Forecasting SET50 Index with Multiple Regression based on Principal Component Analysis

Transcription

1 Journal of Aled Fnance & Bankng, vol.2, no.3, 202, ISSN: (rnt verson), (onlne) Internatonal Scentfc Press, 202 Forecastng SET50 Index wth Multle Regresson based on Prncal Comonent Analyss N. Soan, W. Kanjanavajee and P. Sattayatham 2 Abstract In ths aer, we forecast SET50 Index (The stock rces of the to 50 lsted comanes on SET (Stock Exchange of Thaland)) by usng multle regresson. At the same tme, we consder the exstence of a hgh correlaton (the multcolnearty roblem) between the exlanatory varables. One of the aroaches to avod ths roblem s the use of rncal comonent analyss (PCA). In ths study, we emloy rncal comonent scores (PC) n a multle regresson analyss. As can be seen, 99.4% of varaton n SET50 can be exlaned by all PCAs. Accordngly, we forecast SET50 Index closed rce for the erod /03/20 through 3/03/20 by usng three models. We comare loss functon, the model forecast exlaned by all PCs have a mnmum of all loss functon. Program of Mathematcs and Aled Statstcs, Faculty of Scence and Technology, Nakhon Ratchasma Rajabhat Unversty, Nakhon Ratchasma, Thaland. e-mal: nosoan@gmal.com, wanava29@gmal.com 2 School of Mathematcs, Suranaree Unversty of Technology, Nakhon Ratchasma, Thaland, e-mal: arote@sut.ac.th Artcle Info: Receved : Arl 2, 202. Revsed : May 27, 202 Publshed onlne : June 5, 202

2 272 Forecastng SET50 Index wth Multle Regresson... JEL classfcaton numbers: C53 Keywords: Forecastng, SET50 ndex, Multle regresson analyss, Prncal comonent analyss Introducton The characterstc that all stock markets have n common s uncertanty, whch s related to ther short and long-term future state. Ths feature s undesrable for the nvestor, but t s also unavodable whenever the stock market s selected as an nvestment tool. The best that one can do s to try to reduce ths uncertanty. Stock Market Forecastng (or Predcton) s one of the nstruments n ths rocess. There are two tyes of forecastng, thequaltatve and the quanttatve method. Qualtatve forecastng technques are subjectve, based on the onon and judgment of consumers and exerts, whch s arorate when ast data s not avalable. It s usually aled to ntermedate to long range decsons (e.g. nformed onon and judgment, Delh method). Quanttatve forecastng models are used to estmate future demands as a functon of ast data, whch s arorate when ast data s avalable. It s usually aled to short to ntermedate range decsons (e.g. tme seres methods, causal / econometrc forecastng methods). Tme seres found the stock market follows a random walk, whch mles that the best redcton you can have about tomorrow's value s today's value. Another technque s a causal model whch establshes a cause-and-effect relatonsh between ndeendent and deendent varables.e. regresson analyss whch ncludes a large grou of methods that can be used to redct future values of a varable usng nformaton about other varables. These methods nclude both arametrc (lnear or non-lnear) and non-arametrc technques.

3 N. Sooan, W. Kanjanawajee and P. Sattayatham 273 In ths study we consder multle regresson analyss, whch s s one of the most wdely used methodologes for exressng the deendence of a resonse varable on several ndeendent (redctor) varables. In ste of ts evdent success n many alcatons, however, the regresson aroach can face serous dffcultes when the ndeendent varables are correlated wth each other (McAdams et al., (2000)). Multcollnearty, or hgh correlaton between the ndeendent varables n a regresson equaton, can make t dffcult to correctly dentfy the most mortant contrbutors to a hyscal rocess. One method for removng such multcollnearty and redundant ndeendent varables s to use multvarate data analyss (MDA) technques. MDA have been used for analyzng volumnous envronmental data (Buhr et al., (992, 995); Chang et al., (988); Sanchez et al., (986); Statherooulos et al., (998)). One of method s rncal comonent analyss (PCA), whch has been emloyed n ar-qualty studes (Maenhaut et al., (989); Statherooulos et al., (998); Sh and Harrson, (997); Tan et al., (989); Vadya et al., (2000)) to searate nterrelatonshs nto statstcally ndeendent basc comonents. They are equally useful n regresson analyss for mtgatng the roblem of multcollnearty and n exlorng the relatons among the ndeendent varables, artcularly f t s not obvous whch of the varables should be the redctors. The new varables from the PCA become deal to use as redctors n a regresson equaton snce they otmze satal atterns and remove ossble comlcatons caused by multcollnearty. In ths aer, we forecast SET50 Index (The stock rces of the to 50 lsted comanes on SET(Stock Exchange of Thaland) by usng a multle regresson based on PCA. Fnally, we comare the erformance of some models wth ther loss functon. In the next secton, we resent multle a regresson model and rncal comonent analyss. The emrcal methodology and model estmaton are gven n secton 3 and the concluson s gven n secton 4.

4 274 Forecastng SET50 Index wth Multle Regresson... 2 Models 2. Multle Regresson Model Multle lnear regresson (MLR) attemts to model the relatonshs between two or more exlanatory varables and a resonse varable, by fttng a lnear equaton to the observed data. The deendent varable (Y) s gven by: Y 0 X () where X,,..., are the exlanatory ndeendent varables,, 0,,..., are the regresson coeffcents, and s the error assocated wth the regresson and assumed to be normally dstrbuted wth both exectaton value zero and constant varance (J.C.M Pres et al., (2007)). The redcted value gven by the regresson model ( Y ) s calculated by: Y X (2) 0 The most common method to estmate the regresson arameters, 0,,..., s the ordnary least square estmator (OLS). MLR s one of the most used methods for forecastng. Ths method s wdely used to ft the observed data and to create models that can be used for redcton n many research felds, such as bology, medcne, sychology, economcs and the envronment. Fnance s a research feld where develong redcton models (e.g. for the Tha stock market ndex), where the choce of selecton nut data s mortant. Naturally, the Tha stock market has unque characterstcs, so the factors nfluencng the rces of stocks traded n ths market are dfferent from the factors nfluencng other stock markets (Chagusn et al., 2008a). Examles of factors that nfluence the Tha stock market are the foregn stock ndex, the value of the Tha baht, ol rces, gold rces, the MLR and many others. Some researchers have used these factors to forecast the SET ndex, ncludng

5 N. Sooan, W. Kanjanawajee and P. Sattayatham 275 Tantnakom (996), who used tradng value, tradng volume, nterbank overnght rates, nflaton, the net tradng value of nvestment, the value of the Tha baht, the rce-earnngs rato, the Dow Jones ndex, the Hang Seng ndex, the Nkke ndex, the Strats Tmes Industral ndex and the Kuala Lumur Stock Exchange Comoste ndex. Khumoo (2000) used the Dow Jones ndex, gold rces, the Hang Seng ndex, the exchange rate for the Jaanese yen and Tha baht, the MLR, the Nkke ndex, ol rces, the Strats Tmes Industral ndex and the Tawan weghted ndex. Chotasr (2004) used the nterest rates for Thaland and the US; the exchange rates for the USD, JPY, HKD and SKD; the stock exchange ndces of the US, Jaan, Hong Kong and Sngaore; the consumer rce ndexand ol rces. Chaereonkthuttakorn (2005) used US stock ndces, ncludng the Nasdaq ndex, the Dow Jones ndex and the S&P 500 ndex. Rmcharoen et al. (2005) used the Dow Jones ndex, the Nkke ndex, the Hang Seng ndex, gold rces and the MLR. Worasuchee (2007) used MLR, the exchange rate for Tha baht and the USD, daly effectve over-nght federal fund rates n the US, the Dow Jones ndex and ol rces. Chagusn et al. (2008) used the Dow Jones ndex, the Nkke ndex, the Hang Seng ndex, gold rces, the MLR and the exchange rate for the Tha baht and the USD. Phasarn S. et al. (200) used the Dow Jones ndex, the Nkke ndex, the Hang Seng ndex and the MLR. The common factors that researchers used to redct the SET ndex are summarsed n Table.

6 276 Forecastng SET50 Index wth Multle Regresson... Table : Imact Factor for Stock Exchange of Thaland Index Tantnakom (996) Khumyoo (2000) Chotasr (2004) Chaereon-Kthutt akorn (2005) Rmcharoen et al. (2005) Worasuchee (2007) Chagusn et al. (2008) Phasarn S. et.al (200) Nasdaq ndex Down Jones Index S&P 500 Index X X X X X X X X X X Nkke Index X X X X X X Hang Seng Index Strats Tmes ndustral Index X X X X X X X X X USD X X X X JPY X X HKD SKD X X Gold rces X X X Ol Prces X X X MLR X X X X X *X s selected n multle regresson. 2.2 Prncal Comonent Analyss (PCA) Consder a random varable X ( X,..., X ) wth mean (,..., ), () denotes transose, (,..., ) and varance ( j ), j (, j,..., ). Assume that the rank of s and (3)

7 N. Sooan, W. Kanjanawajee and P. Sattayatham 277 are the egenvalues of. In the PCA we want to fnd uncorrelated lnear functon of X,..., X, say, Z,..., Z m, ( m ), such that varances V( Z),..., V( Z m) account for most of the total varances among X,...,, X Also, we requre V( Z) V( Z2)... V( Z m ). Algebracally, rncal comonents are artcular lnear combnatons of X,...,, X Geometrcally, the rncal comonent reresents a new coordnate system obtaned by rotatng the orgnal axes X,...,, X The new axes reresent the drects wth maxmum varablty. Let (,..., ),,..., m be a vector of weghts for the resectve comonents of X. Consder the lnear functon Z X X (4) Our am s to fnd such that V( Z ) s maxmum subject to the condton. It s clear that V( Z ) can be ncreased by multlyng by some constant. To elmnate ths arbtrarness we restrct our attenton to coeffcent vectors of unt lengths. Now, V( Z ). Hence, we are requred to fnd such that (5) s maxmum subject condton. To maxmze subject to, the standard aroach s to use the technque of Lagrange multlers. Maxmze ( ), where s a Lagrange multler.

8 278 Forecastng SET50 Index wth Multle Regresson... Dfferentaton wth resect to gves 0, or I ( ) 0, (6) where I s the ( ) dentty matrx. Snce, 0, there can be a soluton only f I s sngular,.e. f I 0 such that f s a latent root of and s ts corresondng normalzed latent vector. Thus, s an egenvalue of and s the corresondng egenvector. To decde whch of the egenvectors gves X wth maxmum varance, note that the quantty to be maxmzed s (by (6)) so must be as large as ossble. Thus, s the egenvector corresondng to the largest egenvalue of, and Var[ X ], the largest egenvalue (by (3)). In general, the kth PC of X s Zk kx and Var[ kx ] k, where k s the kth largest egenvalue of, and k s the corresondng egenvector. Ths wll now be roved for k = 2; the roof for k 3 s slghtly more comlcated, but very smlar. The second PC, Z 2 2 X, maxmzes 2 2 subject to beng uncorrelated wth Z X, or equvalently subject to Cov[ Z, Z ] Cov[ X, X ] 0, 2 2 where Cov[ x, y] denotes the covarance between the random varables x and y. But Cov[ Z, Z ] Cov[ X, X ] Thus, any of the equatons

9 N. Sooan, W. Kanjanawajee and P. Sattayatham 279 0, 0, 0, could be used to secfy zero correlaton between Z X and Z 2 2 X. Choosng the last of these (an arbtrary choce), and notng that a normalzaton constrant s agan necessary, the quantty to be maxmzed s ( ) where, are Lagrange multlers. Dfferentaton wth resect to 2 gves and multlcaton of ths equaton on the left by gves 2 2 0, whch, snce the frst two terms are zero and, reduces to 0. Therefore, 2 2 0, or equvalently ( I ) 2 0, so s once more an egenvalue of, and 2 the corresondng egenvector. Agan, 2 2, so s to be as large as ossble. Assumng that does not have reeated egenvalues, cannot equal. If t dd, t follows that, volatng the constrant 2 0. Hence s the second largest 2 egenvalue of, and 2 s the corresondng egenvector. The second rncal comonent s, therefore, Z X wth V( Z2) To fnd the k th rncal comonent, Zk k X, we are to fnd k such that V( Z ) s maxmum subject to the condton and 0 k, ( k k, k, k,..., m). It follows that Z k k X wth V( Zk) k, k,..., m where k s the normalzed egenvector corresondng corresondng to k. Clearly, k k k k

10 280 Forecastng SET50 Index wth Multle Regresson... Cov( Z, Z ) Cov( X, X ) = =0. k k k k k k k k k k k By Sectral Decomoston Theorem, we can wrte AΛA where A (,..., ), Dag.(,..., ). Note that some of the s may be zeros. Therefore, the total oulaton varance among X,..., X s V( X ) tr tr(aλa) tr( AA) tr( ) snce AAI V( Z ). The total oulaton varance among Z,..., Z s the same as the total oulaton varance among X,..., X. The roorton of the total varance accounted for by the kth P.C. s k. The frst m P.C. s wth the m largest varance account for m roorton of the total varance of X. If, therefore, most (80-90%) of the total varance n X s accounted for by the frst m comonents Z,..., Z m, then for large,these comonents can relace the orgnal X,..., X to exlan the varablty among the varables and the subsequent comonents Z,..., m Z can be dscarded. 2.3 Multle regressons by rncal comonents Let { X, t T} and { Y, t T} be dscrete tme stochastc t t rocesses defned as T {,2,..., n}, n,,...,. Let us assume the arallel evoluton of rocesses to be known untl a gven nstant of tme. We deal wth the roblem of forecastng the rocess { Y t } (outut rocess) by usng the addtonal nformaton of the rocess { X t } (nut rocess). If { X t } rocess has multcollnearty, the forecastng rocedure can be

11 N. Sooan, W. Kanjanawajee and P. Sattayatham 28 erformed by means of the PCA of rocesses. So, a multle regresson by rncal comonents model states how the outut s related to the values of the nut through the random varables n the orthogonal decomoston for the outut rocess. A multle regresson wth PCA model conssts of exressng the outut rocess Y, as a functon of the nut rocess, n a smlar way to ts orthogonal decomoston through the rncal comonents. The redcted value gven by the regresson model ( Y ) s calculated by: Y Z (7) 0 m where Z { Z,..., Z m }, s the PCA matrx of X,, 0,,..., m, m s the regresson arameters. 3 Emrcal Methodology and Model Estmaton Results 3. Data The data sets used n ths study are a deendent varable, whch s the daly closed rces of SET50 Index at tme t ( SET 50 t ) and the exlanatory ndeendent varables are the dfferences between the daly closed rce factors whch nclude: SET50 t : Stock Exchange of Thaland Index at tme t. FTSE : London Stock Exchange Index at tme t. DAX : Frankfurt Stock Exchange Index at tme t. DJIA : Dow Jones Index at tme t. SP 500 : S&P 500 Index at tme t. NIX : Nkke Index at tme t. HSKI : Hang Seng Index at tme t.

12 282 Forecastng SET50 Index wth Multle Regresson... STI : Strats Tmes Industral Index at tme t. KLSE : Kuala Lumur Stock Exchange Index at tme t. PSI : Phlne Stock Exchange Index at tme t. JKSE : Jakarta Comoste Index at tme t. KOPI : South Korea Stock Exchange (200) Index at tme t. USD : Currency n Tha Baht to one dollar at tme t. JPY : Currency n Tha Baht to 00 Yens at tme t. HKD : Currency n Tha Baht to one dollar of Hong Kong at tme t. SKD : Currency n Tha Baht to one dollar of Sngaore at tme t. GOLD : Gold Prce at tme t. OIL : Ol Prce at tme t. All data s n the erod 4/0/2007 through 30/03/20 (t,,,038 observatons). The data set s obtaned from the Stock Exchange of Thaland. The data set s dvded nto n-samle ( R,05 observatons) and out-of-samle ( n 23 observatons). Descrtve statstcs and correlatons are gven n Table 2 and Table 3. As can be seen from Table 3, hgh correlaton coeffcents were found between deendent varables ( SET50) and exlanatory varables wth a hgh sgnfcance (<0.0). Also hgh correlaton coeffcents were found between exlanatory varables wth hgh sgnfcance (<0.0) whch show that there was a multcollnearty roblem. Multle regresson analyses based on raw data also show that there was a multcollnearty roblem wth the varance nflaton factor (VIF) n Table (VIF >=5.0). Once of the aroaches to avod ths roblem s PCA. Hence, rncal comonent analyss has been comleted based on eghteen exlanatory varables, and the overall results of the PCA are shown n Tables 3-5, resectvely.

13 N. Sooan, W. Kanjanawajee and P. Sattayatham 283 Table 2: Descrtve Statstcs of SET50 Index and exlanatory varables Index Mean Std. Devaton VIF SET SET50 (t-) FTSE DAX DJIA SP NIX HSKI STI KLSE PSI JKSE KOSPI USD JPY SGD HKD Gold Ol Kaser-Meyer-Olkn Measure of Samlng Adequacy Bartlett's Test of Shercty Arox df 53 Sg

14 284 Forecastng SET50 Index wth Multle Regresson... Table 3: Correlaton matrx of SET50 ndex and exlanatory varables Index SET50 SET50 (t- ) FTSE DAX DJIA SP500 NIX HSKI STI KLSE PSI JKSE KOSPI USD JPY SGD HKD Gold Ol SET SET50 (t-) **.0000 FTSE 0.743** **.0000 DAX ** ** **.0000 DJIA ** ** ** **.0000 SP ** ** ** ** **.0000 NIX ** ** ** 0.839** ** **.0000 HSKI ** ** ** ** ** 0.775** **.0000 STI ** ** 0.950** ** 0.928** 0.936** ** 0.882**.0000 KLSE 0.947** ** ** ** 0.678** ** ** 0.856** 0.855**.0000 PSI 0.902** ** ** ** ** ** ** 0.750** ** **.0000 JKSE ** ** ** 0.474** ** ** ** 0.670** 0.589** ** **.0000 KOSPI ** ** ** 0.783** ** ** ** ** ** 0.984** 0.870** 0.854**.0000 USD ** ** ** ** ** ** ** ** ** ** ** ** **.0000 JPY ** ** ** ** ** ** ** ** ** ** ** 0.32** ** **.0000 SGD ** -0.44** ** ** ** ** ** ** ** ** ** ** -0.0** 0.397** **.0000 HKD ** ** ** ** ** ** 0.27** ** ** ** ** ** ** ** ** -0.02**.0000

15 N. Sooan, W. Kanjanawajee and P. Sattayatham 285 Gold 0.463** 0.455** -0.92** ** ** ** ** 0.096** ** ** ** 0.756** ** ** ** ** **.0000 Ol ** 0.567** 0.40** 0.469** ** ** ** ** ** 0.402** ** ** ** ** ** ** ** 0.670**.0000 **Correlaton s sgnfcant at the 0.0 level (2-taled).

16 286 Forecastng SET50 Index wth Multle Regresson Results of Prncal Comonent Analyss Frstly, the results of Bartlett s shercty test are shown n Table 2 Ths test s for all correlatons are zero or for testng the null hyothess where the correlaton matrx s an dentty matrx (M.Mendes, 2009) whch was used to verfyng the alcablty of PCA. The value of Bartlett s shercty test SET70 had 50, whch suggests that the PCA s alcable to our data sets (P < 0.000). Overall Kaser s measure of samlng adequacy was also comuted as whch ndcated that samle szes were enough to aly the PCA (KAISER, 960). Table 4: Egenvalues for PCAs Comonent Intal Egenvalues Total % of Cumulatve Accordng to the results of PCA (Table 4), there are three rncal comonents rncal comonents out of eghteen (PCA-3) wth egenvalues greater than whch were selected for multle regresson analyss (Forecast ).

17 N. Sooan, W. Kanjanawajee and P. Sattayatham 287 Because egenvalues reresent varances and a comonent wth an egenvalue of less than s not sgnfcant. Thus, the frst of three rncal comonents rovdes an adequate summary of the data for most uroses. Only frst three rncal comonents, exlanng % of the total varaton, should be suffcent for almost any alcaton (Table 4). Accordng to the results of the correlaton matrx of SET50 and PCAs (see Table 5), out of eghteen rncal comonents there are four rncal comonents (PCA-2, <=0.05, PCA9, PCA3, <=0.0) wth correlatons between SET50 and PCA not zero whch were selected for multle regresson analyss (Forecast 2.). Lastly, we selected all PCAs to forecast SET50 for multle regresson analyss (Forecast 3.).

18 288 Forecastng SET50 Index wth Multle Regresson... Table 5: Correlaton Matrx of SET50 and PCAs Comonent SET50 PCA PCA2 PCA3 PCA4 PCA5 PCA6 PCA7 PCA8 PCA9 PCA0 PCA PCA2 PCA3 PCA4 PCA5 PCA6 PCA7 PCA8 SET PCA 0.939**.000 PCA ** PCA PCA PCA PCA PCA PCA PCA * PCA PCA PCA PCA * PCA PCA PCA PCA PCA **, * Correlatons sgnfcant at the 0.0, 0.05 level (2-taled), resectvely.

19 N. Sooan, W. Kanjanawajee and P. Sattayatham Results of Multle Regresson wth Prncal Comonent Analyss In ths study, two aroaches were emloyed usng rncal comonent scores n multle regresson analyss. As can be seen from Table 6, 97.4% of varaton n SET50 can be exlaned by the frst three PCA (Panel A.: Model Forecast.), 98.4% of varaton n SET50 can be exlaned by the PCA, PCA2, PCA9 and PCA3 (Panel B.: Model Forecast 2) and 99.4% of varaton n SET50 can be exlaned by all PCAs (Panel C.: Model Forecast 3). For the Forecasts -3 redcted SET50 rces were obtaned for the followng models: Model Forecast. SET PCA PCA PCA3 Model Forecast 2. SET PCA PCA PCA PCA3 Model Forecast 3. SET PCA PCA2 2.32PCA3 2.63PCA PCA5 2.36PCA6 5.06PCA7 4.26PCA PCA PCA PCA0.969PCA PCA32.770PCA PCA5 2.89PCA PCA7 0.82PCA8 In Panel D. we forecast the SET50 Index closed rce for the erod /03/20 through 3/03/20 by three models. We comare loss functon, loss functon for the model forecast 3 whch exlaned by all PCAs have mnmum of all MSE, MAE and MAPE. Fgure dslays the SET50 Index closed rces and three models are used for forecast from the erod /03/20 through 3/03/20.

20 290 Forecastng SET50 Index wth Multle Regresson... Table 6: Multle Regresson Model based on PCA Panel A. Multle regresson model based on frst three PCA (Forecast ) Model B Std. Error t Sg. (Constant) PCA PCA PCA RMSE = R 2 = DW= Panel B. Multle regresson model base on correlaton PCA wth SET50 (Forecast 2 ) Model B Std. Error t Sg. (Constant) PCA PCA PCA PCA RMSE = R 2 = DW= 0.69 Panel C. Multle regresson model based on all PCA wth SET50 (Forecast 3) Model B Std. Error t Sg. (Constant) PCA PCA PCA PCA PCA PCA PCA PCA PCA PCA PCA PCA

21 N. Sooan, W. Kanjanawajee and P. Sattayatham 29 PCA PCA PCA PCA PCA PCA RMSE = R 2 = DW=2.047 Panel D. Loss functon for a comarson of out of samle SET50 Index closed rces for the erod /03/20 through 3/03/20 Model MSE MAE MAPE Forecast Forecast Forecast Fgure : Grah of SET50 Index closed rces, Forecast SET50 wth MLR based on frst three PCs (Forecast), four most closely correlated PCs (Forecast2) and all PCs (Forecast 3) for the erod /03/20 through 3/03/20

22 292 Forecastng SET50 Index wth Multle Regresson... 4 Concluson Earler studes showed that the relatonsh between SET50 Index and varous factors.e. other stock markets, foregn exchange, gold rce, MLR and many others (Phasarn et.al.,200). Results of ths study showed that regresson models estmatng SET Index can be used usng these factors. However, the number of sgnfcant correlaton coeffcents between the exlanatory varables whch were hghest affect redctons for SET50 Index. Therefore, the relatonshs between exlanatory varables, the multle lnear regresson analyss of the redcton of the multcolnearty roblem occurrng between the exlanatory varables. As for the hgher correlatons among the varables, some ndrect effects on the SET50 Index become nevtable. In ths case, t s very dffcult to use multle regresson analyss to see and dscuss the relatonshs correctly. In such cases, rncal comonent analyss can be used to both reduce the number of varables and to get rd of the multcolnearty roblem as well as to get a meanngful and easy analyss to see the comlex relatonshs. It has been observed that when the raw data of the study were used for the regresson analyss for forecast SET50 Index, a multcolnearty roblems exsted (VIF >= 5.0). On the other hand, when the PCA analyss was comleted on the exlanatory varables and the PC scores were ncluded n the multle regresson analyss as redctor varables nstead of orgnal redctor values, that roblem dmnshed. Therefore, usng the rncal comonent scores n multle regresson analyss for redctng SET50 Index s more arorate than usng the orgnal exlanatory varables data. Results of PCA showed that for, frstly, Bartlett s shercty test for all correlatons s zero or for testng the null hyothess that the correlaton matrx s an dentty matrx. It used to verfy the alcablty of PCA. Overall Kaser s measure of samlng adequacy ndcated that samle szes are enough to aly the PCA. Accordng to the results of eghteen rncal comonents there are three

23 N. Sooan, W. Kanjanawajee and P. Sattayatham 293 rncal comonents wth egenvalue greater than whch were selected for multle regresson analyss(forecast.). Thus, the frst of three PCs rovdes an adequate summary of the data for most uroses. If only the frst three PCs are selected, ths can exlan % of the total varaton. Accordng to the results of correlaton matrx of SET50 and PCAs, out of eghteen PCs there are four rncal comonents wth correlaton between SET50 and PCA not zero whch was selected for multle regresson analyss(forecast 2.). Lastly, we selected all PCA to forecast SET50 for multle regresson analyss (Forecast 3.). In ths study, two aroaches were emloyed n usng rncal comonent scores n multle regresson analyss. As can be seen 97.4% of varaton n SET50 could be exlaned by the frst three PCs, 98.4% of varaton n SET50 could be exlaned by the PCA, PCA2, PCA9 and PCA3 and 99.4% of varaton n SET50 could be exlaned by all PCAs. Accordngly, we forecast SET50 Index closed rces for the erod /03/20 through 3/03/20 by three models. When we comare loss functon, the model forecast 3 s exlaned by all PCs whch have a mnmum of all MSE, MAE and MAPE. References [] K. Chaereonkthuttakorn, The Relatonsh between the Stock Exchange of Thaland Index and the Stock Indexes n the Unted States of Amerca, Master s Thess n Economcs, Chang Ma Unversty, Chang Ma, Thaland, [2] S. Chagusn, C. Chrathamjaree and J. Clayden, Soft comutng n the forecastng of the stock exchange of Thaland (SET), Management of Innovaton and Technology, ICMIT 2008, 4th, (2008). [3] S. Chotasr, The Economc Factors Affectng the Fluctuaton of The Stock Exchange of Thaland Index, Master Thess n Economcs, Chang Ma Unversty, Chang Ma, Thaland, 2004.

24 294 Forecastng SET50 Index wth Multle Regresson... [4] I.T. Jollffe, Prncal Comonent Analyss, 2 nd ed. Srnger-Verlag, New York Inc, [5] C. Khumyoo, The Determnants of Securtes Prce n the Stock Exchange of Thaland, Master s Thess n Economcs, Ramkhamhaeng Unversty, Bangkok, Thaland, [6] M. Mendes, Multle lnear regresson models based on rncal comonent scores to redct slaughter weght of broler, Arch.Geflugelk, 73(2), (2009), [7] P. Mukhoadhyay, Multvarate Statstcal Analyss, World Scentfc Publshng Co. Pte. Ltd., London, [8] J. Pres, Selecton and valdaton of arameters n multle lnear and rncal comonent regressons, Envronmental Modellng & Software, 23, (2008), [9] S. Rmcharoen, D. Sutvong and P. Chongsttvatana, Predcton of the Stock Exchange of Thaland Usng Adatve Evoluton Strateges, Tools wth Artfcal Intellgence, ICTAI 05, 7th, (2005). [0] P. Sutheebanjard and W. Premchaswad, Analyss of Calendar Effects: Day-of-the-Week Effect on the Stock Exchange of Thaland (SET), Internatonal Journal of Trade, Economcs and Fnance, (), 200. [] P. Sutheebanjard and W. Premchaswad, Factors Analyss on Stock Exchange of Thaland (SET) Index Movement, The 7th Internatonal Conference on ICT and Knowledge Engneerng, ICTKE2009, Bangkok, Thaland, (December -2, 2009). [2] T. Tantnakom, Economc Factors Affectng Stock Exchange of Thaland Index, Master s Thess n Economcs, Chang Ma Unversty, Chang Ma, Thaland, 996. [3] C. Worasuchee, A New Self Adatve Dfferental Evoluton: Its Alcaton n Forecastng the Index of Stock Exchange of Thaland, Evolutonary Comutaton, 2007.