Modelling the Volatility in Short and Long Haul Japanese Tourist Arrivals to New Zealand and Taiwan*

Transcription

1 Modelling he Volailiy in Shor and Long Haul Japanese Touris Arrivals o New Zealand and Taiwan* Chia-Lin Chang** Deparmen of Applied Economics Deparmen of Finance Naional Chung Hsing Universiy Taichung, Taiwan Michael McAleer Economeric Insiue Erasmus School of Economics Erasmus Universiy Roerdam and Tinbergen Insiue The Neherlands and Insiue of Economic Research Kyoo Universiy and Deparmen of Quaniaive Economics Compluense Universiy of Madrid Chrisine Lim Division of Markeing and Inernaional Business Nanyang Technological Universiy Singapore EI Revised: July 2011 * For financial suppor, he firs auhor acknowledges he Naional Science Council, Taiwan, and he second auhor acknowledges he Ausralian Research Council, Naional Science Council, Taiwan, and he Japan Sociey for he Promoion of Science.. ** Corresponding auhor: Chia-Lin Chang, Deparmen of Applied Economics, Naional Chung Hsing Universiy, Taichung, 250 Kuo Kuang Road, Naional Chung Hsing Universiy Taichung 402, Taiwan. changchialin@nchu.edu.w. 1

2 Absrac This paper esimaes he effecs of shor and long haul volailiy (or risk) in monhly Japanese ouris arrivals o Taiwan and New Zealand, respecively. In order o model appropriaely he volailiies of inernaional ouris arrivals, we use symmeric and asymmeric condiional volailiy models ha are commonly used in financial economerics, namely he GARCH (1,1), GJR (1,1) and EGARCH (1,1) models. The daa series are for he period January 1997 o December The volailiy esimaes for he monhly growh in Japanese ouriss o New Zealand and Taiwan are differen, and indicae ha he former has an asymmeric effec on risk from posiive and negaive shocks of equal magniude, while he laer has no asymmeric effec. Moreover, here is a leverage effec in he monhly growh rae of Japanese ouriss o New Zealand, whereby negaive shocks increase volailiy bu posiive shocks of similar magniude decrease volailiy. These empirical resuls seem o be similar o a wide range of financial sock marke prices, so ha he models used in financial economics, and hence he issues relaed o risk and leverage effecs, are also applicable o inernaional ourism flows. Keywords: Touris arrivals, long haul, shor haul, risk, condiional volailiy, asymmeric effec, leverage. JEL Classificaions: C22, G32, L83. 2

3 1. Inroducion As a ourism source, Japan is a significan supplier of ouriss o many counries, including New Zealand and Taiwan. Japan is New Zealand s larges Asian ouris source marke. Touris arrivals from Japan had been increasing by abou 15% per annum from 1980 o Afer 1996, New Zealand sared o experience a decline in he Japanese marke when he annual growh rae dramaically decreased by 2.4%, on average. Various evens have conribued o he sharp decline in he Japanese marke. They include he 1997/1998 Asian economic and financial crises, a coninuing economic slowdown in he Japanese economy since he mid-1990s, SARS and he appreciaion of he New Zealand dollar (Lim e al, 2007). Modelling of volailiy has been underaken by many applied economiss and policy analyss. If he volailiy of inernaional ourism arrivals and/or growh behave like hose in financial markes, here will be a risk inerpreaion for inernaional ourism flows along he lines of financial asses, namely ha he variaions in inernaional ouris arrivals are essenially equivalen o he prices of financial asses if he rae of growh in ourism spending is consan. Hence, an analysis of he volailiy associaed wih inernaional ouris arrivals is imporan for ourism managemen and informed policy decision-making. In his paper, we will examine he shor and long haul volailiy (or risk) in Japanese oubound ourism o Taiwan and New Zealand, respecively. According o he inernaional visior surveys conduced in 2005, mos Japanese visiors o New Zealand were package ravellers, and very few were repea ouriss. As a long haul desinaion, New Zealand is a popular desinaion for older Japanese ouriss, wih 37% of all visiors aged 55 years and above. The surveys also indicaed ha shopping and eaing ou were he mos popular aciviies engaged in by Japanese ouriss (Tourism New Zealand 2006). Auckland (in he Norh Island), followed by Canerbury and Queensown (in he Souh Island), were he mos popular regions in New Zealand for Japanese ouriss. No surprisingly, hoels were he dominan ype of accommodaion used by hese visiors. 3

4 On he oher hand, as a shor haul ouris desinaion, Japan is Taiwan s larges Asian ouris source marke, which accouned for over 30% of all inernaional ouriss in Taiwan, and has increased by more han 4% annually beween 1981 and 2005 (Taiwan Tourism Bureau, 2006). Taiwan was a colony of Japan from 1895 o 1945, prior o he Kuominang Pary's fligh o Taiwan from China o exercise is sovereigny (see, for example, Lim e al. (2007)). During ha ime, only he Japanese language and educaion were allowed o be spoken and learned by he island residens. Thus, Taiwan s lifesyle has been heavily influenced by he Japanese culure. I is sriking ha Taiwanese and Japanese enjoy similar leisure aciviies, such as shopping, dining, and soaking in ho springs all year round. Japanese ouris arrivals o Taiwan, on average, are 12 imes larger han o New Zealand from 1980 o 1996, and more han 6 imes he number from 1996 o The annual growh rae of Japanese ouriss o New Zealand during he period 1996 o 2007 was around 3.7%. According o a survey conduced by he Taiwan Tourism Bureau (2006), abou 50% of Japanese ravelled o Taiwan for pleasure, followed by business (30%), and visiing relaives and friends (3%). On average, he duraion of say among Japanese shor-erm ouriss was 5 days, compared wih 7 days on average for all shor-erm visior arrivals. The survey found ha Tienhsiang, Taroko Gorge (locaed on he easern side of Taiwan) and he nigh markes in Taipei were he major scenic spos for Japanese ouriss. Addiionally, cuisine and hisorical relics were he major aracions for mos Japanese ouriss. Using monhly daa, Lim e al. (2008) examine he dynamic relaionship beween ravel demand and real income in Japan, using linear and nonlinear models, o disinguish beween inernaional ravel demand o Taiwan and New Zealand, which are wo imporan shor and long haul markes for Japan, respecively. Their empirical resuls show ha New Zealand has a higher income elasiciy of demand han does 4

5 Taiwan. An exension of heir analysis is o model he shor and long haul volailiy of Japanese ouris arrivals o Taiwan and New Zealand, respecively. The analysis of volailiy is sill relaively new o ourism research, wih few sudies o dae having analysed inernaional ourism demand volailiy (see, for example, Chan e al. (2005), and Shareef and McAleer (2007, 2008)). Since volailiy is no consan, and hence needs o be modelled, i is necessary o use daily or monhly daa o esimae ime-varying volailiy. Monhly daa were used in pas sudies which examined he volailiy in inernaional ouris arrivals o Ausralia, Maldives and Seychelles. These sudies examined beween four and eigh major source markes, which comprised shor and long haul ravel from Oceania, Asia, Europe and he USA. The purpose of he paper is o model he shor and long haul volailiy (or risk) in Japanese ouris arrivals o Taiwan and New Zealand, respecively, from January 1997 o December The remainder of he paper is organized as follows. Secion 2 presens he daa for monhly Japanese ouris arrivals o New Zealand and Taiwan and discusses ime varying volailiy. Secion 3 performs uni roo ess on he levels, logarihms and growh raes of monhly ouris arrivals. Secion 4 discusses he economeric mehodology, which presens symmeric and asymmeric condiional volailiy models for ouris arrivals. The empirical resuls are discussed in Secion 5. Finally, some concluding remarks are given in Secion Daa The daa se comprises monhly Japanese ouris arrivals o New Zealand and Taiwan from January 1997 o December 2007, giving a oal of 348 observaions for each daa. The daa were obained from he New Zealand Deparmen of Saisics and he Taiwan Tourism Bureau. Figures 1 and 2 show he rends and volailiy in monhly Japanese ouris arrivals (TA) o New Zealand and Taiwan, respecively. Figures 3 and 4 plo he logarihm of monhly Japanese ouris arrivals, L(TA), o New Zealand and o Taiwan, respecively. 5

6 Figures 5 and 6 plo he log difference (or growh rae) of monhly Japanese ouris arrivals, DL(TA), o New Zealand and Taiwan, respecively. Volailiy is defined as he squared deviaion of TA from he sample mean. As shown in Figures 1 and 3, monhly Japanese ouris arrivals, as well as he log monhly Japanese ouris arrivals series, show a significan increase before he period 1997, level off during he period 1997 o 2003, and hen decrease afer On he oher hand, as shown in Figures 2 and 4, monhly Taiwanese ouris arrivals, as well as he log monhly Taiwanese ouris arrivals series, show a sligh increase, wih an oulier in around 2003 because of SARS. In his case, he wo ouliers from Japan o Taiwan are omied from he sample. Furhermore, he series from boh ourism sources in levels and logarihms migh be saionary or non-saionary, bu he log difference series is clearly saionary. As shown in Figures 5 and 6, here is clear volailiy clusering in monhly Japanese ouris arrivals o New Zealand and Taiwan for he log difference series. However, he volailiy would seem o be greaer for Japanese ourism o New Zealand han o Taiwan. Alhough i appears from he figures ha boh levels and logarihms are non-saionary, here is he possibiliy of obaining apparenly significan regression resuls from apparenly unrelaed daa when non-saionary series are used in regression analysis. In he nex secion, we will show ha he daa are non-saionary by using formal uni roo ess of he series in levels, logarihms and log differences (or growh raes) in he respecive series before modelling he ime-varying volailiy. Finally, ime series observed a monhly frequencies ofen exhibi seasonaliy. Lim and McAleer (2001) highlighed seasonaliy in ourism ime series daa. In order o exrac he underlying rend componen of he ime series, he muliplicaive moving average mehod echnique was used o remove seasonal movemens in he daa of Japanese ouris arrivals. 6

7 Table 1 gives he summary saisics for Japanese ouris arrivals o New Zealand and Taiwan from January 1997 o December As described above, wo ouliers arising from SARS in he daa from Japan o Taiwan are omied from he sample. Finally, we have a oal of 348 observaions from Japan o New Zealand and 346 observaions from Japan o Taiwan. 3. Uni Roo Tess I is well known ha radiional uni roo ess, primarily hose based on he classic mehods of Dickey and Fuller (1979, 1981), suffer from low power and size disorions. However, hese shorcomings have been overcome by modificaions o he esing procedures, such as he mehods proposed by Perron and Ng (1996), Ellio, Rohenberg and Sock (1996), and Ng and Perron (2001). The ADF uni roo es, ADF GLS, was applied o he ime series of monhly Japanese ouris arrivals o New Zealand and Taiwan. In essence, ADF GL es uses he modified Akaike informaion crierion (MAIC) o selec he opimal runcaion lag. The asympoic criical values for he ADF ess are given in Dickey and Fuller (1981). The resuls of he uni roo ess are obained from he economeric sofware package EViews. Table 2 shows he resuls of he uni roo ess for Japanese ouriss o New Zealand and Taiwan. As shown in Table 2, he null hypohesis of a uni roo is no rejeced for he levels of Japanese ouris arrivals o New Zealand and Taiwan in he models wih a consan and wih a consan and rend as he deerminisic erms. A similar resul holds for he logarihm of monhly Japanese ouris arrivals o each counry, where he ADF ess do no rejec he null hypohesis of a uni roo for he models wih a consan and wih a consan and rend for Japanese ourism o New Zealand. However, for he series in log differences (or growh raes) for Japanese ouriss o New Zealand and Japanese ouriss o Taiwan, he null hypohesis of a uni roo is rejeced by he ADF. 7

8 As shown in he uni roo ess, he empirical resuls srongly sugges he use of growh raes in monhly Japanese ouris arrivals o esimae alernaive univariae condiional mean and condiional volailiy models simulaneously. For his reason, condiional mean and condiional volailiy models will be esimaed in Secion 4 using only he growh raes of Japanese ouris arrivals. 4. Economeric Mehodology The alernaive ime series models o be esimaed for he condiional means of he monhly inernaional ouris arrivals, as well as heir respecive condiional volailiies, are discussed below. As Figures 1-6 illusrae, monhly Japanese ouris arrivals o New Zealand and Taiwan, he levels and logarihmic series do no show persisence in volailiy, whereas he firs differences (ha is, he log difference or growh rae) of Japanese ouris arrivals show periods of persisen volailiy in he sample period. One implicaion of his persisen ime-varying volailiy is ha he assumpion of condiionally homoskedasic residuals would seem o be inappropriae for sensible empirical analysis. For a wide range of financial daa series, ime-varying condiional variances can be explained empirically hrough he auoregressive condiional heeroskedasiciy (ARCH) model of Engle (1982). When he ime-varying condiional variance has boh auoregressive and moving average componens, his leads o he generalized ARCH(p,q), or GARCH(p,q), model of Bollerslev (1986). The lag srucure of he appropriae GARCH model can be chosen by informaion crieria, such as hose of Akaike and Schwarz, alhough i is very common o impose he widely esimaed GARCH(1,1) specificaion in advance as i ypically capures boh shor and long run volailiy persisence adequaely. In he seleced condiional volailiy model, he residual series should follow a whie noise process. Bollerslev e al. (1992) documen he adequacy of he GARCH(1,1) specificaion. Li e al. (2002) provide an exensive review of recen heoreical resuls for univariae and mulivariae ime series models wih condiional volailiy errors. 8

9 McAleer (2005) reviews a wide range of univariae and mulivariae, condiional and sochasic, models of financial volailiy. McAleer e al. (2007) discuss recen developmens in modeling univariae asymmeric volailiy, while McAleer e al. (2008) develop he regulariy condiions and esablish he asympoic properies of a general model of ime-varying condiional correlaions. As shown in Figures 5 and 6, he log difference monhly ouris arrivals display ime-varying volailiy persisence, so i is naural o esimae alernaive condiional volailiy models. Consider he saionary AR(1)-GARCH(1,1) model for ouris arrivals (or heir growh raes, as appropriae), y (see, for example, McAleer (2005)): y 1 (1) 1 2 y 1, 2 for 1,..., n, where he shocks (or movemens in monhly ouris arrivals, or growh raes, as appropriae) are given by: h, h ~ iid (0,1) h 2 1 1, (2) and w 0, 0, 0 are sufficien condiions o ensure ha he condiional variance h 0. The AR(1) model in equaion (1) can easily be exended o univariae or mulivariae ARMA(p,q) processes (for furher deails, see Ling and McAleer (2003a)). In equaion (2), he ARCH (or ) effec indicaes he shor run persisence of shocks, while he GARCH (or ) effec indicaes he conribuion of shocks o long run persisence (namely, + ). The saionary AR(1)-GARCH(1,1) model can be modified o incorporae a non-saionary ARMA(p,q) condiional mean and a saionary GARCH(r,s) condiional variance, as in Ling and McAleer (2003b). In equaions (1) and (2), he parameers are ypically esimaed by he maximum likelihood mehod o obain Quasi-Maximum Likelihood Esimaors (QMLE) in he 9

10 absence of normaliy of, he condiional shocks (or sandardized residuals). The condiional log-likelihood funcion is given as follows: n l 1 1 n 2 log h 2 1 h. The QMLE is efficien only if is normal, in which case i is he MLE. When is no normal, adapive esimaion can be used o obain efficien esimaors, alhough his can be compuaionally inensive. Ling and McAleer (2003b) invesigaed he properies of adapive esimaors for univariae non-saionary ARMA models wih GARCH(r,s) errors. The exension o mulivariae processes is raher complicaed. The GARCH process in equaion (2) is a funcion of he uncondiional shocks, so he momens of need o be invesigaed. Ling and McAleer (2003a) showed ha he QMLE for GARCH(p,q) is consisen if he second momen of is finie. For GARCH(p,q), Ling and Li (1997) demonsraed ha he local QMLE is asympoically normal if he fourh momen of is finie, while Ling and McAleer (2003a) proved ha he global QMLE is asympoically normal if he sixh momen of is finie. The well known necessary and sufficien condiion for he exisence of he second momen of for GARCH(1,1) is 1. As discussed in McAleer e al. (2007), Elie and Jeanheau (1995) and Jeanheau (1998) esablished ha he log-momen condiion was sufficien for consisency of he QMLE of a univariae GARCH(p,q) process (see Lee and Hansen (1994) for he proof in he case of GARCH(1,1)), while Boussama (2000) showed ha he log-momen condiion was sufficien for asympoic normaliy. Based on hese heoreical developmens, a sufficien condiion for he QMLE of GARCH(1,1) o be consisen and asympoically normal is given by he log-momen condiion, namely 2 E (log( )) 0. (3) The log-momen condiion for he GARCH(1,1) model involves he expecaion of a funcion of a random variable and unknown parameers. Alhough he sufficien 10

11 momen condiions for consisency and asympoic normaliy of he QMLE for he univariae GARCH(1,1) model are sronger han heir log-momen counerpars, he second momen condiion is more sraighforward o check. In pracice, he log-momen condiion in equaion (3) would be esimaed by he sample mean, wih he parameers and, and he sandardized residual,, being replaced by heir QMLE counerpars. The sandard GARCH model reas he effecs of posiive shocks (or upward movemens in monhly ouris arrivals) on he condiional variance, h, are he same as negaive shocks (or downward movemens in monhly ouris arrivals) of a similar magniude. However, he effecs of posiive and negaive effecs may have asymmeric effecs on volailiy. In order o accommodae asymmeric behaviour, Glosen, Jagannahan and Runkle (1992) proposed he GJR model, for which GJR(1,1) is defined as follows: h 2 I( )) h, (4) ( where 0, 0, 0, 0 are sufficien condiions for h 0, and I ) is an indicaor variable ha is defined by ( 1, I( ) 0, 0 0 as has he same sign as. The indicaor variable differeniaes beween posiive and negaive shocks of equal magniude, so ha asymmeric effecs in he daa are capured by he coefficien. For financial daa, i is expeced ha 0 because negaive shocks increase risk by increasing he deb o equiy raio, alhough his inerpreaion may no hold for ourism daa in he absence of an equivalen inerpreaion in erms of risk. The asymmeric effec,, measures he conribuion 11

12 of shocks o boh shor run persisence,. 2, and o long run persisence, 2 Ling and McAleer (2002a) showed ha he regulariy condiion for he exisence of he second momen for GJR(1,1) under symmery of is given by: 1 1, (5) 2 while McAleer e al. (2007) showed ha he weaker log-momen condiion for GJR(1,1) was given by: 2 E (ln[( I( )) ]) 0, (6) which involves he expecaion of a funcion of a random variable and unknown parameers. An alernaive model o capure asymmeric behaviour in he condiional variance is he Exponenial GARCH (EGARCH(1,1)) model of Nelson (1991), namely: log h h, 1 (7) 1 1 log 1 where he parameers, and have differen inerpreaions from hose in he GARCH(1,1) and GJR(1,1) models. As noed in McAleer e al. (2007), here are some imporan differences beween EGARCH, on he one hand, and GARCH and GJR, on he oher, as follows: (i) EGARCH is a model of he logarihm of he condiional variance, which implies ha no resricions on he parameers are required o ensure h 0 ; (ii) momen condiions are required for he GARCH and GJR models as hey are dependen on lagged uncondiional shocks, whereas EGARCH does no require momen condiions o be esablished as i depends on lagged condiional shocks (or sandardized 12

13 residuals); (iii) Shephard (1996) observed ha 1 is likely o be a sufficien condiion for consisency of QMLE for EGARCH(1,1); (iv) as he sandardized residuals appear in equaion (7), 1 would seem o be a sufficien condiion for he exisence of momens; and (v) in addiion o being a sufficien condiion for consisency, 1 is also likely o be sufficien for asympoic normaliy of he QMLE of EGARCH(1,1). Furhermore, EGARCH capures asymmeries differenly from GJR. The parameers and in EGARCH(1,1) represen he magniude (or size) and sign effecs of he sandardized residuals, respecively, on he condiional variance, whereas and represen he effecs of posiive and negaive shocks, respecively, on he condiional variance in GJR(1,1). Asymmeric effecs are capured by he coefficien,, hough in a differen manner, in he EGARCH and GJR models. The EGARCH model is also capable of capuring leverage hrough he deb o equiy raio, whereby negaive shocks increase volailiy bu posiive shocks of a similar order of magniude decrease volailiy. As in financial markes, asymmery and leverage may also be found in ourism markes. When a negaive shock affecs a ouris desinaion, ourism will suffer and ener a urbulen phase so ha volailiy will increase, whereas a posiive shock on volailiy may be smaller or even in he opposie direcion, so ha he marke may ener a period of ranquiliy. 5. Empirical Resuls I is well known ha he esimaes of volailiy will depend on he adequacy of he specificaion of he condiional mean equaion, which yields he sandardized residuals. Boh he asympoic sandard errors, as well as he robus sandard errors of Bollerslev and Wooldridge (1992), are presened. In virually all cases, he asympoic sandard errors are smaller han heir robus counerpars. As described in Secion 4, we use hree specificaions, GARCH(1,1), GJR(1,1) and EGARCH(1,1), o esimae condiional mean and condiional volailiy models for 13

14 Japanese ouriss o New Zealand and Taiwan. The esimaes are given in Tables 3 and 4. As shown in he uni roo ess, which are given in Table 2, he resuls sugges he use of growh raes in monhly ouris arrivals o esimae alernaive univariae condiional mean and condiional volailiy models simulaneously. Table 3 presens he empirical resuls of he growh raes of monhly Japanese ouris arrivals o New Zealand. These empirical resuls are suppored by he esimaes of he lagged dependen variables in he esimaes of equaion (1), wih all he coefficiens of he lagged dependen variable being less han one in each of he esimaed hree models for he growh raes of monhly Japanese ouris arrivals o New Zealand. This is consisen wih he empirical finding ha he log difference (or growh rae) is saionary. As shown in he second column of Table 3, he GARCH(1,1) esimaes for he log difference (or growh rae) of monhly Japanese ouris arrivals o New Zealand sugges ha he shor run persisence of shocks is 0.009, while he long run persisence is As he second momen condiion, 1, is saisfied, he log-momen condiion is also saisfied. Thus, he regulariy condiions are saisfied, he QMLE are consisen and asympoically normal, and inferences are valid. Therefore, he symmeric GARCH(1,1) esimaes are saisically significan. If posiive and negaive news of a similar magniude o monhly Japanese ouris o New Zealand are reaed asymmerically, his can be evaluaed using he GJR(1,1) model. The resul of GJR (1,1) are shown in he hird column of Table 3. The asymmery coefficien is found o be posiive and significan for monhly Japanese ouris o New Zealand, namely 0.325, which indicaes he negaive shocks increase risk (or volailiy). Moreover, he shor run persisence of posiive and negaive shocks are esimaed o be and 0.260, respecively, and he long run persisence of shocks is esimaed o be for he log difference in daily prices of hogs. As described in secion 4, an alernaive model o examine asymmeric behaviour is he EGARCH model. As shown in he las column of Table 3, each of he EGARCH(1,1) esimaes is saisically significan. The coefficien of he absolue 14

15 lagged dependen variable,, is esimaed o be and is significan, which suggess ha all momens exis, wih he esimaes likely o be consisen and asympoically normal. Overall, he size effec of he sandardized residuals, α, have a negaive bu insignifican impac on he condiional variances. The sign effec of he sandardized residuals,, is negaive and significan, which eviden asymmery. Furhermore, he absolue vale of (0.291) is higher han for he corresponding α esimaes (0.029), which sugges ha he sign effecs have larger impacs han he size effecs on he condiional variances. Finally, here is a leverage effec in he case of he monhly growh of Japanese ouris o New Zealand, whereby negaive shocks increase volailiy bu posiive shocks of a similar magniude decrease volailiy. These empirical resuls are similar o a wide range of financial sock marke prices, so ha he heory of finance, including an analysis of risk is direcly applicable o inernaional ouris arrivals. Wih no resricions on he parameers required o ensure ha volailiy, h 0, his seems o sugges ha he asymmeric EGARCH (1,1) model is beer han he asymmeric GJR (1,1) model. Table 4 shows he saisical resuls for he GARCH(1,1), GJR(1,1) and EGARCH(1,1) models for he monhly growh of Japanese ouris o Taiwan. For he condiional mean esimaes, all he coefficiens of he lagged dependen variable are less han one in each of he esimaed hree models for he growh raes of monhly Japanese ouris arrivals o Taiwan. This is suppored by he esimaes of he lagged dependen variables in equaion (1), and suggess ha he log difference (or growh rae) is saionary. Regarding he condiional volailiy esimaes, he second column of Table 4 shows a relaive low ime-varying persisence in he monhly growh of Japanese ouris o Taiwan, wih an esimaed shor run persisence of shocks of and esimaed long run persisence of shocks of for he symmeric GARCH (1,1) model. However, he esimaed coefficien α is insignifican whileβis significan a he 10% level. As he second momen condiion, 1, is saisfied, he log-momen condiion is 15

16 also saisfied. This is slighly differen from he esimaes for he monhly growh of Japanese ouriss o New Zealand, in which he variance, in he long run has a much smaller ime variaion in he monhly growh rae of Japanese ouriss o Taiwan. For he GJR(1,1) model, boh he second momen and log-momen condiions are saisfied. The asympoic -raio for he esimae is posiive bu is no significan, suggesing ha a negaive shock will no affec risk (or volailiy) any differenly from a posiive shock of equal magniude. Again, he shor run persisence of posiive shocks is no posiive, which suggess he GJR (1,1) model may no ensure a posiive variance. As shown in he las column of Table 4, each of he EGARCH(1,1) esimaes is saisically significan, excep he coefficien. The absolue value of he coefficien of lagged log volailiy,, is esimaed o be and is significan, which suggess ha all momens exis, wih he esimaes likely o be consisen and asympoically normal. Overall, he size effecs of he sandardized residuals, α, have posiive and significan impacs on he condiional variances, and he sign effec of he sandardized residuals,, is posiive bu is no significan. However, he insignifican sign effec,, suggess ha here is no asymmeric differences beween posiive and negaive shocks for monhly growh in Japanese ouriss o Taiwan. This resul is differen from he case of monhly growh in Japanese ouriss o New Zealand. 6. Concluding Remarks The primary purpose of he paper was o esimae he long and shor haul volailiy in monhly Japanese ouriss o New Zealand and Taiwan, respecively. Esimaion of volailiy in inernaional ouris arrivals is imporan for ourism managemen because he paerns of risk have imporan implicaions for ourism policy. The model of condiional volailiy can provide useful insighs o undersand and predic he risk o 16

17 he policy maker of flucuaions in ourism demand and guaraneeing ourism revenues. Following sandard economeric uni roo ess, our resuls srongly sugges he use of growh raes in monhly inernaional ouris arrivals o esimae alernaive univariae condiional mean and condiional volailiy models simulaneously. In order o capure appropriaely he volailiies (or risk) in ouris arrivals, we use symmeric and asymmeric condiional volailiy models, specifically he widely- used GARCH(1,1), GJR(1,1) and EGARCH(1,1) models, o examine he effecs of posiive or negaive shocks of equal magniude on he growh raes of Japanese ouriss o New Zealand and Taiwan. The monhly daa cover he period January 1997 o December An imporan finding was he asymmeric impacs of posiive and negaive shocks of similar magniude on he volailiy of monhly growh of Japanese ouriss o New Zealand. Moreover, he resuls empirically have also shown ha here is a leverage effec in he case of monhly growh of Japanese ouriss o New Zealand, whereby negaive shocks increase volailiy bu posiive shocks of similar magniude decrease volailiy. These empirical resuls seem o be similar o a wide range of financial sock marke prices, so ha he heory of finance is relevan and direcly applicable o inernaional ouris arrivals. In comparison wih asymmeric long haul volailiy in he monhly growh of Japanese ouriss o New Zealand, he resuls sugges a relaively low ime-varying persisence in he monhly growh of Japanese ouriss o Taiwan. However, he empirical resuls also sugges ha here were no asymmeric differences beween posiive and negaive shocks. In general, he resul is differen from he esimaes for he monhly growh of Japanese ouriss o New Zealand, in which he long run variance has a lower ime variaion in he monhly growh of Japanese ouriss o Taiwan. Based on he empirical resuls presened in he paper, a differen paern of long haul and shor haul risk exiss beween Japanese ouriss o New Zealand and o Taiwan. However, Japanese ouriss o New Zealand have larger impacs from negaive shocks han from posiive shocks of a similar magniude, so ha ourism managers can 17

18 develop appropriae sraegies when he ourism indusry is affeced by negaive shocks. Analysing volailiy effecs is imporan for he ourism indusry, in general, and for he airlines, ouris aracions and he lodging secor, in paricular. Volailiy experienced by his indusry has significan implicaions for capial invesmen, resource and yield managemen. The empirical findings of his paper provide useful insighs which can be expeced o be of ineres o he privae and public secors in ourism managemen policy formulaion wih regard o shor and long haul desinaions. I is unusual in empirical ourism research o analyse ourism volailiy. Hence, he heoreical and empirical modelling of ourism volailiy in his paper should make a significan conribuion o he lieraure. While volailiy has an inerpreaion of risk in finance, i is also used o consruc more precise (ha is, accurae) confidence inervals and forecas inervals. Wih respec o he laer, he use of daily daa may be superior o monhly daa for compuing ime-varying sandard errors and ime-varying forecas sandard errors. The poenial usefulness of hese issues will be considered in fuure research. 18

19 References Bollerslev, T. (1986), Generalised auoregressive condiional heeroscedasiciy, Journal of Economerics, 31, Bollerslev, T., Chou, R.Y., and Kroner, K.F. (1992), ARCH modeling in finance - A review of he heory and empirical evidence, Journal of Economerics, 52, Bollerslev, T., and Wooldridge, J. (1992), Quasi maximum likelihood esimaion and inference in dynamic models wih ime varying variances, Economeric Reviews, 11, Boussama, F. (2000), Asympoic normaliy for he quasi-maximum likelihood esimaor of a GARCH model, Compes Rendus de l Academie des Sciences, Serie I, 331, (in French). Chan, F., Lim, C., and McAleer, M. (2005), Modelling mulivariae inernaional ourism demand and volailiy, Tourism Managemen, 26, Dickey, D.A., and Fuller, W.A. (1979), Disribuion of he esimaors for auoregressive ime series wih a uni roo, Journal of he American Saisical Associaion, 74, Dickey, D.A., and Fuller, W.A. (1981), Likelihood raio saisics for auoregressive ime series wih a uni roo, Economerica, 49, Elie, L., and Jeanheau, T. (1995), Consisency in heeroskedasic models, Compes Rendus de l Académie des Sciences, Série I, 320, (in French). Ellio, G., Rohenberg, T.J., and Sock, J.H. (1996), Efficien ess for an auoregressive uni roo, Economerica, 64, Engle, R.F. (1982), Auoregressive condiional heeroscedasiciy wih esimaes of he variance of Unied Kingdom inflaion, Economerica, 50,

20 Glosen, L., Jagannahan, R., and Runkle, D. (1992), On he relaion beween he expeced value and volailiy of nominal excess reurn on socks, Journal of Finance, 46, Jeanheau, T. (1998), Srong consisency of esimaors for mulivariae ARCH models, Economeric Theory, 14, Lee, S.W., and Hansen, B.E. (1994), Asympoic heory for he GARCH(1,1) quasi-maximum likelihood esimaor, Economeric Theory, 10, Li, W.K., Ling, S., and McAleer, M. (2002), Recen heoreical resuls for ime series models wih GARCH errors, Journal of Economic Surveys, 16, Reprined in McAleer, M. and Oxley, L. (eds.), Conribuions o Financial Economerics: Theoreical and Pracical Issues, Blackwell, Oxford, 2002, pp Lim, C., and McAleer, M. (2001), Monhly seasonal variaions in Asian ourism o Ausralia, Annals of Tourism Research, 28, pp Lim, C., Min, J.C.H., and McAleer, M. (2007), ARMAX modelling of inernaional ourism demand, in Oxley, L. and Kulasiri, D. (eds.), MODSIM 2007 Inernaional Congress on Modelling and Simulaion, MSSANZ, Chrischurch, New Zealand, pp Lim C., Min, J. C. H., and McAleer, M. (2008), Modelling income effecs on long and shor haul inernaional ravel from Japan, Tourism Managemen, 29, Ling, S., and Li, W.K. (1997), On fracionally inegraed auoregressive moving-average models wih condiional heeroskedasiciy, Journal of he American Saisical Associaion, 92, Ling, S., and McAleer, M. (2002a), Saionariy and he exisence of momens of a family of GARCH processes, Journal of Economerics, 106,

21 Ling, S., and McAleer, M. (2002b), Necessary and sufficien momen condiions for he GARCH(r,s) and asymmeric power GARCH(r,s) models, Economeric Theory, 18, Ling, S., and McAleer, M. (2003a), Asympoic heory for a vecor ARMA-GARCH model, Economeric Theory, 19, Ling, S., and McAleer, M. (2003b), On adapive esimaion in nonsaionary ARMA models wih GARCH errors, Annals of Saisics, 31, McAleer, M. (2005), Auomaed inference and learning in modeling financial volailiy, Economeric Theory, 21, McAleer, M. (2009), The Ten Commandmens for opimizing value-a-risk, Journal of Economic Surveys, 23, McAleer, M., Chan, F., and Marinova, D. (2007), An economeric analysis of asymmeric volailiy: Theory and applicaion o paens, Journal of Economerics, 139, Nelson, D.B. (1991), Condiional heeroscedasiciy in asse reurns: a new approach, Economerica, 59, New Zealand Deparmen of Saisics ( ), Monhly Touris Arrivals, Wellingon, NZ. Ng, S., and Perron, P. (2001), Lag lengh selecion and he consrucion of uni roo ess wih good size and power, Economerica, 69, Perron, P., and Ng, S. (1996), Useful modificaions o some uni roo ess wih dependen errors and heir local asympoic properies, Review of Economic Sudies, 63, Phillips, P.C.B., and Perron, P. (1988), Tesing for a uni roo in ime series regression, Biomerika, 75,

22 Shareef, R., and McAleer, M. (2007), Modelling he uncerainy in monhly inernaional ouris arrivals o he Maldives, Tourism Managemen, 28, Shareef, R., and McAleer, M. (2008), Modelling inernaional ourism demand and uncerainy in Maldives and Seychelles: A porfolio approach, Mahemaics and Compuers in Simulaion, 78, Shephard, N. (1996), Saisical aspecs of ARCH and sochasic volailiy, in Barndorff-Nielsen, O.E., Cox, D.R., and Hinkley, D.V. (eds.), Saisical Models in Economerics, Finance and Oher Fields, Chapman and Hall, London, pp Taiwan Tourism Bureau ( ), Monhly Repor on Tourism, Tourism Bureau, Taipei. Taiwan Tourism Bureau (2006), 2005 Survey Repor on Visiors Expendiure and Trends in Taiwan, Tourism Bureau, Taipei. Tourism New Zealand (2006), Japan, hp:// s, Ocober 25, World Tourism Organisaion (2006), Tourism Highlighs 2005 Ediion, World Tourism Organisaion, Madrid. 22

23 Table 1 Summary Saisics Saisics Japan o New Zealand Japan o Taiwan Mean Median Maximum Minimum Skewness Kurosis Jarque-Bera (probabiliy) (0.001) 5.28 (0.07) No. observaions

24 Table 2 Uni Roo Tess for Touris Arrivals Japan o New Zealand Japan o Taiwan Variables ADF GLS Z={1} ADF GLS Z={1,} ADF GLS Z={1} ADF GLS Z={1,} Y (12) 0.03 (12) (15) -0.21*** (13) LY -0.05*** (14) (13) (14) -0.21*** (14) DLY *** (13) -6.26***(12) -2.94***(12) -2.95*** (12) Noe: *** denoes he null hypohesis of a uni roo is rejeced a he 1% level. 24

25 Table 3 Condiional Mean and Volailiy Models for he Log Difference in Japanese Touris Arrivals o New Zealand, 1979/ /12 Dependen variable: DL(TA) Parameers GARCH GJR EGARCH (0.016) (0.015) (0.012)*** [0.015] [0.015] [0.014]*** (0.060) [0.051] (0.001)*** [0.001]* GARCH/GJR (0.018)) [0.015] GJR GARCH/GJR (0.025)*** [0.024]*** EGARCH EGARCH EGARCH (0.058) [0.045] (0.001)*** [0.003] (0.027)*** [0.043]** (0.084)*** [0.122]*** (0.028)*** [0.011]*** (0.061) [0.045] (0.030) [0.031] (0.034) [0.038] (0.007)*** [0.010]*** (0.052)*** [0.065]*** Diagnosics Second momen Log-momen No. observaions Noes: DL(TA) is log difference in ouris arrivals. Numbers in parenheses are asympoic sandard errors, while numbers in brackes are he Bollerslev and Wooldridge (1992) robus sandard errors. *and *** denoe significance a he 10% and 1% levels, respecively. 25

26 Table 4 Condiional Mean and Volailiy Models for he Log Difference in Japanese Touris Arrivals o Taiwan, 1979/ /12 Dependen variable: DL(TA)) Parameers GARCH GJR EGARCH (0.009) (0.006) (0.010) [0.008] [0.008] [0.008] (0.056)*** [0.053]*** (0.016) [0.028] GARCH/GJR (0.049) [0.058] GJR GARCH/GJR (0.426)* [1.162] EGARCH EGARCH EGARCH (0.065)*** [0.051]*** (0.002) [0.015] (0.074) [0.069] (0.114) [0.064] (0.399) [0.673] (0.065)*** [0.050]*** (0.614)*** [0.358]*** (0.103)** [0.117]** (0.172)*** [0.101]*** (0.068) [0.060] Diagnosics Second momen Log-momen No. observaion Noes: DL(TA) is log difference in ouris arrivals. Numbers in parenheses are asympoic sandard errors, while numbers in brackes are he Bollerslev and Wooldridge (1992) robus sandard errors. *, ** and *** denoe significance a he 10%, 5% and 1% levels, respecively. 26

27 24,000 20,000 16,000 12,000 8,000 4, Figure 1. Monhly Touris Arrivals from Japan o New Zealand 27

28 140, , ,000 80,000 60,000 40,000 20, Figure 2. Monhly Touris Arrivals from Japan o Taiwan 28

29 Figure 3. Log Monhly Touris Arrivals from Japan o New Zealand 29

30 Figure 4. Log Monhly Touris Arrivals from Japan o Taiwan 30

31 Figure 5. Log difference in Monhly Touris Arrivals from Japan o New Zealand 31

32 Figure 6. Log difference in Monhly Touris Arrivals from Japan o Taiwan 32