FORECASTING THE DEMAND OF CONTAINER THROUGHPUT IN INDONESIA

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1 [Memoirs of Consrucion Engineering Research Insiue Vol.47 (paper) Nov.2005] FORECASTING THE DEMAND OF CONTAINER THROUGHPUT IN INDONESIA Syafi i, Kasuhiko Kuroda, Mikio Takebayashi ABSTRACT This paper forecass he demand of conainer hroughpu in Indonesia. The analysis was done in mulivariae auoregressive model. ADF es was used o check he saionariy of daa and order of inegraion. To find he exisence and he number of coinegraion relaionship, Johansen approach was used. The number of coinegraion relaions was esablished by a sequenial likelihood raio es on he rank of an esimaed parameer marix from VEC model and Impulse response funcion (IRF) was performed o know response o a shock of a variable of oher variables. The empirical analysis demonsraed ha he esimaion model provides indicaion of goodness-of-fi and of he forecasing poenial of he model. Mos of he model esimaion resul follows he long-erm developmen of he acual daa series closely. The impulse response of a shock of a variable o iself and oher variables die ou afer cerain period. This verified he sabiliy of all he esimaed models. The forecas of conainer hroughpu in Indonesia generaed by VECM indicaed he reasonable resul. 1. INTRODUCTION As he bigges archipelago counry in he world wih over 17,000 islands, he exisence of sea ransporaion in Indonesia play imporan role as he engine of growh, rade and developmen. According o Saisical book of Indonesia 1), from 1977 o 2002, he average annual growh of expor accouned for 7.96% and 8.47% for impor. Approximaely 90% of hose Indonesia s exernal rade is ranspored via sea. I indicaes he growh of exernal rade will coninue o increase and he imporance of sea ransporaion. As he rising rend of conainerized cargo in he world, Indonesian conainerized cargo also show he same paern wih average annual growh of 14.7% (from 1990 o 2002). In 2002, oal conainer handled in Indonesian conainer por was 4,539,884 TEU, wih he rank posiion of 15 from he world conainer raffic (Conainerisaion Inernaional book, 2004) 2). The increasing rend will coninue o he fuure year due o he economic developmen and rising share of conainerized cargo for foreign and domesic rade. The high growh of conainerized cargo in Indonesia has compelled he improvemen por performance and faciliy, and he consrucion of new por. One of he key issues for developing por faciliies and consrucion of new por is informaion abou he demand of conainer hroughpu. In por planning and developmen, forecasing of conainer hroughpu demand is a necessary sep in predicing fuure revenues for a proposed developmen projec. Hence, analysis of conainer hroughpu demand is very imporan for por managemen. Moreover, i also will be useful for he fuure liner shipping sraegy in deermining services nework. Unforunaely, up o now, here is almos no published paper deal wih forecasing he demand of conainer hroughpu in Indonesia. In ligh of he above consideraion, his paper aemps o solve he problem. The approaches in esimaing demand of rade marke are ofen associaed wih ime series daa. The sandard classical mehods such as he ordinary leas squares (OLS) and hypoheses esing are based on he assumpion ha he ime series are saionary. Broadly, a series is saionary if is means and variance are consan over ime and he value of he covariance beween he wo ime periods depends only on he disance or gap or lag beween he wo ime periods and no he acual ime a which he covariance is compued (Gujarai, 2003) 3). A non-saionary series is said o be inegraed of order d or I(d) if i mus be differenced d imes o make i saionary. Since he disribuion heory in nonsaionary series is differen from he sandard Gaussian asympoic heory, applicaion of classical esimaion mehods such as OLS for esimaing relaionships beween non-saionary variables may cause o spurious regressions which means he regression yields look good wih high R 2, bu have no meaning. The problems wih esimaion of single equaion framework wih inegraed or non-saionary variables are: non-sandard disribuion of coefficien esimaes,

2 error process no being saionary, explanaory variables generaed by processes ha display auocorrelaion, exisence of more han one coinegraing vecor and failure of weak exogeneiy (Banerjee e al. 1986) 4). To solve he problem of inegraed variables, we can use coinegraion es and esimaion of vecor error correcion model (VECM) o disinguish beween shor run and long run relaionship. The exisence of coinegraion can preven he errors in he long run relaionship from becoming larger and larger. This is modeled hrough he popular economerics specificaion of error correcion model which inegraes he long-run equilibrium analysis and shor-run dynamic adjusmen by including in he shor-run dynamic models a measure of disequilibrium in he las period. The aim of his paper is o forecas he demand of conainer hroughpu in Indonesia by presening mulivariae auoregressive model. The res of his paper is organized as follows. Secion 2 describes daa collecion. Secion 3 describes economerics model and mehodology. Secion 4 provides empirical resuls and discussion. Finally, conclusion is given in secion 5. All calculaion concerning daa analysis and model esimaion was performed hrough TSP sofware. 2. DATA In forecasing he demand of conainer hroughpu, some variables are included, namely, conainer hroughpu (TEU), GDP (million US $), populaion, expor (million US $), and impor (million US $) wih ime series daa from 1982 o Since he conainer por characerisic and managemen policy ime series daa is difficul o find, he model does no consider he por characerisic and managemen policy. Conainer hroughpu daa was aken from Conainerisaion Inernaional book, while Saisical book of Indonesia provides GDP, populaion, expor, and impor daa. The ime series daa of he above variables is shown in Table 1. Table 1 Conainer hroughpu, GDP, populaion, expor and impor in Indonesia Con. GDP Populaion Expor Impor (TEU) (Million US $) (Million US $) (Million US $) ,352 90, ,307,298 3,929 13, ,379 78, ,702,058 5,005 12, ,093 83, ,171,503 5,870 11, ,619 87, ,629,618 5,869 8, ,008 67, ,930,442 6,528 9, ,131 77, ,986,776 8,580 11, ,267 86, ,722,564 11,537 12, ,256 99, ,502,125 13,480 15, , , ,379,000 14,604 19, ,156, , ,320,816 18,248 23, ,329, , ,329,109 23,296 25, ,600, , ,387,039 27,077 26, ,912, , ,514,264 30,360 29, ,048, , ,755,000 34,954 37, ,764, , ,916,781 38,093 39, ,478, , ,082,865 41,821 37, ,000, , ,312,593 40,976 24, ,551, , ,587,425 38,873 20, ,797, , ,843,000 47,757 27, ,901, , ,724,802 43,685 25, ,539, , ,003,000 45,046 24,763 Source : Conainerisaion Inernaional book and Saisical book of Indonesia, various years 3. ECONOMETRICS MODEL AND METHODOLOGY 3.1 Uni roo es Before esimaing coinegraion space and deerminaion of coinegraion rank, i is imporan o es he order of inegraion of each variable or o check he exisence of uni roos, which make he series non-saionary. Tesing for

3 uni roos has become a sandard ool in modern economerics daa analysis. Convenional saisical analysis assumes ha he ime series a hand are saionary, and a uni roo implies non-saionary (Mills, 1990) 5). Tesing for uni roos enables direc inference on he degree of non-saionary and subsequen degree of differencing o ransform a ime series o saionariy. Several es are available in he lieraure. In his paper, we resric o he augmened Dickey-Fuller (ADF) es (Dickey and Fuller, 1979) 6). The basic equaion of ADF ess is as follows: ΔY m 1 + β 2 + δy 1 + α i ΔY 1 + ε i= 1 = β (1) where ε is a pure whie noise error erm and ΔY 1 = ( Y 1 Y 2), ΔY 2 = ( Y 2 Y 3), ec. β 1, β 2, δ, α i are parameers and is he ime or rend variable. The number of lagged difference (m) erms o include is ofen deermined empirically, he idea being o include enough erms so ha he error erm is serially uncorrelaed. The null of non-saionariy is equivalen o esing he significance of δ = 0; ha is, here is a uni roo - he ime series is nonsaionary. The alernaive hypohesis is ha δ is less han zero; ha is, he ime series is saionary. 3.2 Coinegraion Having esablished uni roo es, o find he exisence and he number of coinegraion relaionship, we can perform coinegraion es. The fundamenal idea of coinegraion is ha alhough wo series or more are non-saionary, or inegraed, such ha firs difference are required o obain saionariy, a liner combinaion of hese series can be saionary. This linear combinaion is known as coinegraing vecor or coinegraing relaionship. The coinegraing relaionship may, herefore, be hough of, as a long-run seady sae of dynamic relaionship hough here can be finie shor-run variaions around he long-run relaionship. The variables comprising he coinegraing relaionship would no drif oo far apar relaive o each oher owing o equilibraing forces ha end o keep hem ogeher. Therefore, his idea of coinegaion is in inuiive consonance wih he observed co-movemen of number of economic variables. The concep of coinegraion was inroduced by Engle and Granger, ) provided he issue of inegraing shor-run dynamics wih long-run equilibria. Alhough widely used in empirical research, he Engle-Granger (EG) mehod has several shorcomings such as he size disorion, non-unique sample properies depending on he variable used for normalizaion and is inabiliy o idenify muliple coinegraing vecors (Banerjee e al., 1993) 8). The ohers mehods for esimaion of long-run equilibrium relaionship have been proposed by Sock (1987) 9) which suggesed non-linear leas squares (NLS), Engle and Yoo (1991) 10) suggesed hree seps procedure, maximum likelihood model was proposed Johansen (1988,1991) 11),12) and Johansen and Julius (1990,1994) 13),14). Gonzalo (1994) 15) has shown ha Johansen approach has beer properies han oher esimaors and heir finie sample properies are consisen wih asympoic resuls. In his paper we concern o he Johansen and Julius (1990,1994) procedure. The Johansen echnique proceeds by ransforming a vecor auoregressive model in levels ino an equivalen differenced form, including lagged differences and an implied se of coinegraing vecors as he righ hand explanaory variables. The differenced form is hen esimaed by using maximum likelihood mehods. The implied vecor coinegraing vecors are exraced using reduced rank regression echnique. By Johansen approach, VECM can be esimaed in which error correcion erm is included in each equaion. Two ypes of likelihood raio es saisics can be derived from Johansen procedure, namely, he race es saisics, k race( r k) = T ln(1 λ ) (2) i= r+ 1 and max-lamda es saisics, i λ max = T ln( 1 λr+ 1) (3) where r is coinegraion relaionship, k is number of variables, T is number of observaions, and λ i is he i-h eigenvalue. If race es saisics (r k) and λ max greaer han c k, criical value, hen rejec H(r). H(r) denoes he hypohesis ha he rank of Π (see equaion 4 for erm Π) in H(k) is r; for example, H(0) saes he rank of Π is 0, H(1) saes he rank of Π is 0 or Vecor auoregressive model A vecor auoregressive (VAR) model is a mulivariae ime series model whose general mahemaical form wih K- dimensional is given by he following formulaion:

4 Y = Π1 Y Π ky k + ΦD + ε (4) where Y = ( y 1,... y KT ), Π i are K x K coefficien marix, k is he order of he VAR, ε is residual error-erm, and ~ N( O, Σ) (where Σ is a K x K posiive definie marix). The deerminisic erm D can conain a consan, a liner erm, ε seasonal dummies, inervenion dummies, or oher regressors ha we consider fixed and non-sochasic. The Granger represenaion heorem saes, under he hypohesis of coinegraion, he VAR can be wrien as a vecor error correcion (VEC) model as he following formulaion. ΔY = k 1 Γi ΔY i + ΠY 1 i= 1 + ΦD + ε (5) The K x K marix Π can be expressed as Π = αβ ' where boh α and β are K x r marix of full rank. For he model used in his sudy, K = 5, Y = (Conainer, GDP, Populaion, Expor, Impor). β is a marix represening coinegraion relaion such ha β Y is saionary and is inerpreed as long run equilibrium relaionship beween he joinly deermined variables. I is imporan o emphasize ha one can no esimae he individual coefficien of β unless one specifies a normalizaion or idenificaion. There may be sochasic shocks forcing o he sysem during he shor-run, however, wih he exisence of coinegraion relaionship, here will be forcing variables which cause he sysem converge o he long-run relaionship. The deviaion from equilibrium relaions β Y form a saionary process and α is he speed of adjusmen coefficien for he equaion. Under he reduced rank hypohesis of he Π marix, he maximum eigenvalue and he race saisics are employed o ascerain he number of coinegraing vecor. If Π has zero rank, no saionary linear combinaion can be idenified, i.e. he variables in Y are no coinegraed. If he rank r of Π is greaer han zero, here exis r possible saionary linear combinaions. The shor-run models are esimaed consisenly afer aking ino accoun parameric resricions implied by long-run relaionships. The vecor error-correcion model (VECM) allows a number of variables o adjus simulaneously a differen raes in response o shor run disequilibrium. The approach provides a good approximaion o he unknown daa-generaing process since he heory is ofen no adequae for describing he dynamic adjusmen process. 3.4 Impulse response funcion In applied work, i is ofen ineres o find he response of one variable o an impulse in anoher variable in a sysem ha involves a number of variables as well. If here is a reacion of one variable o an impulse in anoher variable we may call he laer causal for he former. The impulse response funcion (IRF) race ou he moving average represenaion of he sysem and describes how he variable responds over ime o a single surprise increase in iself or in any oher variables. The variance decomposiion ells us how much of he average squared forecas error variance of one variable a he k-h sep ahead is associaed wih surprise movemens in each variable of he model. Boh he innovaion accouning ools can be used o make inferences regarding he naure of dynamic ineracions beween variables and variable exogeneiy and Granger non-causaliy. For, example, if he variance of a paricular variable is explained primarily by is own innovaions hen he variable is weakly exogenous o he sysem. The impulse responses or dynamic mulipliers can be obained from infinie moving average represenaion of a K-dimensional VAR model (Lukepohl, 1991) 16) as follows: Y + = A1 Y ApY p u (6) n Φ (ϕ = Φ A (7) n ik, n ) j= 1 n j j where n =1,2,..,, Φ 0 = I K, A j = 0 for j > p and ϕ ik,n (he ik-h elemen of Φ n ) represens he response of variable y i o a shock in variable k, n periods ago. Since he covariance marix of a VAR, Σ u, is posiive definie, i is essenial o ransform he innovaion of he sysem ino a conemporaneously uncorrelaed form. If disurbance across equaions are correlaed, an innovaion in one of he equaions will describe is dynamic response o a complex combinaion of several economically inerpreable shocks. In order o have economically inerpreable shocks, he orhogonalisaion requires imposiion of resricions on conemporaneous coefficiens of underlying srucural VAR and hence imposing a paricular causal order on he relaionship. The orhogonalised impulse responses proposes by Sims (1980) 17), which derived from he Choleski decomposiion of he variance-covariance marix of he VAR, are no in general unique since hey depend on he paricular orderings of

5 he variables in he VAR. They are unique only if he variance-covariance marix is diagonal. However, orhogonalized impulse responses have advanages since differen orhogonalised ordering give rich addiional informaion abou he dynamic of he model as some variables migh consisenly across differen orderings. The generalised impulse responses proposed by Koop e al (1996) 18) overcome he non-uniqueness problem of he orhogonalised impulse responses. The generalized impulse responses have advanage ha hey ake ino accoun he properies of he daa generaing process. However, he generalized impulse responses have disadvanage since hey are derived solely from daa. On his sudy, we resric he analysis hrough he orhogonalised impulse responses. The impulse responses, in he conex of vecor auoregression, are an efficien ool o deermine he sabiliy of he esimaed equaion. The sabiliy is indicaed by he convergence of he impulse response o zero. 4. EMPIRICAL RESULT AND DISCUSSION 4.1 Uni roo es Prior o perform uni roo ess, he logarihmic of he original series have been used in order o reduce he possibiliy of heeroskedasiciy and o make he series more comparable. As previously menioned, he uni roo es is inended o find he saionariy of daa and inegraed order. The resuls of uni roo ess by augmened Dickey-Fuller (ADF) are presened in Table 2. ADF ess were performed on he full sample for he period boh on levels as well as differenced forms o find he order of inegraion. All he variables are found o be non-saionary a heir levels. A nonsaionary series can be made saionary by differencing. The variables become saionary a firs difference, or inegraed order 1 or I(1) since he null of uni roo is rejeced a firs difference. Table 2 Uni roo es by Augmened Dickey-Fuller (ADF) Series Level Firs difference Inegraed order log(conainer) * I(1) log(gdp) * I(1) log(populaion) * I(1) log(expor) * I(1) log(impor) * I(1) Noes: The Dickey-Fuller regressions include an inercep and a linear rend erm (random walk wih deerminisic rend). The null hypohesis is ha he series is non-saionary. This hypohesis is rejeced if he es saisics is larger in absolue value han he criical value. Criical value for ADF es a 5% level of significance is * denoes rejecion of he null hypohesis of non-saionary a he 5% significance level. 4.2 Coinegraion es To find he exisence and he number of coinegraion relaionship, we compue he maximum eigen values (λ max ) and he race saisics by applying Johansen procedure. The number of coinegraion relaions is esablished by a sequenial likelihood raio es on he rank of an esimaed parameer marix from VEC model. Resuls of hese ess wih 95% criical values are repored in Table 3. The λ max and race es rejec he null hypohesis of no coinegraion (r = 0) a a 5% significance level. However, neiher of he crieria can rejec he null hypohesis of r 4 agains he alernaive hypohesis of r = 5 a 5% significance level. We, herefore, can conclude here exis four coinegraion relaionship a 5% significance level, and here exis considerable evidence of he exisence of long-run relaionship. Table 3 Coinegraion es by Johansen procedure λ max Trace es Ho Null H1 Tes 95% Criical Tes 95% Criical (alernaive) saisic value saisic value r = 0 r = * * r 1 r = * * r 2 r = * * r 3 r = * r 4 r =

6 Noe: r indicaes he number of coinegraion relaionships. The null hypohesis is if here is no coinegraion. This hypohesis is rejeced if λ max and race es saisics is larger han he criical value. * denoe rejecion of null a 5% significance level. The opimal lag lengh of VAR was seleced by AIC. Opimal order of VAR was Vecor error correcion model (VECM) As saed earlier ha under he hypohesis of coinegraion, he VAR can be wrien as a vecor error correcion model (VECM). In his secion we show he regression resul of vecor error correcion model based on he Johansen procedure. Coefficien marix of VECM is given in Table 4. To evaluae he accuracy of he model, we generae a series over a sample period and observe how well his esimaion series mach wih he acual daa. The process is sraighforward; he firs and second daa in he sample are fed in he model as saring values for he calculaion of ΔY as given in equaion 5. Adding he laer o he saring value provides he model esimaion Y for he hird year in he sample. The process is repeaed for each year in he sample period. The esimaion series (in logarihmic) is ransformed again o he original value (level). Comparison of he model esimaion Y wih he acual daa is shown in Figure 1. The figure provides indicaion of goodness-of-fi and of he forecasing poenial of he model. Mos of he model esimaion resul follows he long-erm developmen of he acual daa series raher closely. Since here was a shock of GDP due o he economic crisis in 1997, he esimaion resul of GDP and impor around 1997 are significanly differen wih he acual daa. Table 4 Coefficien marix of vecor error correcion model Coef. marix of he lagged variable in difference Coef. marix of he lagged variable in levels Δ Y Δ X Δ Z Δ E Δ I Y-1 X-1 Z-1 E-1 I-1 C onsan Δ Y coef sd.error value Δ X coef sd.error value Δ Z coef sd.error value Δ E coef sd.error value Δ I coef sd.error value Noe: Y = C onainer,x = G D P,Z = P opulaion,e = E xpor,i = im por. TEU 5,000,000 4,500,000 4,000,000 3,500,000 3,000,000 2,500,000 2,000,000 1,500,000 1,000, ,000 0 C onainer hroughpu (TEU) Acualdaa M odelesimaion million US $ 250, , , ,000 50,000 0 G D P (m ilion U S $) A cualdaa M odelesimaion

7 (a) (b) 220,000,000 P opulaion 60,000 Expor (m ilion US $) 210,000,000 50, ,000, ,000, ,000,000 milion U S $ 40,000 30,000 20, ,000,000 10, ,000, Acualdaa M odelesimaion A cualdaa Modelesimaion (c) (d) 45,000 Im por (m ilion U S $) 40,000 35,000 milion US $ 30,000 25,000 20,000 15,000 10,000 5, A cualdaa M odelesimaion (e) Fig. 1 Comparison beween acual daa and model esimaion (a) Conainer hroughpu, (b) GDP, (c) Populaion, (d) Expor, (e) Impor 4.4 Impulse response funcion Impulse response funcion was performed o know response o a shock of a variable of oher variables. If a variable does reac o he shock of anoher variable, i is said ha he laer causes former. We found he impulse response of a shock of each variable o i self and oher variables die ou afer cerain period as depiced in Figure 2. This verifies he sabiliy of all he esimaed models. Figures 2 (a) plo he IRF of conainer hroughpu o iself and ohers variables. A shock of conainer hroughpu is responded posiively o iself and oher variables as well; he effecs las for 5-6 periods. The imporan hing from he figure is GDP and expor reacs more posiively han impor and populaion. I can be inerpreed as increasing of conainer hroughpu will give more significan impac on GDP and expor volume han populaion and impor. This illusraion also maches wih Figure 2 (a) and (c). A shock of GDP provides posiive responses o iself and oher variables as shown in Figure 2 (b); i is easy o undersand, increasing in GDP will increase expor and impor which in urn increasing oal conainer hroughpu. The growh of populaion will direcly impac on expor and impor cargo which in urn increasing conainer hroughpu, his condiion is also refleced in Figure 2 (c). As he indicaor of economic developmen, he growh of expor will cause rising in GDP and ohers facors as depiced in Figure 2 (d) which shows a shock in expor give posiive responds o

8 iself and oher variables. Figure 2 (e) shows ha a shock of impor is responded posiively o iself and all variables excep expor, and conainer hroughpu is responded more posiively han oher variables. I means he rising of impor will give more significan impac on he increasing of conainer hroughpu han oher variables Im pulse responses o a shock of conainer Im pulse responses o a shock of G D P Horizon Conainer GDP Populaion Expor Impor (a) Im pulse responses o a shock of populaion (c) Horizon Conainer GDP Populaion Expor Im por Horizon Conainer GDP Populaion Expor Impor (b) Im pulse reponses o a shock of expor Horizon C onainer GDP Populaion Expor Im por (d) Im pulse responses o a shock of im por Horizon Conainer GDP Populaion Expor Im por (e) Fig. 2 Impulse responses of a shock of (a) conainer hroughpu, (b) GDP, (c) Populaion, (d) Expor, (e) Impor

9 4.5 Forecasing of conainer hroughpu Since he objecive of his sudy is o forecas he conainer hroughpu, we only show forecasing of conainer hroughpu from 2003 o In forecasing he model, we adop he following assumpions: - Variables included in he model are conainer hroughpu, GDP, populaion, expor and impor. - Saisical srucure of he model will no change subsanially in he fuure. - Por managemen policy is no included in he model. - There is no significan change in liner shipping nework. The procedure for forecasing is he same wih he procedure o generae a series over a sample period as menioned earlier. The las known value of ime series is used as saring value for he calculaion of ΔY +1. Adding he laer o he saring value provides he model esimaion Y +1 for he +1 in he forecasing year. The process is repeaed for each year up o The forecasing resul is shown in Figure 3. The figure indicaes conainer hroughpu increases from 4,982,755 TEU in 2003 o 18,712,042 TEU in 2015 wih he average annual growh 11.69%. If we compare wih he acual daa from 1982 o 2002 wih he average annual growh of conainer hroughpu was 20.72%, he forecasing resul seems o be reasonable. Moreover, he proporion of goods raded inernaionally in conainer is expeced o increase, as radiional bulk cargo such as coal, grain and sal are increasingly being shipped in conainer. Wih his huge poenial demand of conainer hroughpu, Indonesian por auhoriies should implemen he bes sraegy for developing he fuure conainer por in order o provide beer qualiy services for shippers and liner shipping companies. Beside ha, in order o mee he fuure demand, he consrucion of new pors are ineviably due o he curren conainer pors capaciy can no handle such huge conainer demand. Forecasing of conainer hroughpu in Indonesia (TEU) 20,000,000 18,000,000 16,000,000 14,000,000 12,000,000 TEU 10,000,000 8,000,000 6,000,000 4,000,000 2,000, Fig. 3 Forecasing of conainer hroughpu in Indonesia 5. CONCLUSION The high growh of conainerized cargo in Indonesia has compelled he improvemen por performance and faciliy, and he consrucion of new por. One of he key issues for developing por faciliies and consrucion of new por is informaion abou he demand of conainer hroughpu. In por planning and developmen, forecasing of conainer hroughpu demand is a necessary sep in predicing fuure revenues for a proposed developmen projec. Hence, analysis of conainer hroughpu demand is very imporan for por managemen. This paper presened forecasing demand of conainer hroughpu in Indonesia. The analysis was done in mulivariae auoregressive model. ADF es was used o check he saionariy of daa and order of inegraion. Johansen approach was used o find he exisence and he number of coinegraion relaionship. The number of coinegraion relaions was esablished by a sequenial likelihood raio es on he rank of an esimaed parameer marix from VEC model. Impulse response funcion (IRF) was performed o know response o a shock of a variable of oher variables. The empirical analysis demonsraed ha he esimaion model provides indicaion of goodness-of-fi and of he forecasing poenial of he model. Mos of he model esimaion resul follows he long-erm developmen of he acual daa series raher closely. The impulse response of a shock of a variable o iself and oher variables die ou afer cerain period. This verified he sabiliy of all he esimaed models. The forecas of conainer hroughpu in Indonesia

10 generaed by VECM indicaed he reasonable resul. In 2015, we esimaed conainer hroughpu is 18,712,042 TEU wih he average annual growh 11.69%. Wih his huge poenial demand of conainer hroughpu, Indonesian por auhoriies should implemen he bes sraegy for developing he fuure conainer por in order o provide beer qualiy services for shippers and liner shipping companies. Beside ha, in order o mee he fuure demand, he consrucion of new pors are ineviably due o he curren conainer pors capaciy can no handle such huge conainer demand. REFERENCES: 1) Saisical book of Indonesia, Cenral Bureau of Saisics (BPS), Saisics Indonesia, various years. 2) Conainerisaion Inernaional book, Informa, UK, various years 3) Gujarai, D.N.: Basic Economerics, MCGraw-Hill, (2003) 4) Banerjee, A., Dolado, J.J., Galbraih, J.W., and Hendry, D.F: Exploring equilibrium relaionship in economerics hrough saic models: some Mone-Carlo evidence, Oxford Bullein of Economics and Saisics, 48, pp , (1986). 5) Mills, T.C.: Time Series Techniques for Economiss, Cambridge Universiy Press, Cambridge, Unied Kingdom (1990). 6) Dickey, D.A., and Fuller, W.A.: Disribuion of Esimaors for Auoregressive Time Series Wih A Uni Roo, Journal of he American and Saisics Sociey, 74, pp (1979) 7) Engle, R.F and Granger, C.W.J.: Coinegraion and Error-correcion: represenaion, esimaion, and esing, Economerica 55, (1987) 8) Banerjee, A., Dolado, J.J., Galbraih, J.W., and Hendry, D.F: Coinegraion, Error Correcion, and he Economeric Analysis of Non-saionary Daa, Oxford Universiy Press, Oxford, (1993) 9) Sock, J.H.: Asympoic Properies of Leas Square Esimaion of Coinegraing Vecors. Economerica, 55, , (1987) 10) Engle, R.F., and Yoo, B.S: Coinegraed Economic Time Series: An Overview wih New Resuls. Oxford Universiy Press, Oxford, U.K. (1991) 11) Johansen, S.: aisical Analysis of Coinegraing Vecors, Journal of Economic Dynamic and conrol, 12, pp , (1988) 12) Johansen, S.: Esimaion and Hypohesis Tesing of Coinegraed Vecors in Gaussian Vecor Auoregressive Models, Economerica, 59, pp , (1991) 13) Johansen, S., and Julius, K.: The Full Informaion Maximum Likelihood Procedure for Inference on Coinegraion wih Applicaion o The Demand of Money, Oxford Bullein of Economics and Saisics, 52, pp , (1990) 14) Johansen, S., and Julius, K.: Idenificaion of The Long-run and The Shor-run Srucure: An Applicaion o The ISLM Model, Journal of Economerics, 63, pp. 7-36, (1994) 15) Gonzalo, J.: Five Alernaive Mehods of Esimaing Long-run Equilibrium Relaionships, Journal of Economerics, 60, pp , (1994) 16) Lukepohl, H.: Inroducion o muliple ime series analysis, Springer-Verlag, (1991) 17) Sims, C.A.: Macroeconomics and realiy, Economerica, 48, pp. 1-48, (1980) 18) Koop, G., M.H. Pesaran, and Porer, S.M.: Impulse Response Analysis in Nonlinear Mulivariae Models, Journal Of Economerics, 74, , (1996) AUTHORS Syafi i Kasuhiko Kuroda Mikio Takebayashi Ph.D. suden, Graduae School of Science and Technology, Kobe Universiy Saff, Dr. Eng., Professor, Transporaion Planning Saff, Dr. Eng., Associae Professor, Transporaion Economy