A TIME SERIES ANALYSIS OF THE UNCERTAINTY IN INTERNATIONAL TOURIST ARRIVALS TO THE CANARY ISLANDS. Michael McAleer

Transcription

1 Proceedings of he 005 Inernaional Conference on Simulaion and Modelling V. Kachivichyanakul, U. Purinrapiban, and P. Uhayopas, eds. A TIME SERIES ANALYSIS OF THE UNCERTAINTY IN INTERNATIONAL TOURIST ARRIVALS TO THE CANARY ISLANDS Suhejla Hoi School of Economics and Commerce Universiy of Wesern Ausralia Carmelo J. León Deparmen of Applied Economic Analysis Universiy of Las Palmas de Gran Canaria Michael McAleer School of Economics and Commerce Universiy of Wesern Ausralia ABSTRACT Inernaional ourism is an imporan source of service expors o Spain and is regions, paricularly he Canary Islands. Tourism is he major indusry in he Canary Islands, accouning for abou % of GDP. This paper examines he ime series properies of inernaional ourism demand o he Canary Islands colleced by he Naional Airpor Adminisraion (AENA) a airpors from informaion regarding he number of ouris arrivals from abroad. The daa se comprises monhly figures for he Canary Islands from 4 leading ouris source counries, as well as oal ouris arrivals, from 990()-003(). Touris arrivals and he associaed uncerainy of monhly ouris arrivals are esimaed for he 5 daa series. The univariae esimaes sugges ha condiional volailiy (or uncerainy) models provide an accurae measure of uncerainy in monhly inernaional ouris arrivals from he 4 leading source counries, and oal monhly ouris arrivals. The esimaed condiional correlaions indicae wheher here is specializaion, diversificaion or independence in he inernaional ourism demand shocks o he Canary Islands. A he mulivariae level, he condiional correlaions in he monhly ouris arrivals shocks are generally posiive, varying from small negaive o large posiive correlaions. These esimaes sugges ha he shocks from alernaive ouris sources are independen or specialized raher han diversified. Therefore, he Canary Islands should specialize on ouris sources ha provide he larges numbers and growh in ouris arrivals raher han diversify he ourism base.. INTRODUCTION Tourism is a fas growing indusry, aracing invesmen and scarce economic resources in differen counries and desinaions. This process is driven by a growing marke which accommodaes new desinaions and ransformaions in he producs offered by esablished desinaions, boh naionally and inernaionally. In his conex, an undersanding of ourism demand plays an imporan role in decisions regarding he managemen of ouris producs and invesmen decisions ha are necessary o accommodae he growing numbers of ouriss. Tourism demand has radiionally been modelled using a variey of approaches, including srucural equaions and ime series echniques, which have been able o forecas changes in he number of ouriss over ime (see, for example, Marin and Wi (989)). These models usually consider a random erm which incorporaes all he unknown effecs on ourism demand over ime. Unil recenly, he uncerainy in he random (or unpredicable) shocks o ourism demand, which can be modelled as heeroscedasiciy in he shocks, had no been of major concern o ourism researchers. I is well known ha he presence of heeroscedasiciy can yield imprecise esimaes of ourism demand, hereby reducing he forecasing performance of he models. However, i is only recenly ha ime-varying models of heeroscedasiciy have been applied o ourism research (see Chan, Lim and McAleer (004)). Volailiy (or uncerainy) refers o he changes in he variabiliy of shocks o ourism demand over ime, and is defined as he squared deviaion of each observaion from he respecive sample mean ouris arrivals or deseasonalized ouris arrivals. As a resul of many facors ha can affec he ourism marke, i is clear ha shocks o ourism demand may no have he same variabiliy over ime. In he case of ourism, uncerainy may be presen due o various unexpeced facors which can affec consumer decisions, such as changes in disposable income and wealh, adverising

2 campaigns, and random evens. Moreover, he uncerainy could also vary across differen desinaions and sources. For a single desinaion, changes in ourism demand could indicae uncerainy according o he various ourism sources, while a given ourism source may have uncerainy in ouris demand according o a wide range of possible ouris desinaions. In his paper we esimae univariae and mulivariae (or sysems) models of inernaional ouris arrivals and uncerainy from a se of ourism sources for a paricular ouris desinaion, he Canary Islands, Spain. Annual inernaional ouris arrivals o he Canary Islands range from a minimum of 3.5 million o a maximum of.4 million over he sample period, namely January 990 o December 003. Tourism is he major indusry in he Canary Islands, accouning for abou % of GDP. This indusry has grown rapidly over he las hiry years, wih an average growh rae of 5.4% beween 990 and 00. However, in he las few years, he rae of ourism growh has declined slighly as a resul of sauraion effecs and he economic slowdown in he world economy. The esimaed correlaion coefficiens from he mulivariae models of uncerainy provide useful informaion regarding he specializaion, diversificaion or independence in he inernaional ourism demand shocks o he Canary Islands. Variaions in he degree of uncerainy across ouris source markes need o be appreciaed in order o make opimal managemen and markeing decisions regarding paricular markes. In addiion, models of uncerainy permi a disincion o be made beween he shor and long run persisence of shocks o ourism demand, which provide useful informaion regarding he effecs of shocks on uncerainy. Shocks in one marke can affec ourism demand in oher markes differenly, depending on he degree of correlaion in uncerainy across markes. The inerrelaionship of he shor and long run effecs of shocks o uncerainy, and he correlaion coefficiens across differen source markes, permi a classificaion of markes according o uncerainy. Wih regard o he esimaed correlaions in he uncerainy of ouris arrivals shocks, ouris source counries wih a high posiive correlaion are specialized markes, in which case he Canary Islands should concenrae on hose ourism sources which provide he larges numbers and growh in ouris arrivals. On he oher hand, ouris source counries wih a high negaive correlaion are diversified markes, in which case he Canary Islands should concenrae on diversifying he ourism base. Correlaions in ouris arrivals shocks ha are close o zero indicae independen markes, so ha neiher specializaion nor diversificaion in ourism source markes would be required. Such issues based on models of uncerainy have no previously been considered in he ourism demand lieraure. The plan of he paper is as follows. Secion describes he daa sources for he empirical analysis, and discusses he salien feaures of he monhly inernaional ouris arrivals daa for he Canary Islands from 4 leading ouris source counries, as well as oal ouris arrivals. Seasonaliy in he ouris arrivals daa from he various counry sources, as well as oal ouris arrivals, is also discussed. Univariae and mulivariae models of uncerainy for monhly ouris arrivals are presened in Secion 3. The empirical resuls for he models of uncerainy are analysed in Secion 4. Some concluding commens are given in Secion 5.. DATA SOURCE AND DESCRIPTION The Canary Islands accoun for abou 0% of oal ourism in Spain, wih a larger proporion in he winer season as compared wih he summer season. The effec of seasonaliy varies significanly across he ourism source counries, showing he larges paerns for he Scandinavian counries. In paricular, ouris arrivals from he Scandinavian counries o he Canary Islands drop dramaically during he period from May hrough o Sepember, which includes he European summer. Seasonaliy for he oal number of ouriss is invered wih respec o ourism demand in he res of Spain, wih he srong season for he Canary Islands being mid-november o mid-march. During his ime of he year, he Canary Islands sill enjoy pleasan weaher. Moreover, he ravel ime o he Canary Islands from virually any European ourism source counry is relaively shor. During he summer season, he Canary Islands compee in similar condiions wih oher leading ouris desinaions, such as hose in he Medierranean. This paper examines he ime series properies of inernaional ourism demand o he Canary Islands colleced by he Naional Airpor Adminisraion (AENA) a airpors from informaion regarding he number of ouris arrivals from abroad. The daa se comprises monhly figures for differen islands in he Canary Islands from 4 leading inernaional ouris source counries, as well as oal ouris arrivals, for he period 990()-003(), hereby giving 5 separae daa series. Seven descripive saisics, namely mean, maximum, minimum, sandard deviaion (SD), coefficien of variaion (CoV), skewness and kurosis have been calculaed. While SD is frequenly regarded as an adequae indicaor of variabiliy, he CoV enables a comparison beween SD associaed wih differen means. The mean ouris arrivals vary subsanially across he 4 counries, ranging from,334 from

3 Ausria o 4,739 from UK. Of he 4 leading inernaional ouris source counries, Ausria, Belgium, Denmark, Finland, France, Ireland, Ialy, Norway, Oher and Swizerland have means ha are less han 0,000, while Holland and Sweden have means of 3,343 and 30,574, respecively. The means of German and UK monhly ouris arrivals, which are he wo major ouris source counries for he Canary Islands, are boh well above 00,000 ouriss. Excluding oal ouris arrivals, monhly ouris arrival figures from he 4 source counries vary from 0 for Finland and Norway o 389,803 for UK. Alhough SD has a wide range from,88 o 66,757, his primarily reflecs differences in mean monhly ouris arrivals. In comparison, CoV does no vary as subsanially across he 5 source counries, wih he lowes CoV being observed for Germany a 0.0 and he highes for Finland a Apar from monhly ouris arrivals from Germany, UK and Toal, ouris arrivals o he Canary Islands are all posiively skewed, wih he kurosis ranging from.690 for Finland o for Oher. The descripive saisics for he volailiy (or uncerainy) in monhly inernaional ouris arrivals show ha he 5 means vary subsanially across counries, ranging from 8,54,44 for Ausria o 5,40,000,000 for UK. Apar from he uncerainy associaed wih oal ouris arrivals, he wo highes uncerainy means are for Germany and UK. Overall, he uncerainy associaed wih ouris arrivals from he 4 source counries vary from a minimum of 9 for Belgium o a maximum of,00,000,000 for UK. While he SD for all 5 ouris uncerainy has a wide range from,93,093 o 5,480,000,000, CoV does no vary subsanially across he ourism source counries. The lowes CoV is observed for Finland a 0.83 and he highes is observed for Oher a.888. There is posiive skewness for he 4 counries and oal, wih he kurosis ranging from 3.78 for Norway o for France. Descripive saisics are also calculaed for he uncerainy in deseasonalised monhly ouris arrivals. The 5 uncerainy means vary subsanially across all counries, ranging from 6,79,53 for Ausria o 5,0,000,000 for UK, wih Germany and he UK having he wo highes uncerainy means of he 4 source counries. Excluding he uncerainy in oal ouris arrivals, he uncerainy associaed wih ouris arrivals from he 4 source counries varies from a minimum of for Holland o 0,00,000,000 for UK. In erms of variabiliy, SD for all 5 ouris uncerainy ranges from 0,037,994 for Ausria o 3,400,000,000 for Toal, while CoV varies from 0.90 for UK o.0 for Finland. There is posiive skewness for all 4 counries and oal, wih he kurosis ranging from.33 for UK o.47 for Oher. Finally, descripive saisics are also obained for he proporions of monhly ouris arrivals relaive o monhly oal ouris arrivals for he 4 counry sources. UK and Germany joinly accoun for almos 68% of he oal inernaional ouris arrivals o he Canary Islands, wih means of % and 3.79%, respecively. The mean proporions of he remaining leading inernaional ouris arrival counries are subsanially lower han for UK and Germany. Moreover, he proporions vary only slighly, ranging from.77% for Ausria o 4.737% for Holland. Overall, he ouris proporion figures for he 4 source counries vary from a minimum of 0% for Finland and Norway o a maximum of % for UK. Alhough SD has a range of o 6.484, CoV is generally low and does no vary subsanially across he 4 ourism sources and he oal. The lowes CoV is observed for Germany a and he highes is observed for Finland a.090. Apar from he ouris proporions for UK and Germany, he ouris proporions o he Canary Islands are posiively skewed, wih he kurosis ranging from.536 for Sweden) o 6.74 for Belgium. Inernaional monhly ouris arrivals, he uncerainy associaed wih monhly ouris arrivals and deseasonalised monhly ouris arrivals, and he proporions of ouris arrivals o he Canary Islands, for he 4 leading source counries and oal, are also available. There is significan seasonal variaion in he monhly inernaional ouris arrivals for all 4 leading source counries and oal ouris arrivals. The paerns in uncerainy are reasonably similar for nine of he ouris sources, and significanly differen for six sources, namely Denmark, Finland, Germany, Norway, Oher and Sweden. This makes i clear ha he four Scandinavian counries have disincive seasonal paerns, which disinguishes hem from mos of he oher leading ourism sources for he Canary Islands. There is also disincive seasonaliy in he proporions of he monhly ouris arrivals for all 4 leading source counries. 3. MODELS OF UNCERTAINTY FOR TOURIST ARRIVALS The purpose of his secion is o model he level and uncerainy in monhly inernaional ouris arrivals from he 4 leading source counries, as well as oal monhly inernaional ouris arrivals, o he Canary Islands. The specificaion and properies of he Consan Condiional Correlaion (CCC) GARCH model of Bollerslev (990), which will be used o esimae he correlaions beween all pairs of ouris arrivals shocks, will be discussed briefly. Consider he following specificaion: ( ) y = E y F + ε ε = Dη, ()

4 ,..., ' = m measures he ouris arrivals from he 4 leading source counries and oal ouris arrivals, η (,..., ) ' = η ηm is a sequence of independenly and idenically disribued (iid) random vecors ha is obained from sandardizing he ouris arrivals shocks, ε, using he / / sandardizaion D = diag( h,..., hm ), F is he pas informaion available o ime, m (=5) is he number of ourism source counries, including oal ouris arrivals, and =,,68 monhly observaions for he period 990() o 003(). where y ( y y ) The CCC model assumes he uncerainy in ouris arrivals shocks from source i, h i, i =,,m, follows a univariae GARCH process, ha is, r h = ω + α ε + β h i i i, j i, j j= j= s () where α represens he ARCH effecs, or he shorrun persisence of shocks o ouris source i, and β represens he GARCH effecs, or he conribuion of shocks o ouris source i o long-run persisence. Alhough he CCC specificaion in () has a compuaional advanage over oher mulivariae GARCH models wih consan condiional correlaions, such as he Vecor Auoregressive Moving Average GARCH (VARMA-GARCH) model of Ling and McAleer (003) and VARMA Asymmeric GARCH (VARMA-AGARCH) model of Chan, Hoi and McAleer (00), i assumes independence of uncerainy across ourism sources, and hence no spillovers in uncerainy across differen ourism sources, and does no accommodae he asymmeric effecs on uncerainy of posiive and negaive shocks. I is imporan o noe ha he condiional correlaion marix for he CCC model, Γ, is assumed o be consan, wih he ypical elemen of Γ being given by ρ = ρ for i, j =,,m. When he correlaion ji coefficien of ourism arrivals shocks, ρ, is close o +, he Canary Islands should specialize on ouris sources ha provide he larges numbers and growh in ouris arrivals. However, when he correlaion coefficien of ourism arrivals shocks, ρ, is close o -, he Canary Islands should concenrae on diversifying he ourism base raher han concenraing on sources wih he larges numbers and growh in ouris arrivals. Independen ourism sources are hose pairs of counries wih a correlaion coefficien, ρ, close o zero, in which case neiher specializaion nor diversificaion in ourism source markes would be required for opimal managemen of ourism arrivals. When he number of ourism source counries is se o m =, such ha a univariae model is specified raher han a mulivariae model, equaions ()-() become: ε = η h h r s = ω+ α jε j + β j h j, (3) j= j= and ω > 0, α 0 for j =,,r and β 0 for j = j,,s are sufficien regulariy condiions o ensure ha uncerainy is defined sensibly, namely h > 0. The decomposiion in (3) permis he uncerainy in he ouris arrivals shocks, ε o be modelled by, on, he basis of hisorical daa. Using resuls from Nelson (990), Ling and Li (997) and Ling and McAleer (00a, 00b), he necessary and sufficien regulariy condiion for he exisence of he second momen of ouris arrivals shocks, ε, for he case r = s = is given by α + β <. This resul ensures ha he esimaes are saisically adequae, so ha a sensible empirical analysis can be conduced. Equaion (3) assumes ha a posiive shock ( ε > 0 ) o monhly ouris arrivals has he same impac on uncerainy, h, as a negaive ouris arrivals shock ( ε < 0 ), bu his assumpion is ypically violaed in pracice. In order o accommodae he possible differenial impac on uncerainy from posiive and negaive ouris arrivals shocks, Glosen, Jagannahan and Runkle (99) proposed he following specificaion for h : h r s ( I( )) h (4) = ω+ α + γ ε ε + β j j j j j j j= j= When r = s =, ω > 0, α 0, α + γ 0 and β 0 are sufficien condiions o ensure ha uncerainy is posiive, namely h > 0. The shor-run persisence of posiive (negaive) monhly ouris arrivals shocks is given by α ( α + γ). Under he assumpion ha he sandardized shocks, η, follow a symmeric disribuion, he average shor-run persisence of ouris arrivals shocks is α + γ, and he conribuion of ouris arrivals shocks o average long-run persisence is α + γ +β. Ling and McAleer (00a) showed ha he necessary and sufficien regulariy condiion for he second momen of ouris arrivals shocks o be finie, and hence for sensible saisical analysis, is α + γ + β <. The parameers in equaions (), (3) and (4) are ypically obained by Maximum Likelihood Esimaion (MLE) using a join normal densiy for he sandardized j h

5 ouris arrivals shocks, η, afer uncerainy has been modelled. When η does no follow a join mulivariae normal disribuion, he parameers are esimaed by Quasi-MLE (QMLE). The condiional log-likelihood funcion is given as follows: ε n n l = log h + = = h. Ling and McAleer (003) showed ha he QMLE for GARCH(r,s) is consisen if he second momen regulariy condiion is finie. Jeanheau (998) showed ha he log-momen regulariy condiion given by E ( log ( αη + β) ) < 0 (5) is sufficien for he QMLE o be consisen for he GARCH(,) model of uncerainy, while Boussama (000) showed ha he QMLE is asympoically normal for GARCH(,) under he same condiion. I is imporan o noe ha (5) is a weaker regulariy condiion han he second momen condiion, namely α + β <. However, he log-momen condiion is more difficul o compue in pracice as i is he expeced value of a funcion of an unknown random variable and unknown parameers. McAleer, Chan and Marinova (00) esablished he log-momen regulariy condiion for he GJR(,) model of uncerainy, namely ( (( α γ I( η )) ) η β E log + + ) < 0, (6) and showed ha i is sufficien for he consisency and asympoic normaliy of he QMLE for GJR(,). Moreover, he second momen regulariy condiion, namely α + γ + β <, is also sufficien for consisency and asympoic normaliy of he QMLE for GJR(,). In empirical examples, he parameers in he regulariy condiions (5) and (6) are replaced by heir respecive QMLE, he sandardized residuals, η, are replaced by he esimaed residuals from he GARCH and GJR models of uncerainy, respecively, for =,,n, and he expeced values in (5) and (6) are replaced by heir respecive sample means. 4. EMPIRICAL RESULTS Using he monhly daa on inernaional ouris arrivals, univariae and mulivariae uncerainy models are esimaed for 4 ourism source counries, as well as oal ouris arrivals, for he period 990()-003(). There is a disinc seasonal paern in each ouris arrivals series. Alhough here are several alernaive mehods for modelling seasonaliy, welve seasonal dummy variables are included for simpliciy in he respecive ouris arrivals models of monhly inernaional ouris arrivals from source i =,,5,, as follows: TA i i j = TA i = φ D + ε, where D = in monh j =,..,, and D = 0 elsewhere. In addiion o esimaing he ouris arrivals for each source counry, he univariae ARCH(), ARCH(), GARCH(,) and GJR(,) models of uncerainy are used o esimae he uncerainy associaed wih he 4 leading ourism source counries and oal ouris arrivals. As he esimaed GARCH(,) model was always found o be preferable o he ARCH() and ARCH() models, and also generally superior o he asymmeric GJR(,) model, in wha follows he empirical resuls will be discussed only for he GARCH(,) model of uncerainy. On he basis of he univariae esimaes of he sandardized ouris arrivals shocks, he CCC model is used o esimae he correlaion coefficiens of he monhly inernaional ouris arrivals shocks beween all pairs of ourism source counries. This can provide useful informaion on various source markes in erms of he inernaional ourism arrivals shocks o deermine if he Canary Islands should specialize on ouris sources ha provide he larges numbers and growh in ouris arrivals or diversify he ourism base. All he esimaes in his paper are obained using he Bernd, Hall, Hall and Hausman (BHHH) (974) algorihm in he EViews 4 economeric sofware package. Virually idenical esimaes are obained from using he RATS 6 economeric sofware package. Several differen ses of iniial values have been used in each case, bu do no lead o subsanial differences in he esimaes. 4. Univariae Models of Uncerainy Esimaes of he parameers of he ouris arrivals and uncerainy for he univariae GARCH(,) model are presened in Tables and, respecively. The ouris arrivals esimaes for GARCH(,) in Table vary across he 4 ourism source counries, as well as oal ouris arrivals. There is highly significan seasonaliy in ouris arrivals for each counry and each monh, excep for Finland for he monhs of May-Sepember inclusive. Alhough no repored here, he univariae esimaes of uncerainy generally sugges ha here is lile

6 asymmery, such ha posiive and negaive monhly inernaional ouris arrivals shocks have similar effecs on he uncerainy in ourism arrivals. Table repors he GARCH(,) esimaes of he uncerainy in ouris arrivals by he 4 leading ourism source counries, as well as oal ouris arrivals. Boh he asympoic and Bollerslev-Wooldridge (99) robus -raios are repored o enable valid saisical inference. In general, he robus -raios are smaller in absolue value han heir asympoic counerpars. The persisence of shocks o he uncerainy in monhly ouris arrivals shocks is an imporan aspec of modelling volailiy. Toal ouris arrivals, as well as ouris arrivals from UK, Ireland and Sweden, have only shor run persisence in ouris arrivals shocks, ha is, for abou one monh. On he oher hand, Germany has only long run persisence in ouris arrivals shocks raher han shor run persisence, which means ha he ouris arrivals shocks from Germany do no have an immediae impac bu end o accumulae over several monhs. Regarding he regulariy condiions of he GARCH(,) model, boh he log-momen and second momen condiions are saisfied for Ausria, Belgium, France, Germany, Ialy and Swizerland. Alhough he log-momen condiion could no be calculaed for Finland, Norway and Sweden, he second momen condiion is saisfied, so ha he QMLE are consisen and asympoically normal. Such resuls sugges ha he empirical esimaes are saisically valid for hese ourism source counries. Three ineresing resuls are found for Holland, Ireland and oal ouris arrivals, in which he second momen regulariy condiion is no saisfied bu he log-momen condiion is saisfied, so ha he QMLE are consisen and asympoically normal. Only hree ses of regulariy condiions are no saisfied, namely Denmark, Oher and UK, in which he log-momen regulariy condiion could no be calculaed and he second momen condiion was no saisfied. Overall, hese univariae resuls sugges ha, in general, he GARCH(,) model provides an accurae measure of he uncerainy in inernaional monhly ouris arrivals shocks for he 4 leading source counries, as well as oal ouris arrivals, o he Canary Islands. 4. Mulivariae Models of Uncerainy Esimaes of he consan condiional correlaion coefficiens for monhly inernaional ouris arrivals shocks by source counry, and oal ouris arrivals, are given in Table 3. These correlaion correlaions are calculaed using he esimaed ouris arrivals shocks afer modeling uncerainy for he 4 leading ourism source counries as well as oal inernaional ouris arrivals. In Table 3, here are a number of high correlaion coefficiens in he ouris arrivals shocks, especially beween oal monhly ouris arrivals and some leading ourism source counries. Of he 4 condiional correlaions wih oal ouris arrivals, of which wo are negaive, he range is from -0.9 o The highes correlaion coefficiens for oal ouris arrivals are wih UK, Norway, Ireland, Sweden, Belgium, Denmark, Holland and Germany. Wih he excepion of Finland, he Scandinavian counries have highly correlaed ouris arrivals shocks wih oal ouris arrivals. I is surprising ha Germany, which is he second mos imporan source of ouris arrivals o he Canary Islands, has he eighh highes correlaion coefficien in he ouris arrivals shocks wih oal ouris arrivals a These resuls sugges ha, in general, he shocks from alernaive ouris sources are independen or specialized raher han diversified. Of he 9 possible pairs of correlaion coefficiens beween he 4 leading ouris source counries, of which 7 are posiive, he en highes condiional correlaions in he sandardized shocks hold beween he following pairs of counries: (Norway, Sweden), (Denmark, Sweden), (Denmark, Norway), (Norway, UK), (Belgium, UK), (Ireland, UK), (Sweden, UK), (Belgium, Germany), (Ireland, Norway) and (Belgium, Norway), wih he highes being 0.78 and he lowes being The correlaion coefficiens vary from a low of o a high of The UK and hree of he four Scandinavian counries have high correlaion coefficiens in he ouris arrivals shocks, wih Belgium, Ireland and Germany also having some high correlaion coefficiens. This suggess ha hese ourism sources are similar, and hence specialized, in erms of ouris arrivals shocks. On he oher hand, Ialy and Finland have very low condiional correlaions in he ouris arrivals shocks wih all counries, which sugges ha hese wo counries have independen shocks. 5. CONCLUSION Inernaional ourism is an imporan source of service expors o Spain and is regions, paricularly he Canary Islands. Tourism is he major indusry in he Canary Islands, accouning for abou % of GDP. This paper examined he ime series properies of inernaional monhly ouris arrivals o he Canary Islands colleced by he Naional Airpor Adminisraion (AENA) a airpors from informaion regarding he number of ouris arrivals from abroad. The daa se comprised monhly figures for he Canary Islands from 4 leading ouris source counries, as well as oal ouris arrivals, from 990()-003(). Touris arrivals and he associaed uncerainy of monhly ouris arrivals are esimaed for he 4 source counries, as well as oal ouris arrivals, for he 5 daa series.

7 The univariae esimaes suggesed ha he GARCH(,) condiional volailiy model provides an accurae measure of uncerainy in monhly inernaional ouris arrivals from he 4 leading source counries, and oal monhly ouris arrivals. The esimaed condiional correlaion coefficiens indicaed wheher here is specializaion, diversificaion or independence in he inernaional ourism demand shocks o he Canary Islands. A he mulivariae level, he condiional correlaions in he monhly ouris arrivals shocks were generally posiive, varying from small negaive o large posiive correlaions. These esimaes suggesed ha he shocks from alernaive ouris sources are independen or specialized raher han diversified. Therefore, he Canary Islands should specialize on ouris sources ha provide he larges numbers and growh in ouris arrivals raher han diversify he ourism base. AKNOWLEDGEMENTS The auhors wish o hank Andreu Sansó for helpful commens and suggesions. The firs and hird auhors wish o acknowledge he Ausralian Research Council for financial suppor. REFERENCES Bernd, E.K., B.H. Hall, R.E. Hall and J.A. Hausman (974), Esimaion and inference in nonlinear srucural models, Annals of Economic and Social Measuremen, 3, Bollerslev, T. (986), Generalised auoregressive condiional heeroscedasiciy, Journal of Economerics, 3, Bollerslev, T. (990), Modelling he coherence in shor-run nominal exchange raes: A mulivariae generalized ARCH approach, Review of Economics and Saisics, 7, Boussama, F. (000), Asympoic normaliy for he quasi-maximum likelihood esimaor of a GARCH model, Compes Rendus de l Academie des Sciences, Serie I, 33, 8-84 (in French). Chan, F., S. Hoi and M. McAleer (00), Srucure and asympoic heory for mulivariae asymmeric volailiy: Empirical evidence for counry risk raings, paper presened o he 00 Ausralasian Meeing of he Economeric Sociey, Brisbane, Ausralia, July 00. Chan, F., C. Lim and M. McAleer (004), Modelling mulivariae inernaional ourism demand and volailiy, o appear in Tourism Managemen. Engle, R.F. (98), Auoregressive condiional heeroscedasiciy wih esimaes of he variance of Unied Kingdom inflaion, Economerica, 50, Glosen L., R. Jagannahan and D. Runkle (99), On he relaion beween he expeced value and volailiy of nominal excess reurn on sock, Journal of Finance, 46, Jeanheau, T. (998), Srong consisency of esimaors for mulivariae ARCH models, Economeric Theory, 4, Ling, S. and W.K. Li (997), On fracionally inegraed auoregressive moving-average models wih condiional heeroskedasiciy, Journal of he American Saisical Associaion, 9, Ling, S. and M. McAleer (00a), Saionariy and he exisence of momens of a family of GARCH processes, Journal of Economerics, 06, Ling, S. and M. McAleer (00b), Necessary and sufficien momen condiions for he GARCH(r,s) and asymmeric power GARCH(r,s) models, Economeric Theory, 8, Ling, S. and M. McAleer (003), Asympoic heory for a vecor ARMA-GARCH model, Economeric Theory, 9, Marin, C.A. and S.F. Wi (989), Forecasing ourism demand: A comparison of he accuracy of several quaniaive mehods, Inernaional Journal of Forecasing, 5, 7-9. McAleer, M., F. Chan and D. Marinova (00), An economeric analysis of asymmeric volailiy: Theory and applicaion o paens, paper presened o he Ausralasian meeing of he Economeric Sociey, Brisbane, Ausralia, July 00, o appear in Journal of Economerics. Nelson, D.B. (990), Saionariy and persisence in he GARCH(,) model, Economeric Theory, 6, AUTHORS BIOGRAPHIES SUHEJLA HOTI is an ARC Research Fellow in he School of Economics and Commerce, Universiy of Wesern Ausralia. Her research ineress are in macroeconomics, counry risk, environmenal risk, environmenal modelling, finance, financial economerics, ime series analysis, and ourism research. CARMELO J. LEÓN is Professor of Environmenal and Tourism Economics and UNESCO Chair on Tourism Planning and Susainable Developmen a he Universiy of Las Palmas de Gran Canaria, Spain. His research ineress are in applied economics, environmenal modelling, susainable developmen, applied ime series analysis and ourism research. MICHAEL MCALEER is Professor of Economics (Economerics) in he School of Economics and Commerce, Universiy of Wesern Ausralia. His research ineress are in economerics, financial economerics, finance, saisics, ime series analysis, inellecual propery, inegraed environmenal sysems, environmenal risk, and ourism research.

8 Table : Esimaes of Monhly Touris Arrivals Models Counry δ δ δ 3 δ 4 δ 5 δ 6 δ 7 δ 8 δ 9 δ 0 δ δ Ausria Belgium Denmark Finland France Germany Holland Ireland Ialy Norway Oher Sweden Swizerland UK Toal

9 Table : GARCH(,) Esimaes of Uncerainy Counry ω α β Log-Momen nd Momen Ausria Belgium Denmark N.C Finland N.C France Germany Holland Ireland Ialy Norway N.C Oher N.C Sweden N.C Swizerland UK N.C Toal Noe: The hree enries corresponding o each parameer are heir esimaes, heir asympoic -raios, and he Bollerslev and Wooldridge (99) robus -raios. Table 3: Consan Condiional Correlaions of Touris Arrivals Shocks Counry Ausria Belgium Denmark Finland France Germany Holland Ireland Ialy Norway Oher Sweden Swizerland UK Toal Ausria Belgium Denmark Finland France Germany Holland Ireland Ialy Norway Oher Sweden Swizerland UK Toal.000