A study of Forecasting Methods for the Cross-Straits Trade

A study of Forecastig Methods for the Cross-Straits Trade Departmet of Tourism ad Leisure Maagemet Chi-Mi Istitute of Techology, Istructor Departmet of Idustrial Egieerig ad Maagemet Uiversity of Yua-Ze, Ph.D. studet 0, Hsue-Fu Rd., Tou-Fe, Miao-Li 35, Taiwa, R.O.C. Tel: 886-37-605670 Fax: 886-37-605674 s99507@mail.yzu.edu.tw Abstract: - Both Chia ad Taiwa have already obtaied the WTO membership ad officially participated i the iteratioal trade system. The ecoomic ad trade relatioship betwee Chia ad Taiwa should develop by followig the rules of iteratioal trade developmet. Due to the high rate of growth of the ecoomic ad trade exchage betwee Chia ad Taiwa, up util ow, Taiwa has relied heavily o the mailad for its exports ad vice versa. This study is iteded to probe the issue. We established forecast models for the cross-strait trade through the methods of grey forecastig, simple regressio, ad expoetial smoothig. I additio, it tests the accuracy of the forecast models through relevat data, ad used MAPE ad MSE to evaluate the forecast models. The results idicate that for model selectio, it is more correct to perform the forecast o trade volume based o the statistical iformatio released by Taiwa Customs. It ca be see from this model, the cross-strait trade volume i 008 will exceed USD $73,500 millio, with imports ito Taiwa above USD $36,373 millio. It is hoped to uderstad the cross-strait trade growth tred i the future with the forecast model established by our research istitute ad thus providig the govermet or the agecies cocered with referece iformatio for makig their cross-strait policies. Key-words: - Cross-strait Trade, Grey Forecast, Expoetial Smoothig, Simple Regressio. INTRODUCTION Accordig to Maagemet Tred of SMEs [], it is idicated that the global ecoomic situatio i 007 was fairly uquiet, maily because of the U.S. sub-prime problems ad the iteratioally rocketig oil price, with lots of regios ad areas affected i depth, ad leadig to a stir i the global ecoomy. Lookig back at the performace to Taiwa s exports to Chia, the cross-strait trade volume i 007 exceeded USD $70,000 millio at the first, ad the ratio of export to import reached its highest poit ever followig a growth patter of two digits cosecutively sice 00. However, it also behaved like a polarizig pheomeo. The growth rate of exports hit its highest poit, but imports dropped to the lowest it has bee i the last three years, which led the highest trade surplus i history. Chia is still the first major trade parter of Taiwa, the first major export market, the secod major source of import ad the biggest source of trade surplus. Due to the ecoomic ad trade exchage betwee Chia ad Taiwa growig at a high speed, up util ow, Taiwa has heavily relied o the mailad for its exports ad vice versa. This study iteds to discuss the issue of which directio will the cross-strait trade develop towards? This paper establishes a forecast model for the cross-strait trade growth based o the forecast mode, GM (, ), of the grey forecast uder the grey theory. I additio, as for the applicatio of multiple forecast methods, the data closest to the curret time 6

ca represet the future data more accurately tha the historical data, ad the expoetial smoothig method deals with the time related data i the simplest ad most logical way [3]. Therefore, this paper also tests the correctess of the forecast model with the expoetial smoothig method ad the simple regressio mode as well as through the related data such as MAPE ad MSE.. Literatures Review. Related Literature about Forecast Methods Zhag[], with the expoetial smoothig method ad the Bayes auto regressive aalysis method, suggested that i order to reduce the potetial ivetory cost, usig the forecast result obtaied by the expoetial smoothig method is better tha that by the Bayes regressio method. Che[6] foud that whe forecastig the future price of crude oil ad chage i the exchage rate with ARIMA, (the auto regressive itegrated movig average) usig the expoetial smoothig method has a better forecast ability for the purpose of icreasig profit. Syder etc.[8] suggested that the expoetial method is most commoly used for ivetory cotrol to accurately forecast the ivetory volume ad the lead time demad i order to provide help to ivetory maagemet ad defie the most suitable strategy. Syder etc.[9] forecasted the lead time demad ad calculated the safety ivetory with the expoetial smoothig method i order to adjust the seasoal demad ad peak demad of commodities, ad they foud out that the safety ivetory forecast for the seasoal demad is highly accurate. Zhog ad Li[3]performed a forecast of the Baltic Sea vessel freight idex with the expoetial smoothig method ad grey forecast mode, ad they foud out that the expoetial smoothig method has a excellet forecast ability. Che[5], performed forecast of the Baltic dry idex (BDI) with the expoetial smoothig method, ARIMA mode ad grey theory, ad he foud out that the forecast doe with the expoetial smoothig method ca reach a accuracy of higher tha 90 %. Deg[5] proposed the grey theory i 98, maily for establishig a grey mode to perform forecast ad decisio-makig. The grey forecast has bee extesively employed ad has achieved a lot i recet years. Che[4] ad Huag etc. [], [] forecasted the goods demad at shippig ceters outside Taiwa usig the grey theory, aalyzed the data of mothly ad quarterly shippig volumes from May 997 to April 998, ad forecasted the mothly ad quarterly shippig volumes respectively with the grey mode GM (,). Zhog etc. [] established the BDI forecast mode with the GM (, ) i order to uderstad the tred of freight ad charterig rate chages ad reduce the shippig market risk effectively. Huag etc. [3], lookig at the import ad export volumes by cotaier i Taiwa, established GM (, ) with the grey theory, costructed a model with the data obtaied from differet years, performed accuracy compariso amog differet modes, ad foud out that the GM (, ) is suitable for forecastig seaport cotaier shippig volumes with data for a period of four to te 0 years. Ma[7] used GM (,) for forecastig the growth rates of the ecoomy ad shippig volume, umber of icomig ad outgoig vessels, umber of cotaiers loaded ad uloaded ad goods throughput. It was foud out that the grey forecast mode (GM) was reliable ad ratioal. For forecastig with the grey theory, Tseg ad Tzeg[0] believed that four sets of data were sufficiet to produce excellet forecast results, ad could reduce the forecast error sigificatly. Zhuag[4] forecasted the productio value ad growth rate for the game market ad foud out that the best forecast results were achieved with the four data to geerate of GM (,).. Aalysis of Cross-strait Trade Situatio i 007[] There was little exchage betwee Chia ad Taiwa before Chia adopted the reform ad opeig policy. Sice the Taiwa govermet agreed to coduct trade activities with Chia via a third regio i 987, the cross-strait trade via Hog Kog has grow at a ubelievably high rate. 6

Except for the missile trial lauchig crisis i 996, which led to a egative growth of the cross-strait trade volume the first time, the trade volume betwee Chia ad Taiwa, whether accordig to the statistics doe by Hog Kog, Taiwa Customs, or the Customs of Chia, has bee growig at a icreasigly high speed. Accordig to the statistics released by the Bureau of Foreig Trades uder the Miistry of Ecoomic Affairs, Executive Yua of the Public of Chia, the amout of ivestmet from Taiwa to Chia from Jauary to August 007 reached USD $6.3 billio, a icrease of 35.8 % over the same period of the previous year. The ivestmet evets 693 was a slight icrease of.6 %, ad the amout of each ivestmet teded to icrease gradually. As estimated by the Bureau of Foreig Trades uder the Miistry of Ecoomic Affairs, the trade volume from Taiwa to Chia from Jauary to October 007 reached USD $49.990 billio, a icrease of 5.3 % over the same period of the previous year, accoutig for.4 % of the foreig trade volume of Taiwa. To classify ivestmets by regio, from Jauary to August, the approved ivestmet cases orieted with Chia were maily cocetrated i the regios such as: Jiagsu Provice (accoutig for 37.87 %), Shaghai Muicipality (8.79 %), Cato Provice (8.44 %), Zhejiag Provice (6.5 %) ad Fujia Provice (4.5 %) etc., amoutig to about 85.5 % of the total approved ivestmet. Whe classifyig by idustry, the five leadig idustries are the electroics parts ad compoets maufacturig idustry (accoutig for 8.56 %), the computer, electroic products, ad optic products maufacturig idustry (5. %), the power equipmet maufacturig idustry (9.73 %), the wholesale ad retailig idustry (5.5 %) ad the plastic products maufacturig idustry (4.8 5%), amoutig to 63.40 % of the total approved ivestmet for this period. Taiwa Customs, Hog Kog Customs ad the Customs of the Mailad of Chia have kept their respective trade data i detail. But due to differet samplig methods, great differeces exist amog the data by these three customs. The Amout of Export from Taiwa to Hog Kog doe by Taiwa Customs is far higher tha that of The Amout of Import to Hog Kog from Taiwa. Therefore, the exports from Taiwa to Chia will be uderestimated if it is oly based o the statistics doe by Hog Kog Customs. Therefore, this paper performs aalysis o the cross-strait trade based o the data released o the Mothly Cross-strait Ecoomic Statistics. Accordig to the results from the related study with the grey theory, it is suggested that grey forecast mode is suitable for performig aalysis with short-term data or cases where complete data is uavailable. There has log bee high ucertaity i the cross-strait market, ad the grey theory has the feature of icomplete iformatio system eviromet. Therefore, this paper establishes the model with the commoly used four rules of the grey theory to costruct the forecast mode for the cross-strait trade growth ad explore the growth tred, ad it also carries out the accuracy compariso with the expoetial smoothig method ad the regressio mode. 3. MODEL FORECAST AND EVALUATE 3. Grey Forecast Method The grey system theory, proposed by Deg[5], is a system aalysis method, uder the coditios of icomplete iformatio ad ucertai cause-effect relatioship. The covetioal forecast method requires lots of data, amely, it is limited by the assumptios that the matrix assigmet shall follow. Nevertheless, the grey system ca overcome all the above limitatios, ad its most strikig feature is that oly four sets of data are eeded to establish a model, ad it is ot ecessary to make strict assumptios for the assigmet of research sample matrix [4]. I the cross-strait market, there has existed a high ucertaity betwee the supply ad demad of vessels ad commodities, i coformity with the grey theory s feature of the icomplete iformatio system eviromet. 63

GM (, ) modelig [5] is a specific example of GM (,h) modelig whe = ad h =. The order of the differetial equatio is oe, ad there is oly oe variable, amely series X, i GM (, ) modelig sequece. GM (, ) modelig values are cosidered as the ceter of state i the Grey-Markov chai forecastig model. A group of origial data with equal time iterval is supposed X = { x (), x (),..., x ( N)} () The first-order accumulated geeratig operatio (-AGO) of X is provided. The grey-geerated model, based o the series () () () X = { x (), x (),..., x ( N)} () Eq.() is give by the differetial equatio dx dt () + ax () () = u (3) where t deotes the idepedet variable i the system, a represets the developed coefficiet, u is the cotrolled variable i the grey model. a ad u are the parameters that required to be determied i the model. Eq.(3) is called the first-order grey differetial equatio ad deoted by GM (, ), where the first stads for the first-order derivative of the -AGO series of X, ad the secod stads for oly series havig to do with the grey system. From Eq.() ad (3) ad equatio-least squares method, coefficiet ^ a becomes ^ T T T a = [ a, u] = ( B B) B Y (4) N Furthermore, accumulated matrix B is () () ( x () + x ()) () () ( x (3) + x ()) B = (5)...... () () ( x ( N ) + x ( N )) The costat vector N Y N Y = [ x (), x (3),..., x ( N )] (6) The approximate relatioship give below ca be obtaied by the substitutio of is T i the differetial equatio ad by solvig Eq.(4). () ^ u x ( k + ) = ( x () ) exp( ak) + a ^ ^ u a (7) Whe x () = x, the sequece of oe-order iverse-accumulated geeratig operatio (IAGO) is required ad the sequece must be reduced to obtai Eq.( 7) ^ () ^ () ^ x ( k) = x ( k) x ( k ) (8) ^ where x ( k) is the origial series ^ () forecasts, x ( k) is the geerated series for the forecasts. Suppose k=,3,..., N, the sequece of reductio is obtaied as follows ^ ^ ^ ^ x = ( x (), x (3),..., x ( N )) (9) 3. Expoetial Smoothig Methods The time series is to observe a target object cotiuously based o fixed time itervals, thus figurig out the rules of the time series with chage of time ad to evolve the future time series. I may applicatios, the data closest to the curret time ca represet the future data more accurately tha the historical data, ad the expoetial smoothig method ca deal with the time related data i the simplest ad most logical way. The expoetial smoothig method, with the chage of the α value, ca easily obtai a correct aswer, while the simple regressio mode offers the simplicity of the covetioal statistical forecast method. Forecastig methods usig smoothig techiques which weight past observatios may be desirable because they reduce the fluctuatios due to the irregular compoet i the observed time series. Averagig methods compute a forecast as a average of 64

past observatios, with equal weightig give to each observatio. Alteratively, liear expoetial smoothig models ca also be applied to obtai forecasts, i which the highest weight is assiged to the most recet observatio, with weights decreasig expoetially for more distat observatios. Sigle (or simple) expoetial smoothig is the earliest kow expoetial smoothig techique. It requires the curret level of the series to be estimated, which the forms the forecast of the series as it represets the latest assessmet available of the sigle (costat) predictable elemet of the time series [8]. Usig the sigle expoetial smoothig method, the forecast for t+i is give by the expoetially smoothed arrivals series i t, which is the weighted average of the actual ibouds i t ad the smoothed lag series (amely, the forecast made i the previous period). A sigle expoetial smoothig method, which produces a i-period-ahead forecast at time t ( F t ), ca be calculated recursively, as follows: F t = A t At = αat + ( α) At = αat + ( α) Ft, 0 < α <, i (0) where =actual arrivals at time t; A t =smoothed estimate of arrivals at time t; F t =sigle expoetial smoothig forecast of time t; α=smoothig coefficiet. The forecasts are give by the latest available smoothed value such that, at time t, A t the previous smoothed estimate,, is updated as the ew observatio, A t, becomes available. The ew smoothed estimate,, is the weighted average of A t A t A t ad. The forecast i period t is based o weightig the observatio i period t by a smoothig coefficiet, α, ad the most recet forecast by (-α). Thus, F t is a weighted average of all curret ad past observatios, ad is a smoothed statistic. Eq. (0) ca be rewritte as: F F F + α ( A F ) () t = t t t Or t+ = Ft + ( At Ft ) α = F + αe t t () from which it ca be see that the sigle expoetial smoothig procedure adjusts the forecast by a proportio of the most recet forecast error: if α is close to oe, the ew forecast would equal the previous forecast ad a substatial proportio of the most recet forecast error; if α is close to zero, the ew forecast would equal the previous forecast with little ifluece from the most recet forecast error. 3.3 Simple Regressio Method Statisticias routiely apply regressio aalysis to fit models to observatios. To deal with outliers, we seek for robust ad resistat regressio procedures. Quite some umber of perspectives exists i the literature regardig the defiitio of robustess. For example, Huber [4] studied robustess from the poit of view of miimax variace. Hampel [9],[0] proposed the idea of ifluece fuctio as a asymptotic tool to study robustess. Breakdow poit is aother importat otio i robust aalysis. Huber [4] defied a fiite-sample versio of breakdow poit. Cosider the classical liear model y = xβ + ε (3) where y = ( y, y,..., y )', β = ( β, β,..., β )', ε, ε,..., ε )' = ). ε = ( ad X ( x ij i=,...,, j=,..., p 3.4 Model Evaluatio To achieve correctess i the forecast mode, idicators to evaluate whether the mode is accurate or ot are eeded. The commoly used evaluatig idicators are: Mea Square Error, (MSE), Mea Absolute Value of Error, (MAE) ad Mea Absolute Percetage Error (MAPE), ad U Statistical Measure. They are expressed as: 65

MSE MAE [ X i = = ^ ( i) X ( i) ] X ( i) X ( i) i = = ^ X X i ( ^ ( ) : Actual Value i) : Forecast Value (4) (5) Both MSE ad MAE are obtaied from equatios () ad () are absolute values, ot relative values. Although MES exerts a pealty o the error, it will chage sigificatly for differet samples ad differet measurig uits. It is irratioal that weight is used for each error or square error, because it does ot relate to the degree of the value origially observed. For this study, two idicators as MAPE ad U statistical measure are used to evaluate the correctess i the mode: ^ X ( i) X ( i) i= X ( i) (6) MAPE = *00% U = Where: ( FPE i APEi ) i= ( APE i ) i= ^ (7) X ( i) X ( i ) FPE i = X ( i ) Relative chage rate of forecast X ( i) X ( i ) APE i = X ( i ) Actual relative chage rate MAPE is a relative value, ad suitable for comparig the forecast errors from differet time uits. U statistical measure ot oly cosiders to exert a pealty o the error (square term), but also is the combiatio of the ormal forecast method ad ative method. Meaig, it is to coduct relative compariso by forecastig the value i the ext period based o the observed value i this period without performig a forecast. Therefore, whe ^ U=0, X ( i) = X ( i + ), the forecast mode established is a perfect forecast. Whe ^ U=, X ( i) = X ( i), the result forecasted with the mode is the same without a forecast. For the same reaso, if U< (or U>), the forecast mode established is superior to (or iferior to) the method without a forecast. Therefore, it ca be see that whe U>, o matter how low MSE, MAE or MAPE value is, the forecasted result is worse tha the way without a forecast (has o cost). Therefore by lookig at U value, it ca decide whether the forecast mode is applicable or ot. I this case, the risk affectig the system s operatio due to poor forecast results ca be reduced. Therefore, it is a good forecast error idicator. MAPE is maily used to assess the degree of effect o the terms i the mode which have ot bee explaied. The less the MAPE value, the stroger the ability the forecast mode has to give the correct forecast, ad the results from the forecast mode are closer to matchig the past data. This paper classifies the forecast ability of the mode ito four levels by adaptig the forecast ability levels proposed by Lewis accordig to MAPE value (refer to Table ). Whe MAPE is less tha 0 %, it meas that the forecast ability is highly accurate. Table. Forecast Ability Levels of Mea Absolute Percetage Error MAPE Value Forecast Ability MAPE < 0% Highly Accuracy 0% MAPE 0% Excellet 0% < MAPE 50% Acceptable 66

MAPE > 50% Not Correct The U statistic measuremet ot oly cosiders the pealty o the relative error whether the forecast mode is applicable or ot i this case ad should be able to reduce (square term), but performs relative risk affectig the system s operatio due to compariso for forecastig the value i the ext period based o the observed value i this period. As judged by the U statistical poor mode forecast results. Therefore, it is a good evaluatig idicator for a forecast error [4]. measuremet, refer to Table, it ca decide Table. Judgmet with U Statistics U Statistics Whether to Use Forecast Mode U > Iferior to the results obtaied without forecast U = The same as the results with forecast U < Superior to the results obtaied without forecast U = 0 Perfect forecast Table 3. Trade betwee Taiwa ad Mailad Chia Uit: US millio Period Hog Kog Customs Statistics Taiwa Customs Statistics Mailad Chia Customs Statistics Exports Imports Total Exports Imports Total Exports Imports Total 989,896.5 586.9 3,483.4 - - - - - - 990 3,78.3 765.4 4,043.7 - - -,55.0 39.7,574.7 99 4,667.,6.0 5,793. 0. 93. 93.3 3,639.0 594.8 4,33.8 99 6,87.9,9.0 7,406.9. 747. 748. 5,88.0 698.0 6,579.0 993 7,585.4,03.6 8,689.0 6.,05.5,03.7,933.,46.8 4,394.9 994 8,57.,9.3 9,809.5 3.6,858.7,990.3 4,084.8,4. 6,37.0 995 9,88.8,574.,457.0 376.6 3,09.3 3,467.9 4,783.9 3,098. 7,88.0 996 9,77.6,58.4,300.0 63.4 3,059.9 3,683.3 6,8.,80.7 8,984.9 997 9,75.,743.8,458.9 66.5 3,95.3 4,54.8 6,44.7 3,396.5 9,838. 998 8,364.,654.9 0,09.0 94.9 4,3.9 5,08.8 6,69.6 3,869.6 0,499. 999 8,74.9,68. 9,803.0,60. 4,58.9 7,3.0 9,537.5 3,95.7 3,489. 000 9,593.,980.5,573.6 4,39.5 6,9.3 0,60.8 5,497. 4,994.9 30,49.0 00 8,8.5,693.3 0,504.8 4,895.4 5,903.0 0,798.4 7,339.5 5,000. 3,339.7 00 0,3.8,708.,09.9 0,56.9 7,968.6 8,495.5 38,063. 6,585.9 44,649.0 003,789.4,6. 3,950.5,890.8,07.9 33,908.7 49,36.3 9,004.7 58,367.0 004 4,76.9,485.4 7,47.3 36,349.4 6,79.3 53,4.7 64,778.6 3,545. 78,33.8 005 7,055.9,634.5 9,690.4 43,643.7 0,093.7 63,737.4 74,684.4 6,549.6 9,34.0 006 8,707.,909.8,67.0 5,808.6 4,783. 76,59.7 87,09.0 0,735. 07,844. 007(-0) 7,467.,44.3 9,88.4 49,990.4,967. 7,957.6 8,8.6 9,039.5 00,86. Note:. Accordig to the statistics by Taiwa Customs, o export, statistics error has bee resulted because maufacturers have ot provided the actual destiatios (Mailad Chia), but istead of Hog Kog; O import, i the past, Taiwa restricted the commodity import from the Mailad of Chia, ad some goods made i the Mailad Chia came to Taiwa through smugglig or couterfeit certificate of origi, therefore, the statistics volume is lower. Oly i recet years, Taiwa has eased the restrictio o the import of goods made i the Mailad Chia; therefore, the statistics creditability has bee improved.. Accordig to the statistics by the Customs of the Mailad Chia, i the past, the statistics by coutry of origi ad cosumer coutry was ot be rigidly coducted (mostly, by icomig couty ad outgoig coutry), therefore, statistically, the trade volume with Hog Kog was overestimated, ad that with other coutries uderestimated. Adjustmet has bee made oly from 993 o; therefore, the referece value of the statistics has bee slightly improved. 4. Aalysis o Cross-strait Trade Growth Tred For this study, the data [] is collected accordig to the data released i the Mothly Cross-strait Ecoomic Statistics ad is summarized i Table 3. As it ca be 67

see from Table 3, whether accordig to the statistics results of Hog Kog Customs, Taiwa Customs or the Customs of Chia, the volume of exports from Taiwa to Chia greatly exceeds the volume of imports to Taiwa from Chia, ad the ecoomic ad trade volume also is growig at a high speed. At preset, the degree of reliace of Taiwa o the mailad market becomes deeper. The mailad market is idispesable to the Taiwa market. 4. Aalysis o Grey Forecast ad Simple Regressio Results Accordig to the related studies with the grey theory, it is suggest that the grey forecast mode is suitable for coductig aalyses for short periods of time or cases with icomplete data. For as log as there has bee high ucertaity i the cross-strait trade, the grey theory has had the feature of icomplete iformatio system eviromet. It establishes a model with the commoly used four rules of the grey theory to costruct the forecast mode for the cross-strait trade growth ad to test the accuracy of the mode. The simple regressio mode is also oe of the commoly used forecast tools i statistics. This study forecasts the trade volumes i 007 ad 008 with the data from 003 to 006. The values are give i Table 4 ad 5. For MAPE mode assessmet, the results obtaied with the grey forecast are better tha those with the regressio mode. Takig exports as a example, it is 0.84 %, 0.4 % ad 0.5 % respectively for Hog Kog, Taiwa ad Chia. For imports, it is 0.70 %, 0.67 % ad 0.55 % respectively. Both the grey forecast ad the regressio mode, o matter which authority the data is from, are of high accuracy. Table 4. Forecast Results of Export Volumes betwee Taiwa ad Mailad of Chia Grey Forecast ad Simple Regressio Exports Hog Kog Customs Taiwa Customs Mailad Chia Customs Period GM(,) Regressio GM(,) Regressio GM(,) Regressio 003,789.4,.5,890.8 4,566.0 49,36.3 50,5.7 004 4,907.0 4,46. 36,344.0 33,970.7 64,480.0 6,86.3 005 6,745.0 6,73.0 43,34.0 43,375.5 74,800.0 75,40.9 006 8,80.0 9,035.7 5,684.0 5,780.3 86,760.0 87,455.5 007,9.0,340.5 6,634.0 6,85. 00,640.0 99,770. 008 3,733.0 3,645. 73,500.0 7,589.8 6,740.0,084.6 MAPE 0.84%.9% 0.4% 4.09% 0.5%.59% U 0.03 0.04 0.00 0.05 0.0 0.03 Table 5. Forecast Results of Import Volumes betwee Taiwa ad Mailad of Chia Grey Forecast ad Simple Regressio Imports Hog Kog Customs Taiwa Customs Mailad Chia Customs Period GM(,) Regressio GM(,) Regressio GM(,) Regressio 003,6.,88.4,07.9,48. 9,004.7 9,9.3 004,464.3,47.9 6,6.0 5,94.9 3,403.0 3,048.9 005,669.,667.5 0,06.0 0,40.6 6,599.0 6,868.5 006,89.,907.0 4,580.0 4,86.3 0,556.0 0,688. 007 3,3.5 3,46.5 9,90.0 9,3.0 5,458.0 4,507.7 008 3,39.8 3,386.0 36,373.0 33,780.7 3,58.0 8,37. MAPE 0.70%.3% 0.6%.78% 0.55%.08% U 0.03 0.05 0.0 0.04 0.0 0.03 68

4. Aalysis o Expoetial Smoothig Results I the last te years, the structure of the cross-strait trade has show a big ad sigificat fluctuatio. I order to kow the advatages ad disadvatages amog the differet modes, a α value betwee 0. ad 0.8 is employed (refer to Table 6 ad 7). To forecast the data i 007 based o those from 00 to 006 whe α = 0., for exports, MAPE is 7.34 %, 66.87% ad 40.90 % respectively for Hog Kog, Taiwa ad Chia. For imports, it is 9.30 %, 44.94 % ad 43.67 % respectively. Whe α=0.8, for exports, MAPE is 7.38 %, 45.8 % ad 5.37 % respectively for Hog Kog, Taiwa ad Chia. For imports, it is.87 %, 9.68 % ad 9.08 % respectively. This suggests that for forecastig ad aalyzig the cross-strait trade volume, the expoetial smoothig method is able to produce excellet or acceptable forecast accuracy. Comparig it with the results above metioed, its forecast ability has reduced sigificatly. Therefore i this case, it is suggested ot to perform the forecast with the expoetial smoothig method. Table 6. Forecast Results of Export Volumes betwee Taiwa ad Mailad of Chia Expoetial Smoothig Method Period Hog Kog Customs Taiwa Customs Mailad Chia Customs α= 0. 0.5 0.8 0. 0.5 0.8 0. 0.5 0.8 00 8,8.5 8,8.5 8,8.5 4,895.4 4,895.4 4,895.4 7,339.5 7,339.5 7,339.5 003 9,.6 9,56.7 0,0.7 6,0.7 7,7. 9,400.6 9,484. 3,70.3 35,98.4 004 9,647. 0,675.5,433.9 9,395.5 5,30.0 0,9.8 33,459.8 4,03.8 46,673.5 005 0,670.,78.7 4,096.3 4,786.3 5,85. 33,8. 39,73.6 5,905. 6,57.6 006,947. 4,887.3 6,464.0 0,557.8 34,734.4 4,538.6 46,75.8 63,794.8 7,979.0 007 3,99. 6,797.3 8,58.6 6,807.9 43,7.5 49,754.6 54,794.4 75,45.9 84,083.0 MAPE 7.34%.64% 7.38% 66.87% 54.64% 45.8% 40.90% 3.94% 5.37% U 0.56 0.40 0.30 0.4 0.34 0.8 0.58 0.4 0.30 Table 7. Forecast Results of Import Volumes betwee Taiwa ad Mailad of Chia Expoetial Smoothig Method Period Hog Kog Customs Taiwa Customs Mailad Chia Customs α= 0. 0.5 0.8 0. 0.5 0.8 0. 0.5 0.8 00,693.3,693.3,693.3 5,903.0 5,903.0 5,903.0 5,000. 5,000. 5,000. 003,696.3,700.7,705. 6,36. 6,935.8 7,555.5 5,37.3 5,793. 6,68.8 004,789.,930.9,069.9 7,56.5 8,976.9 0,35.4 6,054.8 7,398.9 8,457.5 005,98.5,08.,40.3 9,63.6,884.6 5,498.9 7,55.9 0,47.0,57.7 006,069.7,4.3,588.,349.7 6,489. 9,74.7 9,35. 3,50.8 5,745. 007,37.7,665.6,845.5 4,036.3 0,636. 3,66.4,68.8 7,3.0 9,737. MAPE 9.30% 5.7%.87% 44.94% 36.35% 9.68% 43.67% 35.46% 9.08% U 0.46 0.34 0.8 0.49 0.37 0.9 0.49 0.37 0.9 5. Coclusios ad Suggestios The cross-strait trade volumes of both import ad export have bee aalyzed based o the statistical data. Meawhile, the forecast modes have bee established through the grey forecast, simple regressio ad expoetial smoothig methods. The followig are importat coclusios ad suggestios after summig up: 5. Coclusios: 69

. Amog the forecast modes established for this study, the grey forecast performs best, ad the simple regressio mode follows immediately. Both methods exhibit a comparatively better forecast ability tha the rest.. As for the data, regardig the exports trade volume, the grey forecast mode established based o the statistical data from Taiwa Customs provides better results. Regardig the imports trade volume, the grey forecast mode established based o the statistical data from Taiwa Customs ad the Customs of Chia provides better results. 3. If the forecast is performed based o the statistical data from Taiwa Customs, the cross-strait trade volume i 008 will exceed USD $73,500 millio for exports from, ad USD $36,373 millio for imports to Taiwa, a sigificat growth over 006. 4. As it ca be see from the data, the degree of reliace of Taiwa o Chia has bee becomig heavier ad heavier year after year, resultig i a risk issue. But i a market previously havig strog competitive force, if the market share of Taiwa decreases, ad there are o other markets to take its place, it meas that the overall competitive force weakes. I this case, we should thik over whether or ot Taiwa faces a deeper security risk. 5. Suggestios:. Through compariso ad aalyses with the models established with the extesively used grey forecast, this study ca almost say completely positive thigs about the forecast ability of the grey theory i a short-term grey situatio. For cotiued study, more complete trade volume data eeds to be gathered i order to forecast the developmet tred of the cross-strait trade more perfectly.. I this study, the social ad ecoomic variats have ot bee icluded ito the forecast modes. It is suggested for cotiued study, that lots of social ad ecoomic data i both the mailad ad Taiwa should be collected. Also, the GM (, ) forecast mode or re-regressio mode could be established i order to observe ad aalyze the effects of the forecast modes. 3. Facig the high growth of the cross-strait ecoomic ad trade exchage i 007, the govermet authority should cosider adjustig the policies toward Chia to create a ew Taiwa Miracle agai o both sides of Taiwa Strait ad i these three regios. Refereces: [] Maagemet Tred of SMEs, the Bureau of Foreig Trades uder the Miistry of Ecoomic Affairs, 005007. [] Mothly Cross-strait Ecoomic Statistics, the Mailad Committee, the Executive Yua of the Public of Chia, 989007. [3] Cao Ruiqi, To Establish Fuzzy Expoetial Smoothig Mode with Grey Forecast, Joural Of The Chiese Istitute Of Egieers 00, 8(6), 95-03. [4] Che Chuiye, A Study of Cross-strait Direct Shippig Volume ad Distributio 998, Masteral Dissertatio, Traffic Maagemet 70

Scieces Research Istitute, Cheg Kug Uiversity. [5] Che Huayi, Study o Baltic Dry Idex Forecast 006, Masteral Dissertatio, Departmet of Shippig Maagemet, Natioal Taiwa Ocea Uiversity. [6] Che Siyig, Study o Selective Risk Avoidace Regardig Price ad Exchage Rate of Crude Oil Imported by CPC Corporatio 000, Masteral Dissertatio, Ecoomics Research Istitute, Natioal Taipei Uiversity, 000. [7] Fag Shirog, A Itroductio to Statistics, Hwatai Cultural Udertakig Co., Ltd., Taipei, 00. [8] Grager, C. W. J., ad P. Newbold, Forecastig Ecoomic Time Series 997, New York: Academic Press. [9] Hampel, F.R., A geeral qualitative defiitio of robustess 97, A. Math. Statist. 4, 887 896. [0] Hampel, F.R., The ifluece curve ad its role i robust estimatio 974, J. Amer. Statist. Assoc. 69,383 393. [] Huag Taili, Wag Xiao e, Zheg Zhogkai, Che Chuiye, Study of Applicatio of Grey Theory i Goods Shippig Demads at Shippig Ceters outside Taiwa 998, Dissertatio Collectio of the 3 th Dissertatio Semiar, Chiese Istitute of Trasportatio,37-46. [] Huag Taili, Wag Xiao er, Che Chuiye Study of Grey Theory i Forecast of Cross-strait Ocea Cotai Shippig Capacity 998, Chag Jug Joural, (), 03-4. [3] Huag Weji, Wu Shegjie, Cheg Peilu, You Rehog, Talkig about Applicatio of Shippig Demad Forecast with Life Cycle Viewpoit Takig Cotaier Shippig Demads at Seaports i Taiwa Regio, Joural of Ocea Shippig 003,, 7-85. [4] Huber, P.J., Robust estimatio of a locatio parameter 964, A. Math. Statist. 35, 73 0. [5] J.L. Deg, Grey Cotrol System 997, Huazhog Uiversity of Sciece ad Techology Press, Wuha. [6] Lewis, C. D., Idustrial ad Busiess Forecastig Method, Butterworths, Lodo, 98. [7] Ma Fegyua, Discussig about Iterrelatioship betwee Ocea Shippig Growth Rate ad Ecoomic Growth, Petroleum Quarterly 005, 4(5), 7-80. [8] Syder, R. D., Koehler, A. B., ad Ordc, J. K., Forecastig for Ivetory Cotrol with Expoetial Smoothig, Iteratioal Joural of Forecastig 00, 8, 5-8. [9] Syder, R. D., Koehler, A. B., Hydma, R. J., ad Ord, J. K., Expoetial Smoothig Models: Meas ad Variaces for Lead-time Demad, Europea Joural of Operatioal Research 004, 58, 444-455. [0] Tseg, F. M. ad Tzeg, G. H., Forecast Seasoal Time Series by Comparig Five Kids of Hybrid Grey Models, Iteratioal Joural of Fuzzy Systems 999, 5(), 45-55. [] Zhag Yifa, Study o Multi-mode Iteractive Medicie Ivetory Cotrol Decisio-makig ad Support i Hospitals 00, Masteral Dissertatio, Iformatio Maagemet Research Istitute, Fu Je Uiversity. [] Zhog Zhegqi, Liag Jishu, Che Huayi, Applicatio of Grey Theory i BCI Forecast 006, Joural of Ocea Shippig, 5, 49-70. [3] Zhog Zhegqi, Li Yousheg, Study of BCI Forecast 007, Dissertatio Collectio, Iteratioal Ecoomy, Trade ad Commerce Semiar, Taipei, 6-3. [4] Zhuag Kuyi, Study of Applicatio of Grey Theory i Electroic Game Idustry Forecast Takig Taiwa Market as a Example 00, Masteral Dissertatio, Eterprise Maagemet Research Istitute, Chaoyag Uiversity of Techology. 7