IJMS 0 vol. 3 (): 111-1 Inernaonal Journal of Muldscplnary Sudes (IJMS) Volume 3, Issue, 0 Forecasng Pos-War Tours Arrvals o Sr Lanka Usng Dynamc Transfer Funcon Modelng Mehod Gnanapragasam SR 1 and Cooray TMJA 1 Deparmen of Mahemacs and Compuer Scence, The Open Unversy of Sr Lanka Deparmen of Mahemacs, Unversy of Morauwa, Sr Lanka ABSTRACT Toursm plays a bg role n erms of economcs n he developmen of a counry. The arrvals were less durng he war perod n Sr Lanka due o he uncerany of secury. Forecasng ours arrvals s essenal for plannng, polcy makng and budgeng purposes. The objecve of he sudy s o f a model o predc ours arrvals by usng dynamc ransfer funcon (DTF) modelng mehod. The monhly ours arrvals from June 009 o June 0 are exraced from he annual repors of Sr Lanka oursm developmen auhory for hs sudy. Pror o model fngs, he followng echnques were carred ou: Augmened Dckey- Fuller es, Kruskal- Walls es, dfference mehod, auo-correlaon funcon and paral auo-correlaon funcon. For model fng, dynamc ransfer funcon model for unvarae me seres process was employed. Anderson- Darlng es, Lagrange s Mulpler es and Whe s General es were appled for he resduals analyss. To evaluae he performance of he model on he bass of he f of he forecasng, mean absolue percenage error (MAPE) was aken no accoun. I s saed ha, over 7.3 mllon ourss had vsed he sland durng he sudy perod. Furher s noed ha, every year here s a posve growh rae. I reveals ha, here s dramac ncrease n oal ours arrvals afer he war. Soon afer he war n Sr Lanka, a rapd ncrease n growh rae n he year 010 s also observed. Accordng o he MAPE value, s concluded ha, he fed DTF model explans over 90% accuracy n erms of forecasng ours arrvals. Based on he ex-pos forecas, s expeced ha nearly 1.105 mllon ourss wll come o Sr Lanka n he las sx monhs n 0. I s approxmaely 14% ncrease n he arrvals over he las sx monhs n he year 015. KEYWORDS: Dynamc ransfer funcon, forecasng, ours arrvals. Correspondng auhor: S. R. Gnanapragasam, Emal: srgna@ou.ac.lk
S. R. Gnanapragasam and T. M. J. A. Cooray 1. INTRODUCTION Toursm, as an ndusry, conrbues o he naonal economy of a counry n a large scale. Now s one of he larges and fases growng economc secors n he world. The case sudes (Balaguer & Canavella, 00; Durbarry, 004) dscovered he mpac of oursm on economc growh n Spansh and Maurus respecvely. An emprcal sudy (Kng & Gamage, 1994) addressed he mpac of oursm on economc growh n Sr Lanka. There s a sgnfcan causal relaonshp from oursm receps o he gross domesc produc (GDP) of Sr Lanka (Wckramasnghe & Ihalanayake, 006). There were several se-backs n he oursm developmen process n Sr Lanka such as global economc crss n 009, Tsunam n 004 and he nernal conflc from he year 193 o he year 009. Durng he conflc perod, manly due o he uncerany of secury, ourss dd no come o Sr Lanka. Neverheless, he conflc s over by now. The records n Sr Lanka oursm developmen auhory (SLTDA) show ha, he ours arrvals are dramacally ncreasng afer he nernal conflc. As per he sascal annual repor 015 of SLTDA, due o he rse of he arrvals o Sr Lanka, oursm was able o upgrade s rank o he hrd level as he larges source of foregn exchange earner of he naonal economy n 015. Those ha ranked above oursm were Foregn Remances and Texles & Garmens ndusres. The poron of conrbuon of oursm o oal foregn exchange earnngs n 015 amouned o 1.4%. I reveals ha conrbuon of oursm o he GDP s sgnfcanly hgh. Toursm bascally conans wo ypes as domesc and nernaonal. Ths sudy s manly focused only on he nernaonal ours arrvals o Sr Lanka. Predcon of ours arrvals s essenal for plannng, polcy makng and budgeng purposes. Thus, he objecve of he sudy s o f a model o predc nernaonal ours arrvals by usng dynamc ransfer funcon (DTF) modellng mehod.. BACKGROUND The general heme of he sudes (Bermudez e al., 007; W e al., 199; Lm & McAleer, 001; Akuno e al., 015) says ha forecasng accuracy s hgh n exponenal smoohng modellng and hs approach obans a level of accuracy comparable o hose of oher more sophscaed models. However, he emprcal sudes (Cho, 001; Chu, 199; Loganahan & Yahaya, 010; Chang e al., 011; Dmros e al., 01; Saayman e al., 010; Praser e al., 00) show ha auoregressve negraed movng average (ARIMA) modellng s overall he mos accurae mehod for forecasng nernaonal ours arrvals. Neverheless, he sae space model ouperforms alernave approaches for shor-erm forecasng and also produces sensble long-erm forecass (Ahanasopoulos & Hyndman, 006). On he oher hand, he neural nework modellng mehod performs he bes n hese sudes (Law, 000; Burger e al., 001; Cho, 003). Therefore, s no ha easy o assgn a modellng mehod o a specfc regon or a counry o forecas oursm demand. Hence, all possble modellng mehods have o be employed and based on he accuracy of he forecas, bes mehod can be recommended. Furhermore, a comprehensve revew of publshed sudes on oursm demand modellng and forecasng snce 000 was carred ou (Song & L, 00). One of he key fndngs of hs revew s ha he mehods used n analysng and forecasng he demand for oursm had been more vared. As far as he forecasng accuracy s concerned, hs revew shows ha, here s no sngle model ha conssenly ouperforms oher models n all suaons. Therefore, s beer o consder several approaches, o oursm demand n Sr Lanka, o denfy he bes model based on he forecasng accuracy. Accordng o he leraure, emprcal sudes of me seres behavour of he pos war nernaonal ours arrvals o Sr Lanka had
Forecasng Pos-War Tours Arrvals o Sr Lanka Usng Dynamc Transfer Funcon Modelng Mehod been carred ou usng dfferen modellng approaches. They are as follows: he classcal me seres decomposon approach (Kurukulasoorya & Lelwala, 014) wh 96% forecasng accuracy, Box-Jenkn s modellng and Hol - Wner s Exponenal Smoohng approaches (Gnanapragasam & Cooray, 0(a) & 0(b)) wh nearly 95% and % forecasng accuracy respecvely and Sae Space modellng approach (Gnanapragasam e al., 0) wh 94% forecasng accuracy. However, dynamc ransfer funcon (DTF) model was no red so far for he purpose of predcng nernaonal ours arrvals o Sr Lanka. Therefore, hs sudy aemps o f ours arrvals o Sr Lanka usng DTF modellng approach. 3. MATERIALS & METHODS The monhly nernaonal ours arrvals, from June 009 o June 0, recorded n he annual sascal repors of Sr Lanka oursm developmen auhory are exraced for hs sudy. 3.1. Prelmnary Analyss A he prelmnary sage pror o f he dynamc ransfer funcon model (DTF) model, he followng echnques were carred ou o ge an dea abou he daa and s behavour. 3.1.1. Plo of Tme Seres I s o nspec for exreme observaons, mssng daa, or elemens of non-saonary such as rend or seasonaly or cyclc paern or rregular varaons. 3.1.. Augmened Dckey- Fuller es Augmened Dckey- Fuller (ADF) es s used o es wheher he seres has a un roo. I s o confrm, sascally, ha he saonary of seres n erms of rend avalably. The es sasc for he model Y Y 1 u ˆ wh, s DF ~ SE( ˆ ) n 1 1 1 where Y s he response varable a me, u s he whe nose and s he number of observaons. The hypohess o be esed n hs es s H 0: seres s non-saonary versus H 1: seres s saonary. 3.1.3. Kruskal- Walls es n 1 1 Kruskal- Walls es s used o confrm he seasonaly n he seres. The hypohess o be esed n hs es s, H 0: seres has no seasonaly versus H 1: seres has seasonaly. The es sasc of ruskal- Walls es s defned as: n 1 R H 3( 1) N N( N 1) 1 n L1 where N s he oal number of rankngs, R he sum of he rankngs n a specfc season, n s he number of he rankngs n a specfc season and L s he lengh of he season. 3.1.4. Dfferencng mehod If he seres has an elemen such as rend or seasonaly, hen by akng he regular or seasonal dfferences hose elemens can be elmnaed from he seres and s defned as W Y Y, where L Y s he response varable a me and s he lengh of he season. Auocorrelaon funcon and paral auo correlaon funcon In me seres analyss, a process of examnng he auocorrelaon funcon (ACF) and paral auocorrelaon funcon (PACF) s o deermne he naure of he process under consderaon. L s
S. R. Gnanapragasam and T. M. J. A. Cooray 3.1.5. Auocorrelaon funcon Auocorrelaon funcon (ACF) a lag k s defned by k cov var Y ˆ ˆ Y Y Y k k Y Yˆ var Y Yˆ k k The frs several auocorrelaons are perssenly large n he graph of ACF and raled off o zero raher slowly, can be assumed ha a rend exss and he me seres s non-saonary. If he seres s saonary, hen ACF graph mus decay exponenally. 3.1.6. Paral auocorrelaon funcon Paral auocorrelaon funcon (PACF) beween Y and Y s he condonal correlaon k beween Y and Y and defned as follows: k corr Y, Y k Y 1, Y,..., Y kk k1 In oher words, he PACF beween Y and Y k s he auocorrelaon beween Y and Y k afer adjusng for,, Y k. 1 Y 1, Y 3.. Dynamc Transfer Funcon modellng mehod Dynamc ransfer funcon (DTF) model s a sascal model descrbng he relaonshp beween an oupu varable Y and one or more npu varables X s. I has many applcaons especally n forecasng urnng pons. 3..1. Dynamc Transfer Funcon Nose model In pracce, he oupu Y s no a deermnsc funcon of X. I s ofen dsurbed by some nose or has s own dynamc srucure. The nose componen N may be serally correlaed, and s assumed ha N follows an ARMA ( p, q ) model as ( B) N ( B) e, where ( ) 1 p B 1 B B... p B and ( ) 1 q B 1 B B... q B are polynomals n of degree B p and q respecvely, and e s a sequence of ndependen and dencally dsrbued random varables wh mean zero and varance e I s noed ha n he above ARMA model, E N and he usual condons of 0 saonary and nverbly apply. Pung ogeher, a smple DTF model can be obaned as ( B) B b ( B) Y c v( B) X N c X e ( B) ( B) where c s a consan, ( B), ( B), ( B)and ( B) are defned smlarly as before wh degree q, p, s, and r e respecvely, and are whe nose seres. The parameer b s called he decay rae of he sysem. The nose componen should be N ndependen of X ; oherwse, he model s no denfable. Furher s noed ha when b 0 he DTF model s useful n predcng he urnng pons of Y gven hose of X. 3.. Dynamc Transfer Funcon model for Unvarae Tme Seres Process A general form of a DTF model can be expressed m ( ) b ( ) as BB B Y c X e 1 ( B) ( B).
Forecasng Pos-War Tours Arrvals o Sr Lanka Usng Dynamc Transfer Funcon Modelng Mehod where ( B) 0 1 B B... B, ( B) 0 1 B B... B, ( ) 1 p B 1 B B... p B and ( ) 1 q B 1 B B... q B are polynomals n of degree q, p, s,and r B respecvely, and e are whe nose seres. The parameer b s called he decay rae wh he h varable. The order of he DTF s sad o be and he added nose model s of order r, s, b p, q. Snce he DTF model s a sragh forward exenson of he ARMA model, for ( B) 0, he model s equvalen o unvarae me seres process (Domnque e al., 00). Thus he DTF for unvarae me seres can be smply wren ( B) as Y e ( B). 3.3. Resdual Analyss Before usng he model for forecasng, mus be checked for adequacy. Dagnosc checks are performed o deermne he adequacy of he model. Accordngly, he resduals should be random and normally dsrbued wh consan varance. The followng ess are carred ou for he resdual analyss: 3.3.1. Anderson- Darlng The Anderson- Darlng (AD) es s used o es f a sample of daa comes from a populaon wh a specfc dsrbuon. I s a modfcaon of Kolmogorov- Smrnov (K-S) es and gves more wegh o he als han does he K-S es. Here he hypoheses are H 0: The daa follow normal dsrbuon versus H 1: The daa do no follow normal dsrbuon. The es sasc of AD es s: N 1 A N ln F( Y ) ln(1 F( Y )) 1 N N 1 where F s he cumulave dsrbuon funcon of he specfed dsrbuon, are he ordered daa and N s he oal number of observaons. 3.3.. Lagrange s Mulpler es Lagrange s Mulpler (LM) es s used o es he ndependency of resduals. I s an alernave es of Durbn Wason es for auo correlaon among resduals. The null hypohess o be esed s ha, H 0: here s no seral correlaon of any order. The ndvdual resdual auocorrelaons should be small. Sgnfcan resdual auocorrelaons a low lags or seasonal lags sugges ha he model s nadequae. The es sasc of LM es s: W nr df where, df s he number of regressors n he auxlary regresson (only lnear erms of he dependen varable are n he R auxlary regresson), s he deermnaon of coeffcens and n s he number of observaons. 3.3.3. Whe s General es Whe s general es s used n order o check consan varance of resduals. Accordngly he null hypohess s H 0: Homoscedascy agans he alernave hypohess H 1: Heeroscedascy. Tes sasc of Whe s General es s: W nr df where, df s he number of regressors n he auxlary regresson (squared erms of he dependen varable are also ncluded n addon o erms n he LM es n auxlary regresson), R s he deermnaon of coeffcens and n s he number of observaons. Model Valdaon I s mporan o evaluae performance of fed model on he bass of he f of he forecasng. Y
S. R. Gnanapragasam and T. M. J. A. Cooray Measure of forecas accuracy should always be evaluaed as par of a model valdaon effor. 3. 4. Mean absolue percenage error Mean absolue percenage error (MAPE) s he average of he sum of he absolue values of he percenage errors. I s generally used for evaluaon of he forecas agans he valdaon sample. To compare he average forecas accuracy of dfferen models, MAPE sascs s used. I s defned as, 1 n Y ˆ MAPE Y 100, where Y n 1 Y s he response varable a me and n s he number of observaons. Praccally f MAPE s less han 10% hen he fed model s hghly recommended for forecasng. 4. RESULTS & DISCUSSIONS In hs secon, he dscussons are based on he resuls obaned from he resuls sofware MINITAB and SAS. 4.1. Prelmnary Analyss The Fgure 1 shows he yearly nernaonal ours arrvals from he year 1967 o 015 o Sr Lanka. arrvals. Ths s he begnnng of he nernal conflc n Sr Lanka. There afer ups and downs n oal arrvals can be seen from he years 193 o 009. Ths s he perod where he nernal conflc ook place n Sr Lanka. Neverheless, from he years 009 o 015, afer he nernal conflc, here s a remarkable upward rend n he oal number of nernaonal ours yearly arrvals o he sland. Ths s he reason for hs sudy s o manly focus on he nernaonal ours arrvals, only afer he conflc, o Sr Lanka. To sudy he behavour of he arrvals, afer he nernal conflc, daa from June 009 o December 015 are consdered whereas only for growh rae calculaon he daa from January 00 are aken. The relevan resuls are summarzed n Table 1. I s noed ha, he orgnal daa s named as Y n he analyss par o handle hs n SAS and MINITAB sofware convenenly. Table 1. Annual ours arrvals and s growh rae Year Arrvals 009 601 010 654476 011 55975 01 1005605 Growh Rae Year Arrvals.15% 46.1% 30.79% 013 174593 014 157153 015 17930 Growh Rae 6.75% 19.1% 17.76% 17.4% Toal arrvals 7,376,343 From he sascs appeared n Table 1, can be saed ha, over 7.3 mllon ourss had vsed he sland durng he sudy perod. Also only n he year 015 nearly 1. mllon ourss had vsed he sland and whch s he bgges h n oursm hsory of Sr Lanka. Fgure 1. Plo of yearly ours arrvals In Fgure 1, s clearly observed ha, from he years 1967 o 19 here s an upward rend n Furher s noed ha, every year here s a posve growh rae. I reveals ha, here s dramac ncrease n oal ours arrvals afer he conflc. A rapd ncrease n growh rae n he year 010, soon afer he nernal conflc n Sr Lanka, s also noed here.
Forecasng Pos-War Tours Arrvals o Sr Lanka Usng Dynamc Transfer Funcon Modelng Mehod The monhly average arrvals afer he conflc are also aken no accoun o see he paern of he arrvals o Sr Lanka. orgnal seres n Fgure 3. Hence, s obvous ha, he orgnal seres Y s non- saonary. Furher, o check he saonary condon of he seres Y, sascally, ACF graph wh ADF and Kruskal- Walls ess are employed as follows: ACF of Y 1.0 0. 0.6 Auocorrelaon 0.4 0. 0.0-0. -0.4-0.6-0. -1.0 Fgure. Plo of monhly average arrvals I can be clearly observed a paern of arrvals, on he average, from Fgure ha n he monhs of December, January and February more ourss do come o Sr Lanka whls he lower numbers of arrvals are recorded n he monhs of May and June on average n every year. 4.. Checkng saonary condon Fgure 3 provdes he me seres plo of he orgnal seres Y from June 009 o December 015. 4 6 1 14 Lag Fgure 4. ACF graph of he seres Y 10 I s very clear from he graph of ACF of Y n Fgure 4 ha does no decay exponenally and hus can be clamed ha he orgnal seres Y s non- saonary. Snce he p- value (0.99) of ADF es confrms he exsence of he rend n he seres Y, he regular dfference s aken o remove he rend and now he frs dfferenced seres s named as D1Y. Agan he me seres plo of he seres D1Y s obaned o observe he behavour of he regular dfferenced seres. 1 0 4 Tme seres plo of Tours Arrvals from 009 June o 015 December 00000 60000 Tme seres plo of he seres D1Y 40000 Tours Arrvals 150000 100000 D1Y 0000 0-0000 50000 1 4 3 40 monh Fgure 3. Plo of Tme seres An upward rend wh seasonal paern can be clearly seen from he me seres plo of he 4 56 64 7-40000 1 3 40 Monh Fgure 5. Tme seres plo of D1Y 4 Now seems from he me seres plo n Fgure 5 ha here s no rend n he seres D1Y. Agan ADF es for he seres D1Y s also appled and hence concludes ha he seres D1Y has no 4 56 64 7
S. R. Gnanapragasam and T. M. J. A. Cooray rend as he p-value of ADF es for D1Y s 0.00. However, he p- value (0.00) of Kruskal- Walls es for he seres D1Y sll confrms he exsence of seasonaly. Auocorrelaon 1.0 0. 0.6 0.4 0. 0.0-0. -0.4-0.6-0. -1.0 4 6 ACF of D1Y 10 1 14 Lag Fgure 6. ACF graph of he seres D1Y From he graph of ACF of D1Y n Fgure 6, can be clearly observed ha, spkes of 1h and 4h lags are hgh and no sgnfcan. Therefore, can be assumed ha he seres D1Y has he seasonaly wh lengh 1. To remove hs seasonaly, he seasonal dfference for lengh 1 s aken and now s named as D1D1Y. D1D1Y 30000 0000 10000 0-10000 -0000-30000 1 Tme seres plo of he seres D1D1Y 4 3 40 Monh Fgure 7. Tme seres plo of D1D1Y Tme seres plo of he seres D1D1Y s obaned o observe he behavour of he 1h dfferenced seres. Tme seres plo n Fgure 7 also suggess ha he seasonal dfferenced seres, D1D1Y, wh lengh 1 has no rend. However, s hard o come o a concluson abou he seasonaly. Thus he relevan sascal ess, ADF and Kruskal- Walls, wh ACF and PACF graphs are o be used o make a concluson on saonary condon of he seres D1D1Y. 4 1 56 0 64 7 4 Auocorrelaon 1.0 0. 0.6 0.4 0. 0.0-0. -0.4-0.6-0. -1.0 4 6 ACF of D1D1Y 10 1 14 Lag Fgure. ACF graph of he seres D1D1Y Excep a he frs lag all he spkes are small and hey are sgnfcan n he graph of ACF of he seres D1D1Y n Fgure. In addon, all he spkes afer frs lag are small and sgnfcan n he graph of PACF of he seres D1D1Y. Boh graphs ndcae ha, he new seres D1D1Y s saonary. Paral Auocorrelaon 1.0 0. 0.6 0.4 0. 0.0-0. -0.4-0.6-0. -1.0 4 6 PACF of D1D1Y 10 1 14 Lag Fgure 9. PACF graph of he seres D1D1Y Moreover, he p-value (0.00) of ADF es for D1D1Y shows ha, has no un roo. Therefore can be concluded wh 95% confdence ha, D1D1Y has no rend. A he same me, from he p-value (0.37) of Kruskal- Walls es, can be concluded ha he D1D1Y s now free from he seasonal paern. Therefore, he new seres D1D1Ys saonary and can be used o f he dynamc ransfer funcon model. 4.3. Fng dynamc ransfer funcon model The saonary daa D1D1Y feed o SAS program o f DTF model for unvarae me seres process. Accordng o s oupu, he 1 1 0 0 4 4
Forecasng Pos-War Tours Arrvals o Sr Lanka Usng Dynamc Transfer Funcon Modelng Mehod esmaed parameer s and p- value of he parameer esmaon s less han 0.0001. Therefore can be concluded wh 95% confdence ha, he parameer of he model s sgnfcan. Hence, he fed DTF model o predc nernaonal ours arrvals o Sr Lanka s: Yˆ Y 1 Y 1 Y 13 0.e 1 where ˆ Y s he esmaed ours arrvals a me Y 1, Y 1 and a me 1, 1 and 13 respecvely Y 13 are he precedng arrvals e 1 s he resduals a one precedng perod 1 4.4. Resdual analyss of he fed DTF model The resdual analyss o he fed model o check for he adequacy s carred ou as follows: 4.4.1. Normaly checkng The probably plo of resduals of fed DTF model s almos lnear n Fgure 10 and furher he p-value (0.0) of he Anderson Darlng es suggess ha he resduals follow normal dsrbuon. Thus can be concluded wh 95% confdence ha he resduals are normally dsrbued. 4.4.. Independency checkng From he plo of resduals versus predced values n Fgure 11, can be seen ha he resduals scaed randomly. Thus can be saed ha he resduals are ndependenly dsrbued. Furher, he p- value (0.6) of Lagrange s Mulpler es confrms ha, he resduals of fed DTF model have no auo correlaon. RESIDUALS 50000 5000 0-5000 -50000 50000 Scaerplo of RES vs FITS 75000 100000 FITS 15000 150000 Fgure 11. Plo of resduals versus predced values 4.4.3. Homoscedascy checkng In addon, he plo of resduals versus observaons order n Fgure 1 shows ha does no follow any sysemac paern and s symmerc abou 0. Thus can be clamed ha he varance of he resduals s consan hroughou. Moreover, he p-value (0.30) of Whe s general es confrms wh 95% confdence ha he resduals of fed DTF model have no heeroscedascy. Scaerplo of RES vs Order 99.9 99 Probably Plo of RES Normal - 95% CI 50000 5000 Percen 95 90 0 70 60 50 40 30 0 10 5 1 0.1-0000 -60000-40000 -0000 0 0000 40000 60000 0000 RESIDUALS Fgure 10. Normal probably plo of resduals RESIDUALS 0-5000 -50000 0 10 0 30 40 Order Fgure 1. Plo of resduals versus observaons order 50 60 70 0
S. R. Gnanapragasam and T. M. J. A. Cooray The resduals of he fed DTF model sasfy all necessary condons of he resdual analyss. Therefore, can be concluded ha he fed DTF model s sgnfcan. Hence, hs model can be recommended for predcng fuure nernaonal ours arrvals o Sr Lanka. 4.5. Model valdaon The plo n Fgure 13 clearly shows ha he predced value from he frs sx monhs n 0 perod s very closer o he acual observaons ha of n he same perods n 0. I s noed ha, n he frs hree monhs he predced values under esmae and however n he las here monhs hey over esmae. Geomerc represenaon of model valdaon n Fgure 13 ndcaes ha he predced values are closer o he observed values. However, has o be jusfed by usng sascal mehod. Fgure 13. Plo of observed and predced values To check he accuracy of fed model as model valdaon, MAPE sasc s calculaed from he perod from January 0 o June 0. The predced arrvals wh he observed arrvals n ha parcular perod are summarzed n Table. Accordng o he MAPE value (.63) n Table, can be concluded ha, he fed DTF model explans over 90% accuracy n erms of forecasng. Ths model can be srongly recommended o forecas fuure ours arrval o Sr Lanka. Table. Observed and predced arrvals n 0 Monh n 0 Observed Predced January 1940 179003 February 197697 19 March 1941 1790 Aprl 136367 144974 May 15044 1366 June 1103 134 MAPE.63 4.6. Forecasng fuure arrvals n 0 The fuure arrvals for las sx monhs n he year 0 are forecased and repored n Table 3. Table 3. Forecased arrvals n 0 Monh n 0 Predced Arrvals July 19,561 Augus 19,367 Sepember 6,131 Ocober 155,037 November 6,904 December,71 Toal Arrvals 1,104,71 Based on he monhly wse forecased arrvals from July 0 o December 0 n Table 3, can be expeced ha over 1.105 mllon ourss wll come o Sr Lanka n he las sx monhs n 0. I s approxmaely 14% ncrease n he ours arrvals over he las sx monhs n he year 015. 5. CONCLUSIONS Based on hs sudy, here we provde some recommendaons whch can be made o mprove he oursm ndusry n Sr Lanka. 5.1. Paern of ours arrvals o Sr Lanka Snce he ours arrvals have been dramacally ncreased n recen pas, parcularly afer he nernal conflc n Sr Lanka, s recommended for more aenon on hs ndusry s needed n
Forecasng Pos-War Tours Arrvals o Sr Lanka Usng Dynamc Transfer Funcon Modelng Mehod he counry. Snce he seasonal paerns are very clearly observed, s recommended o promoe some acves o arac he ourss especally n off perods. 5. Fed DTF model The fed DTF model o predc he nernaonal ours arrvals o Sr Lanka s Yˆ Y 1 Y 1 Y 13 0.e 1 wherey ˆ s he esmaed ours arrvals a me Y 1, Y 1 and a me 1, 1 and Y 13 are he precedng arrvals 13 respecvely e 1 s he resduals a one precedng perod 1 5.3. Predcon of fuure arrvals Over 1.1 mllon nernaonal ourss can be expeced n he las sx monhs of he year 0 and wll be 14% ncrease wh he year 015. Therefore s beer o be ready o faclae he needs of hose vsors n fuure. 5.4. Furher Work Snce oursm conrbues o naonal revenue of Sr Lanka n a large scale, s beer o carry ou a causal relaon sudy of nernaonal ours arrvals o Sr Lanka versus gross domesc produc (GDP) and hen would be useful o f a dynamc ransfer funcon (DTF) model by consderng GDP as he dependen varable and ours arrvals as he ndependen varable. REFERENCES ATHANASOPOULOS G & HYNDMAN RJ. Modellng and forecasng Ausralan domesc oursm. Preprn submed o Toursm Managemen. 006. Avalable n hp://www.robjhyndman.com/papers/ausours m.pdf. Accessed on 9 h Nov 0. BALAGUER J & CANTAVELLA JM. Toursm as a long-run economc growh facor: he Spansh case. Appled Economcs. 00; 34: 77-4. BERMUDEZ JD, SEGURA JV & VERCHER E. Hol- Wners forecasng: an alernave formulaon appled o UK ar passenger daa. Journal of Appled Sascs. 007; 34: 1075-1090. BURGER CJSC, DOHNAL M, KATHRADA M & LAW R. A praconers gude o me-seres mehods for oursm demand forecasng - a case sudy of Durban, Souh Afrca. Toursm Managemen. 001; : 403-409. CHANG JL, HSUEH FC & TIAN SL. Forecasng oursm demand usng me seres, arfcal neural neworks and mulvarae adapve regresson splnes: Evdence from Tawan. Inernaonal Journal of Busness Admnsraon. 011; (): 14-4. CHO V. Toursm forecasng and s relaonshp wh leadng economc ndcaors. Journal of Hospaly and Toursm Research. 001; 4: 399-40. CHO V. A comparson of hree dfferen approaches o ours arrval forecasng. Toursm Managemen. 003; 4: 33-330. CHU F. Forecasng oursm demand n Asan- Pacfc counres. Annals of Toursm Research. 199; 5(3): 597-615. DIMITRIOS G, DIMITRIS P & DANIEL S. Forecasng ours arrvals n Greece and he mpac of macroeconomc shocks from he counres of ourss orgn. Annals of Toursm Research. 01; 39 (): 641-666. DOMINIQUE MH, LEONARD JP & RANDALL LS. Marke response models- Economerc and Tme Seres Analyss (nd Edon). Jehoshua E, edor. Inernaonal Seres n Quanave Markeng. Kluwer academc. 00; 6.
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