng less han 5, nernaonal ourss. Monhly ours arrval fgures from he op 5 communy desnaons n Span show ha he Balearc Islands vary he mos durng he sample perod, wh a mnmum of,88 and a maxmum of,59,699 ourss. The regon ha presens more sably n he number of arrvals s he Communy of Madrd, rangng from 89,494 o 8,44. Alhough he sandard devaon vares subsanally across he 5 communes, from 46,79 for he Communy of Madrd o 6,87 for he Balearc Islands, hs prmarly reflecs dfferences n mean monhly ours arrvals. Tours arrvals o he op 5 communy desnaons n Span are all posvely skewed excep for he Communy of Madrd, wh kuross rangng from.59 for he Balearc Islands o.6 for he Communy of Madrd. Sascs Table. Descrpve sascs for monhly nernaonal ours arrvals. Andalusa Balearc Islands Canary Islands Caalona Madrd Mean 6,4 47,84 5,77 47,9 94,56 Medan 49,7 4,968 45,8 6,8 98,45 Max. 6,57,59,699 8,8 889,56 8,44 Mn. 9,,88 4,47 65,69 89,494 Sd. Dev. 44, 6,87 64,658 5,4 46,79 Skewness Kuross Inernaonal monhly ours arrvals and he uncerany assocaed wh monhly ours arrvals o he 5 mos vsed regons n Span are presened n Fgure. I clear ha here are sgnfcan seasonal varaons n he monhly nernaonal ours arrvals o he communes. However, he seasonal paers are dfferen across he 5 communes. The Balearc Islands and Caalona receve mos ourss durng he European summer, beween July and Augus, whle he Canary Islands receve hem n he European wner, beween November and March. On he oher hand, Andalusa and Madrd, receve mos nernaonal ourss n wo dfferen perods of he year. May s he monh when mos ourss vs Andalusa, followed by July. For Madrd, July and May are he monhs when mos of he ourss vs he communy. The Canary Islands s he regon where monhly ours arrvals vary he mos over he sample perod. For nsance, he monhly mean nernaonal ours arrval was 7,9 n 998 and,76 n 999. Overall, here s an ncreasng rend n he nernaonal ours arrvals o he 5 communes over he me sample. A noceable srucural change s observed for he ours arrvals o he Canary Islands n early 999, whch corresponds wh INE s updae of naonal oursm sascs. However, a slgh ncrease n he number of ours arrvals s also observed for he oher op 4 communy desnaons afer January 999, as INE ncluded daa on one-sar and smlar caegory hoels, n addon o wo-, hree-, slverand gold-sar hoels. Moreover, afer he Sepember errors aacks, he number of ours arrvals o Communy of Madrd, Andalusa, as well as he oher communes decreased subsanally. However, by he end of 94

3 , ours arrval numbers o all communes reurned o her pre-sepember levels ANDALUSIA BALEARIC ISLANDS CANARY ISLANDS 8E+ 7E+ 6E+ 5E+ 4E+ E+ E+ E+ E+ 5E+ 4E+ E+ E+ E+ E+.4E+ E+ VOL_ANDALUSIA VOL_BALEARIC ISLANDS VOL_CANARY ISLANDS ours arrvals seres. Ths mples ha he seres need o be ransformed o saonary processes o enable vald emprcal esmaes and nferences. One way o model seasonal daa and nonsaonary varables s o ake he frs dfference of he annual dfference of he logarhms of monhly nernaonal ours arrvals y, namely ΔΔ ln y (see Ho, McAleer and Sanso (5)). Takng he frs dfference of he annual dfference renders each of he 5 seres saonary, wh he sample sze beng February 995 o February 6 (raher han January 994 o February 6). Hence, he condonal mean model of he monhly nernaonal ours arrvals for each of 5 leadng source counres s as follows: E+ E+ 8E+9 4E+9 E+ ΔΔ ln y ( θ L)( θ L = θ + θ y ) ε, + =,...,46 () CATALONIA VOL_CATALONIA.4E+ E+.6E+ E+ 8E+ 4E+ E+ where y s he lagged dependen varable, and Lε and L ε are he movng average erms a lags and of he error erm. MADRID.4E+ VOL_MADRID. ANDALUSIA 6 VOL_ANDALUSIA 8 4 E+ E+ 8E+9 6E E+9 -. E E+ -. BALEARIC ISLANDS VOL_BALEARIC ISLANDS Fgure. Monhly ours arrvals (lef) and unceranes (rghs) o he op fve communes In Fgure, he monhly ours arrval unceranes for he op 5 communy desnaons show dfferen paerns. Ths s due o he fac ha he 5 communes arac dfferen ypes of ourss. Andalusa shows wo large varaons hrough he year and hey are very exreme. There s a smlar ncreasng rend n he ours arrval uncerany assocaed wh he Balearc Islands and Caalona. The uncerany n Andalusa s perssen all over he sample perod, wh noceable exreme observaons and/or oulers. For he Canary Islands, here s a noceable oursm uncerany hroughou he sample perod, wh he uncerany decreasng owards he end of he sample. However, he assocaed uncerany for Madrd s r-modal and was ncreasng by he end of he sample perod CANARY ISLANDS CATALONIA MADRID VOL_CANARY ISLANDS VOL_CATALONIA VOL_MADRID Fgure also suggess ha monhly nernaonal ours arrvals appear o be non-saonary. Hence, he possbly of spurous regressons wh me seres daa necessaes ess for he presence of un roos n he ndvdual seres. The ADF resuls showed he exsence of un roos n he 5 monhly Fgure. Log-dfferenced monhly ours arrvals (lef) and uncerany (rgh) o he op fve communes. Fgure presens he log-dfferenced monhly ours arrvals and he assocaed uncerany o 95

4 he op 5 desnaons n Span. Afer adjusng for he presence of seasonaly and un roos, he 5 seres do no presen rends and hey all vary around zero, lke ypcal fnancal reurn seres. Overall, he monhly ours arrval seres o he 5 communes vary subsanally, wh noceable peaks over he sample perod. In parcular, wo peaks n 999- domnae he varaons n he ours arrvals o he Canary Islands, reflecng he new ypes of oursm sascs consdered by he INE. Lke for fnancal seres, he posve shock was followed by a negave shock o adjus for he change n he oursm seres. Plos of he uncerany assocaed wh he 5 logdfferenced ours arrvals seres o he op communy desnaon are gven n Fgure. Overall, here are noceable cluserngs of volaly across he 5 seres, wh oulers and/or exreme observaons over he sample perod. The Balearc Islands and he Communy of Madrd have smlar paerns of volaly, especally from -4. For Andalusa and Caalona, he uncerany decreased over he sample perod, whle he Canary Islands show mld uncerany and wo oulers n 999 and. METHODS Consder he specfcaon of he mulvarae CCC model of Bollerslev (99): y = E( y I ) + ε, =,..., n ε = Dη, η ~ d(,) () where y = ( y, y,... ym) measures ours arrvals o he op 5 ours desnaons, he unvarae condonal mean, E( y I ), s he expeced value of y gven he pas nformaon avalable o me, η = ( η, η... ηm) s a sequence of ndependenly and dencally dsrbued (d) random vecors wh mean zero and varance one obaned from sandardzng he ours arrvals shocks, ε, usng / / / he sandardzaon D = dag( h, h,..., hm ), where h s he condonal varance, m (=5) s he number communy desnaons, and =,,46 monhly observaons for he perod January 994 o February 6. The CCC model assumes he condonal varance or uncerany of ours arrvals from a source counry, h, for =,..., m follows a unvarae GARCH(,) process, ha s, h = + + αε, β h, ω () where α represens he ARCH effecs, or he shor-run perssence of shocks, and β represens he GARCH effecs, or he conrbuon of shocks o long-run perssence, ha s, α + β. Alhough he CCC specfcaon n () has a compuaonal advanage over oher mulvarae models, such as he VARMA-GARCH model of Lng and McAleer () and VARMA-AGARCH model of McAleer e al. (7), assumes ndependence of uncerany, across dfferen desnaons, and does no accommodae he asymmerc effecs on uncerany of posve and negave oursm shocks. The CCC model s used o esmae he correlaon coeffcens of he monhly ours arrval shocks beween all pars of communy desnaons analysed n hs paper. When he correlaon coeffcen of oursm arrvals shocks, ρ j, s close o +, Span should specalze on hose communy desnaons ha receve he larges numbers and growh n ours arrvals. However, when he correlaon coeffcen of ours arrval shocks, ρ j, s close o -, Span should concenrae on dversfyng he communy base. Independen oursm communes are hose pars of communes wh a correlaon coeffcen, ρ j, close o zero, n whch case neher specalzaon nor dversfcaon n communes would be requred for opmal managemen of oursm arrvals. When he number of oursm desnaon s se o m =, such ha a unvarae model s specfed, ω >, α and β are suffcen (bu no necessary) regulary condons o ensure ha h >. The parameers n Equaons ()-() are ypcally obaned by he Lkelhood Esmaon (MLE) mehod usng a jon normal densy for he sandardzed ours arrvals shocks, η, afer he uncerany has been modelled. The parameers are esmaed by Quas-MLE (QMLE) when η does no follow a jon mulvarae normal dsrbuon. Lng and McAleer () proved ha he QMLE for GARCH(r,s) s conssen f he second momen regulary condon s fne. A weaker momen s he log-momen regulary condon, gven by E[ln( αη j + β j)] <, whch s suffcen for he QMLE o be conssen and asympocally normal. Equaon () assumes ha he posve shocks ( ε >) o monhly ours arrvals has he same mpac on uncerany, h, as a negave ours 96

5 arrvals shocks ( ε <), bu hs assumpon s normally volaed n pracce. In order o accommodae he possble dfferenal mpac on uncerany from posve and negave nernaonal ours arrval shocks, he GJR(,) model s proposed for specfyng h : h ( ( )) = + α + γi η ε + βh ω (4) where ω >, α, α + γ and β are suffcen (bu no necessary) regulary condons o ensure ha uncerany s posve, namely h >, and I η ) s an ndcaor varable defned: (, ε < I( η ) = (5), ε Under he assumpon ha he sandardzed shocks, η, follow a symmerc dsrbuon, he average shor-run perssence of ours arrvals shocks s, α + γ /, and he conrbuon of ours arrvals shocks o average long-run perssence s α + β + γ /. Lng and McAleer () showed ha he necessary and suffcen regulary condon for he second momen of GJR(r,s) of ours arrvals shocks o be fne s: α + β + γ / <. McAleer, Chan and Marnova (7) esablshed he log-momen regulary condon for he GJR(.) model of uncerany, namely E [ln(( α + γi ( η )) η + β )] <. (6). EMPIRICAL RESULTS The Bernd, Hall, Hall and Hausman (BHHH) (974) algorhm n EVews 5 s used o oban he esmaes of he parameers n hs paper. Boh he asympoc and Bollerslev-Wooldrdge (99) robus -raos are repored o enable vald sascal nference. In erms of he condonal mean (Tables and ), he seasonal sochasc effec s sgnfcan for all 5 nernaonal ours arrval seres, for boh GARCH(,) and GJR(,). The sochasc effec of he prevous monh s also sgnfcan n all he regons excep for he Balearc Islands, for boh GARCH(,) and GJR(,). GARCH(,) esmaes of he condonal uncerany of monhly nernaonal ours arrvals o Andalusa show ha he log-momen condon could no be compued and he second momen was no sasfed. However, for GJR(,), whle he second momen s sll no sasfed, he logmomen regulary condon s sasfed, ensurng ha he QMLE are conssen and asympocally normal. Indeed, here are sgnfcan asymmerc effecs beween posve and negave oursm shocks o Andalusa. Ths means ha negave shocks have a greaer mpac on uncerany han posve shocks of smlar magnude. Tours arrval shocks for Andalusa have a shor run perssence, ha s, for abou one monh. However, conrary o expecaons, he ours shocks have a negave and sgnfcan conrbuon o he longrun perssence. Asymmerc effecs are no sgnfcan for GJR(,) ours arrval esmaes o he Balearc Islands. Hence, GARCH(,) s preferred. Regardng he regulary condons, boh he logand second momen condons are sasfed. Hence, QMLE are conssen and asympocally normal and he emprcal esmaes are sascally adequae. These slands only have shor run perssence n ours arrvals shocks, ha s, for abou one monh. An neresng resul s found for he Canary Islands. When usng GARCH(,), boh he logand second momen condons are sasfed, however, he coeffcens of he GARCH(,) regresson are no sgnfcan. Ths would sugges ha he varance of he error erm s consan. On he conrary, only he log-momen s sasfed for GJR(,) gvng conssency and asympoc normaly o he QMLE of he ARCH effec whch s sgnfcan. Overall, he varance of he error erm for he Canary Islands s consan (under GARCH(,)), wh possble shor run perssence of he ours arrval shocks (under GJR(,) for abou a monh. GARCH(,) esmaes of he monhly nernaonal ours arrvals o Caalona show ha he log-momen condon could no be compued and ha he second momen was no sasfed. However, boh he log-momen and second momen regulary condons are sasfed for GJR(,). Therefore, he QMLE are conssen and asympocally normal. Such resuls sugges ha he emprcal esmaes are sacally vald for ours arrvals o hs communy. There are sgnfcan asymmerc effecs beween posve and negave shock of smlar magnude o ours arrvals. However, unlke he case of Andalusa, negave shocks for Caalona have a lower mpac on uncerany han posve shocks. Ths s an unusual resul, whch hghlghs he dfferences n he properes of ours arrval seres analysed n 97

6 hs paper. Moreover, ours arrval shocks o Caalona have a sgnfcan long run effec, whch accumulaes over me. Lke for Andalusa and Caalona, he log-momen condon could no be compued and second momen was no sasfed for GARCH(,) for he Communy of Madrd. On he oher hand, boh he log- and second momen regulary condons are sasfed for GJR(,), herefore, he QMLE are conssen and asympocally normal. Such resuls sugges ha he emprcal esmaes are sacally vald. However, he shor and long perssence of shocks s found o be nsgnfcan, suggesng ha he GJR(,) s also no approprae for he Communy of Madrd. Overall, he unvarae resuls sugges ha he GJR(,) model provdes an accurae measure of he uncerany n nernaonal monhly ours arrvals o he op 5 oursm communes, excep for Caalona for whch neher GARCH(,) nor GJR(,) was approprae. As he esmaed GJR(,) model was found o be preferable o s GARCH(,) counerpar for he monhly ours arrvals o he 5 auonomous communes, he mulvarae CCC wll be dscussed only for he GJR(,) model of uncerany. Esmaes of he CCC coeffcens for monhly nernaonal ours arrval shocks by auonomous communes are gven n Table 5.. These correlaons are calculaed usng he GJR(,) sandardsed ours arrvals shocks for he 5 mos vsed communes n Span. In Table, he CCC coeffcens are no very hgh, rangng from -.59 (Balearc Islands, Madrd) o.4 (Andalusa, Caalona). The second hghes condonal correlaon s for (Andalusa, Madrd), followed by (Caalona, Madrd) and (Canary Islands, Madrd). These resuls are manly due o wo facors. Frs, he mos nernaonally wellknown Spansh ces, n order of mporance, are Barcelona (Caalona) and Granada and Sevlle (Andalusa). Hence, when ourss ravel o Span, hey vs more han one cy n he counry. Second, Spansh nernaonal and regonal ranspor, by road and/or ar, s cenralsed n he capal cy, Madrd (Communy of Madrd). For hs reason, when ravellng from one communy o anoher, crossng hrough Madrd by road and/or ar, ourss ake a chance o vs he cy. However, he Balearc Islands and Canary Islands, he wo sland communes, do no seem o be srongly relaed n erms of her oursm shocks, whle hey boh seem o be ndependen of he Communy of Madrd n erms of ours arrval shocks. The former occurs because he wo sland communes arac dfferen ypes of ourss and a dfferen mes of he year. Moreover, mos of he nernaonal ourss vsng hese slands are Europeans and almos all of hem reach he slands by ar-ranspor. As he wo sland communes are drecly conneced o he European ces, he ourss do no need o sop by and vs Madrd on her way o he slands. Anoher neresng resul s ha he condonal correlaon beween shocks o he Balearc Islands and Caalona, he wo mos vsed communes n Span and he closes n geographcal dsance s also very low. Ths shows ha Balearc Islands and Caalona are dfferen markes ha arac dfferen ypes of nernaonal ours. The Balearc Islands arac sun, sand and sea ourss ha are neresed n relaxng holdays, whle he ones vsng Caalona are neresed n culural holdays. 4. ACKNOWLEDGMENTS The vews expressed n hs paper are hose of he auhors and do no necessarly reflec hose of he Deparmen of Treasury and Fnance, Wesern Ausrala. The hrd auhor wshes o acknowledge he fnancal suppor of he Ausralan Research Councl. 5. REFERENCES Alvarez, G., S. Ho and M. McAleer (7), Modellng ours arrvals o Span from he op fve source markes, n B. Ekasngh, A. Jnrawe and S. Praummnra (eds.), Smulaon and modelng: owards susanable lvelhood and envronmen, Chang Ma Unversy, Chang Ma, Thaland. Bernd, E.K., B.H. Hall, R.E. Hall and J.A. Hausman (974), Esmaon and nference n nonlnear srucural models, Annals of Economc and Socal Measuremen,, Bollerslev, T. (99), Modellng he coherence n shor-run nomnal exchange raes: a mulvarae generalzed ARCH approach, Revew of Economcs and Sascs, 7, Bollerslev, T. and J.M. Wooldrdge (99), Quas-maxmum lkelhood esmaon and nference n dynamc models wh me-varyng covarances, Economerc Revews, Ho, S., McAleer, M. and Sanso, A. (5), Specalzaon, Dversfcaon and Segmenaon of Brsh and German Tourss o he Balearc Islands, n V. 98

7 Kachvchyanukul, U. Purnrapban and P. Uayopas (eds.), Smulaon and modelng: negrang scences and echnology for effecve resource managemen, Bangkok, Thaland, pp Lng, S. and M. McAleer (), Saonary and he exsence of momens of a famly of GARCH processes, Journal of Economercs, 6, 9-7. Lng, S. and M. McAleer (), Asympoc heory for a vecor ARMA-GARCH model, Economerc Theory, 9, McAleer, M., F. Chan and D. Marnova (7), An economerc analyss of asymmerc volaly: heory and applcaon o paens, Journal of Economercs, 9, McAleer, M., S. Ho and F. Chan (7), Srucure and asympoc heory for mulvarae asymmerc volaly, o appear n Economerc Revews. World Toursm Organzaon (WTO) (6), Toursm hghlghs, 6 Edon, hp:// World Toursm Organzaon (WTO) (7), Srong world oursm growh n 7, hp:// Table. GARCH(,) Esmaes of he Condonal Mean and Uncerany of Monhly Tours Arrvals o he Top Fve Auonomous Communes Vsed n Span Communes θ θ θ θ ω α β Log-Momen nd Momen Andalusa -.E NC Balearc -5.E Islands Canary Islands Caalona NC Madrd NC Table. GJR(,) Esmaes of he Condonal Mean and Uncerany of Monhly Tours Arrvals o he Top Fve Auonomous Communes Vsed n Span Communes θ θ θ θ ω α γ β Log-Momen nd Momen Andalusa Balearc -.E Islands Canary Islands Caalona Madrd -.E Noe: The hree enres correspondng o each parameer are her esmaes, her asympoc -raos, and he Bollerslev and Wooldrdge (99) robus -raos. Table 4. GJR(,) Consan Condonal Correlaons of Monhly Tours Arrvals Shocks o he Top Fve Auonomous Communes Vsed n Span Communes Andalusa Balearc Islands Canary Islands Caalona Madrd Andalusa Balearc Islands Canary Islands.89 - Caalona.9 Madrd 99