Daily Tourist Arrivals, Exchange Rates and Volatility for Korea and Taiwan

Transcription

1 Daily Touris Arrivals, Exchange Raes and Volailiy for Korea and Taiwan Chia-Lin Chang Deparmen of Applied Economics Naional Chung Hsing Universiy Taichung, Taiwan Michael McAleer Economeric Insiue Erasmus School of Economics Erasmus Universiy Roerdam and Tinbergen Insiue The Neherlands and Cener for Inernaional Research on he Japanese Economy (CIRJE) Faculy of Economics Universiy of Tokyo EI November 2009 * For financial suppor, he firs auhor wishes o hank he Naional Science Council, Taiwan, and he second auhor wishes o acknowledge he Ausralian Research Council and Naional Science Council, Taiwan. 1

2 Absrac Boh domesic and inernaional ourism are a major source of service expor receips for many counries worldwide, and is also increasingly imporan in Taiwan. One of he hree leading ourism source counries for Taiwan is he Republic of Korea, which is a source of shor haul ourism. Daily daa from 1 January 1990 o 31 December 2008 are used o model he Korean Won / New Taiwan $ exchange rae and ouris arrivals from Korea o Taiwan, as well as heir associaed volailiy. The sample period includes he Asian economic and financial crises in 1997, and a significan par of he global financial crisis of Inclusion of he exchange rae allows approximae daily price effecs on Korean ourism arrivals o Taiwan o be capured. The Heerogeneous Auoregressive (HAR) model is used o capure long memory properies in exchange raes and Korean ouris arrivals, o es wheher alernaive esimaes of condiional volailiy are sensiive o he long memory in he condiional mean, and o examine asymmery and leverage in volailiy. The empirical resuls show ha he condiional volailiy esimaes are no sensiive o he long memory naure of he condiional mean specificaions. The QMLE for he GARCH(1,1), GJR(1,1) and EGARCH(1,1) models for Korean ouris arrivals o Taiwan and he Korean Won / New Taiwan $ exchange rae are saisically adequae and have sensible inerpreaions. Asymmery (hough no leverage) is found for several alernaive HAR models. Keywords: Korean ouris arrivals, exchange raes, approximae price effecs, global financial crisis, Asian economic and financial crises, GARCH, GJR, EGARCH, HAR, long memory, asymmery, leverage. JEL Classificaions: C22, F31, G18, G32. 2

3 1. Inroducion Boh domesic and inernaional ourism are a major source of service expor receips for many counries worldwide, and is also increasingly imporan in Taiwan, an island in Eas Asia off he coas of mainland China, souhwes of he main islands of Japan, direcly wes of Japan's Ryukyu Islands, and norh o norhwes of he Philippines. I is bound o he eas by he Pacific Ocean, o he souh by he Souh China Sea and he Luzon Srai, o he wes by he Taiwan Srai, and o he norh by he Eas China Sea. The island consiss of seep mounains covered by ropical and subropical vegeaion. The main island of Taiwan is also known as Formosa (from he Poruguese Ilha Formosa, meaning beauiful island ). The populaion is 23 million inhabians (in 2005), consising of 98% Han Chinese and 2% Aboriginal Taiwanese. Taiwan s climae is marine ropical. The norhern par of he island has a rainy season from January o lae March during he souhwes monsoon. The enire island succumbs o ho and humid weaher from June unil Sepember, while Ocober o December is arguably he mos pleasan ime of he year. Naural hazards, such as yphoons and earhquakes, are common in he region. The hree mos imporan inernaional ourism source counries o Taiwan are Japan, USA and Republic of Korea. More han hree million inernaional ouriss visied Taiwan in The majoriy of he Taiwan ouris indusry is suppored by domesic ourism. As a resul of Taiwan s exensive nework of rains and highways, i is possible o raverse he counry (norh-souh) in less han wo hours by high speed rain, and in a few hours by car. The mos well known ouris aracions in Taiwan include he specacular Naional Palace Museum (Taipei), amazing Nigh Markes (especially in Taipei), Taipei 101, formerly he world s alles building, relaxing Sun Moon Lake (near Puli in he cenral highlands), and sunning Taroko Naional Park (eas coas). One of he mos imporan purposes in aracing ouriss is he amoun ha ouriss spend. If he daily expendiure per ouris remains reasonably consan over he sample period, ouris arrivals and oal ourism expendiure will be highly correlaed. Moreover, he rae of growh in ourism expendiure and he rae of growh in ouris arrivals will hen be very similar. The primary purpose of he paper is o model Korean ouris arrivals and he Korean Won / New Taiwan $ exchange rae, and heir respecive volailiies. Daily daa from 1 January 1990 o 31 December 2008 are obained from he Naional Immigraion Agency of Taiwan for Korean ouris 3

4 arrivals, and he Bloomberg daabase for he foreign exchange rae. By using daily daa, we can approximae he modelling sraegy and analysis o hose applied o financial ime series daa. From a ime series perspecive, here are several reasons for using daily daa (see, for example, McAleer (2009)). In paricular, daily daa allow an examinaion of wheher he ime series properies have changed, he ime series behaviour a oher frequencies can be obained by aggregaion of daily daa, and he sample size is increased considerably. Moreover, he use of exchange rae daa allows approximae daily price effecs on Korean ourism arrivals o Taiwan o be capured. The empirical resuls show ha he ime series of Korean ouris arrivals o Taiwan and he Won/NT$ exchange rae are saionary. In addiion, he esimaed symmeric and asymmeric condiional volailiy models, specifically he widely used GARCH, GJR and EGARCH models, all fi he daa very well. In paricular, he esimaed models are able o accoun for he higher volailiy persisence in boh Korean ouris arrivals and he exchange rae ha are observed a he end of he sample period, due primarily o he global financial crisis. The empirical second momen condiions ypically suppor he saisical adequacy of he models for Korean ouris arrivals, and always suppor he adequacy of he empirical models of he exchange rae, so ha saisical inferences are valid. Moreover, he esimaes resemble hose arising from financial ime series daa, wih boh shor and long run persisence of shocks o Korean ouris arrivals and exchange rae, and asymmeric responses o posiive and negaive shocks of equal magniude, hough no leverage effecs are observed. Therefore, volailiy can be inerpreed as risk associaed wih he growh rae in Korean ouris arrivals and he exchange rae. The remainder of he paper is organized as follows. Secion 2 presens he daily Korean ouris arrivals and exchange rae ime series daa. Secion 3 performs uni roo ess on boh series. Secion 4 discusses alernaive long memory condiional mean and condiional volailiy models for daily Korean ouris arrivals and he exchange rae. The esimaed models and empirical resuls for he heerogeneous auoregressive (HAR) model are discussed in Secion 5. Finally, some concluding remarks are given in Secion Daa The daa se comprises daily Korean ouris arrivals from 1 January 1990 o 31 December 2008, giving 6,940 observaions obained from he Naional Immigraion Agency of Taiwan, and an equivalen number of observaions on he Korean Won / New Taiwan $ exchange rae ha are 4

5 obained from he Bloomberg daabase: Taipei Foreign Exchange Marke Developmen Foundaion (URL: hp:// From Figures 1-4 plo he daily Korean ouris arrivals and he Won / NT$ exchange rae, as well as heir respecive volailiies, where volailiy is defined as he squared deviaion from he sample mean. There is higher volailiy persisence a he end of he sample period, due primarily o he global financial crisis. The dominan observaion for he exchange rae and is volailiy occurred on 23 December 1997, a he heigh of he Asian economic and financial crises, when he Won / NT$ exchange rae peaked a (for furher deails on he global financial crisis see, for example, McAleer (2009, 2009a, 2009b, 2010). Boh Korean ouris arrivals o Taiwan and he Won / NT$ daily exchange rae have varied considerably over he sample period, which suggess ha he daily effecs of he approximae price movemens on ourism demand migh be capured using an appropriae model. The exchange rae aside, here would seem o be considerable scope for a significan increase in Korean ourism o Taiwan. In order o manage ourism growh and is volailiy, i is necessary o model adequaely Korean ouris arrivals and heir associaed volailiy. In he nex secion we analyze he presence of a sochasic rend by applying uni roo ess before modelling he ime-varying volailiy ha is presen in Korean ouris arrivals o Taiwan and he Won / NT$ exchange rae series. 3. Uni Roo Tess Sandard uni roo ess based on he classic mehods of Dickey and Fuller (1979, 1981) and Phillips and Perron (1988) are available in he economeric sofware package EViews 6.0, and are repored in Table 1. There is no evidence of a uni roo in daily Korean ouris arrivals o Taiwan in he model wih a consan and rend as he deerminisic erms, or wih jus a consan. However, he oucome for he Won / NT$ exchange rae is ambiguous, wih he es saisics being significan for he model wih jus a consan, bu insignifican for he model wih a consan and deerminisic ime rend. The correlaion coefficiens in Table 2 show ha Korean ouris arrivals o Taiwan and he Won / NT$ exchange rae, and heir respecive volailiies, are generally no highly correlaed. In fac, he 5

6 only hree series ha have meaningful correlaions are he pairs Korean ouris arrivals o Taiwan and is associaed volailiy, he Won / NT$ exchange rae and is associaed volailiy, and Korean ouris arrivals o Taiwan and he Won / NT$ exchange rae, for which he correlaion is Thus, Korean ourism demand and he approximae price effec hrough he Won / NT$ exchange rae is negaive, as expeced. I is worh emphasizing ha he negaive correlaion is wih respec o daily daa, which in iself is insrucive. These empirical resuls allow he use of Korean ouris arrivals daa o Taiwan and he exchange rae beween he wo counries o esimae alernaive univariae long memory condiional mean and condiional volailiy models given in he nex secion. 4. Condiional Mean and Condiional Volailiy Models The alernaive ime series models o be esimaed for he condiional means of he daily Korean ouris arrivals o Taiwan and he Won / NT$ exchange rae, as well as heir respecive condiional volailiies, are discussed below. As shown in Figures 1 and 3, daily Korean ouris arrivals o Taiwan and he exchange rae show periods of high volailiy, followed by ohers of relaively low volailiy. One implicaion of his persisen volailiy behaviour is ha he assumpion of (condiionally) homoskedasic residuals is inappropriae. As discussed in Divino and McAleer (2009, 2010) and Chang e al. (2009), for example, for a wide range of daa series in finance, inernaional finance and ourism research, ime-varying condiional variances can be explained empirically hrough he auoregressive condiional heeroskedasiciy (ARCH) model, which was proposed by 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. In he seleced condiional volailiy model, he residual series should follow a whie noise process. Li e al. (2002) provide an exensive review of recen heoreical resuls for univariae and mulivariae ime series models wih condiional volailiy errors, and McAleer (2005) reviews a wide range of univariae and mulivariae, condiional and sochasic, models of financial volailiy. When Korean ouris arrivals daa and he Korean Won / New Taiwan $ exchange rae display 6

7 persisence in volailiy, as shown in Figures 2 and 4, respecively, i is naural o esimae alernaive condiional volailiy models. The GARCH(1,1), GJR(1,1) and EGARCH(1,1) condiional volailiy models have been esimaed using monhly and daily ouris arrivals daa in several papers, including Chan, Lim and McAleer (2005), Hoi, McAleer and Shareef (2005, 2007), Shareef and McAleer (2005, 2007, 2008), Divino and McAleer (2009, 2010), and Chang e al. (2009). However, hese papers have no esimaed any spillover effecs beween ouris arrivals and exchange raes, and hence have no been able o capure any approximae price effecs affecing ourism demand. The condiional volailiy lieraure has been discussed exensively in recen years (see, for example, Li, Ling and McAleer (2002), McAleer (2005), and McAleer, Chan and Marinova (2007)). Consider he saionary AR(1)-GARCH(1,1) model for daily Korean ouris arrivals o Taiwan (or Korean Won / New Taiwan $ exchange rae), y : y 1 (1) 1 2 y 1, 2 for 1,..., n, where he shocks (ha is, movemens in Korean ouris arrivals or Korean Won / New Taiwan $ exchange rae) are given by: h, h ~ iid (0,1) h 2 1 1, (2) and 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). 7

8 In equaions (1) and (2), he parameers are ypically esimaed by he maximum likelihood mehod o obain Quasi-Maximum Likelihood Esimaors (QMLE) in he 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 complicaed. Since he GARCH process in equaion (2) is a funcion of he uncondiional shocks, 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. Using resuls from Ling and Li (1997) and Ling and McAleer (2002a, 2002b), he necessary and sufficien condiion for he exisence of he second momen of for GARCH(1,1) is 1 and, under normaliy, he necessary and sufficien condiion for he 2 2 exisence of he fourh momen is ( ) 2 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) 8

9 However, his condiion is no easy o check in pracice, even for he GARCH(1,1) model, as i involves he expecaion of a funcion of a random variable and unknown parameers. Alhough he sufficien 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 far 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 effecs of posiive shocks (or upward movemens in daily Korean ouris arrivals) on he condiional variance, h, are assumed o be he same as he negaive shocks (ha is, downward movemens in daily Korean ouris arrivals or he Korean Won / New Taiwan $ exchange rae) in he symmeric GARCH model. 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 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, bu his inerpreaion need no hold for Korean ourism arrivals or he Korean Won / New Taiwan $ exchange rae in he absence of a direc risk inerpreaion. The asymmeric effec,, measures he conribuion of shocks o boh shor run persisence,, and o long 2 9

10 run persisence,. I is no possible for leverage o be presen in he GJR model, whereby 2 negaive shocks increase volailiy and posiive shocks of equal magniude decrease volailiy. 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. If = 0, here is no asymmery, while < 0, and are he condiions for leverage o exis, whereby negaive shocks increase volailiy and posiive shocks of equal magniude decrease volailiy. As noed in McAleer e al. (2007), here are some imporan differences beween EGARCH and he previous wo models, 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 residuals); (iii) Shephard (1996) observed 10

11 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). 5. Esimaed Models and Analysis The Heerogenous Auoregressive (HAR) model was proposed by Corsi (2009) as an alernaive o model and forecas realized volailiies, and is inspired by he Heerogenous Marke Hypohesis of Muller, Dacorogna, Dav, Olsen, Pice, and Ward (1993) and he asymmeric propagaion of volailiy beween long and shor horizons. Corsi (2009) showed ha he acions of differen ypes of marke paricipans could lead o a simple resriced linear auoregressive model wih he feaure of considering volailiies realized over differen ime horizons. The heerogeneiy of he model derives from he fac ha differen auoregressive srucures are presen a each ime scale (for furher deails, see McAleer and Medeiros (2008)). In his secion he HAR model is used o model oal Korean ouris arrivals o Taiwan and he Korean Won / New Taiwan $ exchange rae, ogeher wih he hree condiional volailiy models discussed in he previous secion. The alernaive HAR(h) models o be esimaed o capure long memory are based on he following: y, h y y 1 y2... yh 1 (8) h where ypical values of h are one (daily daa), seven (weekly daa), and 28 (monhly daa). In he empirical applicaion, he hree models o be esimaed for Korean ouris arrivals o Taiwan and he Korean Won / New Taiwan $ exchange rae, are as follows: y 1 21 y x (9)

12 y y 1 21 y x y x (10) ,7 32 1, y x y x y x. (11) ,7 32 1,7 41 1, , 28 The model sin equaions (9)-(11) will be referred o as he HAR(1), HAR(1,7) and HAR(1,7,28) models, respecively. The condiional mean esimaes in Tables 3-8 show ha he HAR(1), HAR(1,7) and HAR(1,7,28) esimaes are all saisically significan, such ha he long memory properies of Korean ouris arrivals o Taiwan and he Won / NT$ exchange rae series are capured adequaely hrough he saisical significance of he long memory variables. The esimaed condiional mean and condiional volailiy models are given in Tables 3-8. The mehod used in esimaion was he Marquard algorihm. As shown in he uni roo ess in Table 1, he Korean ouris arrivals o Taiwan series are saionary. These empirical resuls are suppored by he esimaes of he lagged dependen variables in he esimaes of equaions (9)-(11) for ouris arrivals, wih he coefficiens of he lagged dependen variable being significanly less han one in each of he esimaed models. As he second momen condiion is ypically less han uniy in each case, he regulariy condiions are generally saisfied, and hence he QMLE are consisen and asympoically normal, and inferences are valid. The EGARCH(1,1) model is based on he sandardized residuals, so he regulariy condiion is saisfied if 1, and hence he QMLE are consisen and asympoically normal (see, for example, McAleer e al. (2007)). The GARCH(1,1) esimaes in Tables 3-5 for he HAR(1), HAR(1,7) and HAR(1,7,28) models of Korean ouris arrivals o Taiwan sugges ha he shor run persisence of shocks lies beween 0.04 and 0.093, while he long run persisence is close o uniy. If posiive and negaive shocks o Korean ouris arrivals o Taiwan of a similar magniude are reaed asymmerically, his can be evaluaed in he GJR(1,1) model. The asymmery coefficien is found o be negaive and significan for he HAR(1), HAR(1,7) and HAR(1,7,28) models, which indicaes ha decreases in Korean ouris arrivals decrease volailiy. Therefore, shocks o Korean ouris arrivals o Taiwan can be inerpreed as risk associaed wih Korean ouris arrivals. 12

13 Alhough asymmery is observed for he HAR(1), HAR(1,7) and HAR(1,7,28) models, here is no evidence of leverage. These empirical resuls show ha he condiional volailiy esimaes are no sensiive o he long memory naure of he condiional mean specificaions. As he second momen 1 condiion, 1, is ypically saisfied, he log-momen condiion is necessarily saisfied, 2 so ha he QMLE are consisen and asympoically normal. Therefore, saisical inference using he asympoic normal disribuion is valid, and he asymmeric GJR(1,1) esimaes are saisically significan. The inerpreaion of he EGARCH model is in erms of he logarihm of volailiy. For Korean ouris arrivals o Taiwan, each of he EGARCH(1,1) esimaes is saisically significan for he HAR(1), HAR(1,7) and HAR(1,7,28) models, wih boh he size effec,, and he sign effec,, being posiive in all hree cases. The coefficien of he lagged dependen variable,, is esimaed o be less han uniy, which suggess ha he saisical properies of he QMLE for EGARCH(1,1) will be consisen and asympoically normal. These empirical resuls show ha he volailiy in he shocks o Korean ouris arrivals o Taiwan are no sensiive o he long memory naure of he condiional mean specificaions. Overall, he QMLE for he GARCH(1,1), GJR(1,1) and EGARCH(1,1) models for Korean ouris arrivals o Taiwan are saisically adequae and have sensible inerpreaions. However, asymmery (hough no leverage) was found for he HAR(1), HAR(1,7) and HAR(1,7,28) models. The GARCH(1,1) esimaes in Tables 6-8 for he HAR(1), HAR(1,7) and HAR(1,7,28) models of he Won / NT$ exchange rae sugges ha he shor run persisence of shocks lies beween and 0.081, while he long run persisence is close o uniy. The second momen regulariy condiion is saisfied in all cases, so ha saisical inference using he asympoic normal disribuion is valid. The GJR(1,1) model reas posiive and negaive shocks o he Won / NT$ exchange rae of a similar magniude asymmerically. The asymmery coefficien is found o be negaive and significan for he HAR(1), HAR(1,7) and HAR(1,7,28) models, which indicaes ha decreases in he Won / NT$ exchange rae decrease volailiy. Therefore, shocks o he exchange rae can be inerpreed as financial risk. Alhough asymmery is observed for he HAR(1), HAR(1,7) and HAR(1,7,28) models, here is no evidence of leverage. These empirical resuls show ha he condiional volailiy esimaes are no sensiive o he long memory naure of he condiional mean 13

14 specificaions. As he second momen condiion is saisfied in all cases, he log-momen condiion is necessarily saisfied, so ha he QMLE are consisen and asympoically normal. Therefore, saisical inference using he asympoic normal disribuion is valid. For he Won / NT$ exchange rae, each of he EGARCH(1,1) esimaes is saisically significan for he HAR(1), HAR(1,7) and HAR(1,7,28) models, wih boh he size effec,, and he sign effec,, being posiive in all hree cases. The coefficien of he lagged dependen variable,, is esimaed o be less han uniy, which suggess ha he saisical properies of he QMLE for EGARCH(1,1) will be consisen and asympoically normal. These empirical resuls show ha he volailiy in he shocks o he exchange rae are no sensiive o he long memory naure of he condiional mean specificaions. Overall, he QMLE for he GARCH(1,1), GJR(1,1) and EGARCH(1,1) models for he Won / NT$ exchange rae are saisically adequae and have sensible inerpreaions. As in he case of Korean ouris arrivals o Taiwan, asymmery (hough no leverage) was found for he HAR(1), HAR(1,7) and HAR(1,7,28) models of he exchange rae. 6. Concluding Remarks Alhough i is no ye one of he mos imporan indusries in Taiwan, an island in Eas Asia off he coas of mainland China, he hree mos imporan ourism source counries for Taiwan are Japan, USA and he Republic of Korea, which reflec shor and long haul ouris desinaions. As Korean ourism o Taiwan has no ye achieved he saus of an imporan economic aciviy for Taiwan s finances, here is significan room for improvemen in ourism receips from his ourism source counry. However, he poenial negaive impacs of mass ourism on he environmen, and hence on fuure Korean ourism demand, mus be managed appropriaely. In order o manage Korean ourism growh, i is necessary o model adequaely Korean ouris arrivals and heir associaed volailiy. As he exchange rae allows approximae daily price effecs on Korean ourism arrivals o Taiwan o be capured, i is also necessary o analyse he Korean Won / New Taiwan $ exchange rae, as well as is associaed volailiy. The paper examined daily Korean ouris arrivals o Taiwan from 1 January 1990 o 31 December 2008, as obained from he Naional Immigraion Agency of Taiwan, and he Korean Won / New 14

15 Taiwan $ exchange rae, as obained from he Bloomberg daabase. The Heerogeneous Auoregressive (HAR) model was used o capure he long memory properies in boh daa series. The empirical resuls showed ha he ime series of Korean ouris arrivals o Taiwan and he Won / NT$ exchange rae were saionary. In addiion, he esimaed symmeric and asymmeric condiional volailiy models, specifically he widely used GARCH, GJR and EGARCH models all fi he daa exremely well. In paricular, he esimaed models were able o accoun for he higher volailiy persisence ha was observed a he end of he sample period, due primarily o he global financial crisis. The empirical second momen condiion also generally suppored he saisical adequacy of he models of Korean ouris arrivals o Taiwan, and always so for he Won / NT$ exchange rae, so ha saisical inferences were valid. Moreover, he esimaes resembled hose arising from financial ime series daa, wih boh shor and long run persisence of shocks, and asymmeric effecs of posiive and negaive shocks of equal magniude o volailiy. Alhough asymmery was observed for he HAR(1), HAR(1,7) and HAR(1,7,28) models, here was no evidence of leverage. Overall, volailiy can be inerpreed as risk associaed wih shocks o Korean ouris arrivals o Taiwan and he Korean Won / New Taiwan $ exchange rae. 15

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19 Shareef, R. and M. McAleer (2007), Modelling he uncerainy in inernaional ouris arrivals o he Maldives, Tourism Managemen, 28, Shareef, R. and M. McAleer (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 O.E. Barndorff- Nielsen, D.R. Cox and D.V. Hinkley (eds.), Saisical Models in Economerics, Finance and Oher Fields, Chapman & Hall, London, pp

20 Figure 1. Daily Korean Touris Arrivals o Taiwan 2,800 2,400 2,000 1,600 1, Figure 2. Volailiy of Daily Korean Touris Srrivals o Taiwan 6,000,000 5,000,000 4,000,000 3,000,000 2,000,000 1,000,

21 Figure 3. Daily Exchange Rae of Korean Won / New Taiwan $ Figure 4. Volailiy of Daily Exchange Rae of Korean Won / New Taiwan $

22 Table 1. Uni Roo Tess Variables ADF Z={1} PP Z={1} ADF Z={1,} PP Z={1,} Korean Touris ** ** ** ** Arrivals o Taiwan Variable ADF Z={1} PP Z={1} ADF Z={1,} PP Z={1,} Exchange Rae * * Noes: The criical values for he ADF es are (-2.57) a he 1% (10%) level when Z = {1}, and (-3.13) a he 1% (10%) level when Z = {1,}. The criical values for he PP es are (-2.57) a he 1% (10%) level when Z = {1}, and (-3.13) a he 1% (10%) level when Z = {1,}. ** and * denoe he null hypohesis of a uni roo is rejeced a he 1% and 10% levels, respecively. Table 2. Correlaion Coefficiens Variables Korean Touris Arrivals o Taiwan Exchange rae Volailiy of Korean Touris Volailiy of Korean Arrivals o Taiwan Exchange rae Korean Touris Arrivals o Taiwan Exchange rae Volailiy of Korean Touris Arrivals o Taiwan Volailiy of Exchange rae Noe: The exchange rae refers o he Korean Won / New Taiwan $. 22

23 Table 3: Esimaed Condiional Mean (HAR(1)) and Condiional Volailiy Models for Korean Touris Arrivals o Taiwan Parameers GARCH GJR EGARCH ** (10.393) ** (0.009) ** (0.260) ** (11.053) 0.621** (0.009) ** (0.282) ** (10.539) 0.619** (0.009) ** (0.270) * ** (6.575) (10.601) 0.045** 0.055** GARCH/GJR (0.002) GARCH/GJR 0.956** 0.952** (0.002) (0.002) GJR ** (0.004) EGARCH EGARCH EGARCH Diagnosics (0.012) 0.110** (0.005) 0.032** 0.992** (0.001) AIC BIC Jarque-Bera [p-value] Causaliy es [p-value] Noes: The dependen variable is Korean ouris arrivals o Taiwan. Numbers in parenheses are sandard errors. The log-momen condiion is necessarily saisfied as he second momen condiion is saisfied for GJR model. AIC and BIC denoe he Akaike Informaion Crierion and Schwarz Bayesian Informaion Crierion, respecively. ** and * denoe he esimaed coefficiens are saisically significan a he 1% and 5% levels, respecively. 23

24 Table 4: Esimaed Condiional Mean (HAR(1,7)) and Condiional Volailiy Models for Korean Touris Arrivals o Taiwan Parameers GARCH GJR EGARCH ** (9.436) ** (0.013) ** (11.318) 0.257** (0.013) (2.181) (2.293) 0.680** 0.658** (0.017) (0.017) (2.192) (2.307) ** ** (9.983) (8.193) 0.093** 0.088** GARCH/GJR (0.004) GARCH/GJR 0.915** 0.931** (0.002) GJR ** (0.006) EGARCH EGARCH EGARCH Diagnosics ** (7.036) 0.269** (0.012) (1.605) 0.648** (0.014) (1.598) (0.009) 0.093** (0.005) 0.083** (0.004) 0.991** (0.001) AIC BIC Jarque-Bera [p-value] Causaliy F es [p-value] [0.0005] [0.003] Noes: The dependen variable is Korean ouris arrivals o Taiwan. Numbers in parenheses are sandard errors. AIC and BIC denoe he Akaike Informaion Crierion and Schwarz Bayesian Informaion Crierion, respecively. ** denoes he esimaed coefficien is saisically significan a he 1% level. 24

25 Table 5: Esimaed Condiional Mean (HAR(1,7,28)) and Condiional Volailiy Models for Korean Touris Arrivals o Taiwan Parameers GARCH GJR EGARCH ** ** 1 (9.703) (11.156) 0.244** 0.253** 21 (0.013) (0.013) (2.202) (2.254) 0.565** 0.558** 31 (0.025) (0.025) (2.979) (3.045) 0.142** 0.134** 41 (0.021) (0.022) (1.507) (1.576) ** ** (9.796) (8.016) 0.090** 0.086** GARCH/GJR (0.004) GARCH/GJR 0.918** 0.929** (0.002) GJR ** (0.006) EGARCH EGARCH EGARCH Diagnosics ** (4.689) 0.274** (0.011) (1.424) 0.554** (0.020) (1.629) 0.115** (0.015) (0.765) 0.016* (0.008) 0.050** (0.004) 0.086** 0.994** (0.001) AIC BIC Jarque-Bera [p-value] Causaliy F es [p-value] [0.003] [0.020] [0.011] Noes: The dependen variable is Korean ouris arrivals o Taiwan. Numbers in parenheses are sandard errors. AIC and BIC denoe he Akaike Informaion Crierion and Schwarz Bayesian Informaion Crierion, respecively. ** and * denoe he esimaed coefficiens are saisically significan a he 1% and 5% levels, respecively. 25

26 Table 6: Esimaed Condiional Mean (HAR(1)) and Condiional Volailiy Models for Korean Won / New Taiwan $ Parameers GARCH GJR EGARCH (0.011) 0.024* (0.010) 0.999** 0.999** (0.0003) (0.0003) 8.23E E-06 (5.39E-06) (5.36E-06) ** ** (6.98E-06) (6.22E-06) 0.081** 0.088** GARCH/GJR (0.002) GARCH/GJR 0.918** 0.926** (0.002) (0.001) GJR ** (0.004) EGARCH EGARCH EGARCH Diagnosics 0.023** 0.999** (0.0001) 1.17E-05** (2.91E-06) ** 0.145** 0.037** 0.991** (0.001) AIC BIC Jarque-Bera [p-value] Noes: The dependen variable is he Korean Won / NT$ exchange rae. Numbers in parenheses are sandard errors. The log-momen condiion is necessarily saisfied as he second momen condiion is saisfied. AIC and BIC denoe he Akaike Informaion Crierion and Schwarz Bayesian Informaion Crierion, respecively. ** and * denoe he esimaed coefficiens are saisically significan a he 1% and 5% levels, respecively. 26

27 Table 7: Esimaed Condiional Mean (HAR(1,7)) and Condiional Volailiy Models for Korean Won / New Taiwan $ Parameers GARCH GJR EGARCH (0.012) (0.012) 0.905** 0.906** (0.010) (0.010) 4.87E E-06 (7.55E-06) (7.96E-06) 0.094** 0.093** (0.010) (0.010) 5.90E E-06 (1.02E-05) (1.07E-05) ** ** (6.51E-06) (5.89E-06) 0.077** 0.083** GARCH/GJR (0.002) GARCH/GJR 0.922** 0.930** (0.002) (0.001) GJR ** (0.004) EGARCH EGARCH EGARCH Diagnosics 0.026** (0.002) 0.895** (0.011) 1.74E-05** (6.47E-06) 0.104** (0.010) -1.00E-05 (7.21E-06) ** 0.178** 0.029** 0.988** (0.0004) AIC BIC Jarque-Bera [p-value] Noes: The dependen variable is he Korean Won / NT$ exchange rae. Numbers in parenheses are sandard errors. The log-momen condiion is necessarily saisfied as he second momen condiion is saisfied. AIC and BIC denoe he Akaike Informaion Crierion and Schwarz Bayesian Informaion Crierion, respecively. ** denoes he esimaed coefficien is saisically significan a he 1% level. 27

28 Table 8: Esimaed Condiional Mean (HAR(1,7,28)) and Condiional Volailiy Models for Korean Won / New Taiwan $ Parameers GARCH GJR EGARCH (0.013) (0.013) 0.898** 0.899** (0.011) (0.011) 5.51E E-06 (7.46E-06) (7.90E-06) 0.118** 0.116** (0.014) (0.014) 2.70E E-06 (1.58E-05) (1.64E-05) ** * (0.006) (0.007) 4.31E E-06 (1.66E-05) (1.64E-05) ** ** (6.80E-06) (6.15E-06) 0.078** 0.084** GARCH/GJR (0.002) GARCH/GJR 0.921** 0.929** (0.002) (0.002) GJR ** (0.004) EGARCH EGARCH EGARCH Diagnosics 0.041** (0.002) 0.902** (0.001) -5.41E-07 (6.74E-06) 0.095** (0.001) 4.44E-05** (1.00E-05) 0.001** (0.0001) -3.43E-05** (8.65E-06) ** 0.156** 0.022** 0.990** (0.0004) AIC BIC Jarque-Bera [p-value] Noes: The dependen variable is he Korean Won / NT$ exchange rae. Numbers in parenheses are sandard errors. The log-momen condiion is necessarily saisfied as he second momen condiion is saisfied. AIC and BIC denoe he Akaike Informaion Crierion and Schwarz Bayesian Informaion Crierion, respecively. ** and * denoe he esimaed coefficiens are saisically significan a he 1% and 5% levels, respecively. 28