Procings of th 2011 Confrnc on Tchnologis an Applications of Artificial Intllignc (TAAI 2011) Taiwan Stock Forcasting with th Gntic Programming Siao-Ming Jhou, Chang-Biau Yang an Hung-Hsin Chn Dpartmnt of Computr Scinc an Enginring National Sun Yat-sn Univrsity Kaohsiung 80424, Taiwan Abstract In this papr, w propos a mol for gnrating profitabl traing stratgis for Taiwan stock markt. Our mol applis th gntic programming (GP) to obtain profitabl an stabl traing stratgis in th training prio, an thn th stratgis ar appli to tra th stock in th tsting prio. Th variabls for GP inclu 6 basic information an 25 tchnical inicators. W prform fiv xprimnts on Taiwan Stock Exchang Capitalization Wight Stock Inx (TAIEX) from 2000/9/14 to 2010/5/21. In ths xprimnts, w fin that th traing stratgis gnrat by GP with two arithmtic trs hav mor stabl rturns. In aition, if w obtain th traing stratgis in thr historical prios which ar th most similar to th currnt training prio, w ar abl to arn highr rturn in th tsting prio. In ach xprimnt, 24 cass ar consir. Th tsting prio is rolling upat with th sliing winow schm. Th bst cumulativ rturn 166.57% occurs whn 545-ay training prio pairs with 365-ay tsting prio, which is much highr than th buy-an-hol stratgy. Kywors-stock; Taiwan Stock Exchang Capitalization Wight Stock Inx; gntic programming; annualiz rturn; fatur st. I. INTRODUCTION Pricting th fluctuation of th stock markt is a vry popular rsarch. Many invstors ar intrst in invstmnt, but forcasting th movmnt of th stock markt inx is vry ifficult, bcaus th stock markt is usually affct by many xtrnal factors, such as th intraction of intrnational financial markts, th political factors, th human oprations, tc. Gnrally, invstors o not hav sufficint knowlg an information about invstmnt so that thy cannot gain rturn asily. To gt th pattrns of pric fluctuation hin in th stock markt, som stuis [1], [9], [10] invstigat historical ata to fin a prcis solution of th stock markt volatility by using th mthos of artificial intllignc an statistics. Furthrmor, som stuis tri to gnrat traing stratgis for ciing th timing of buying an slling. Th mthos for forcasting th stock markt fluctuation inclu support vctor rgrssion (SVR) [10], support vctor machin (SVM) [5], [6], [9], [14], gntic algorithm (GA) [1], [3], [4], [5], [6], [7], [11], [16], [17], gntic programming (GP) [13], [19], artificial nural ntwork (NN) [7], [10], [11], [12], [16], [18]. Th goal of ths stuis is to min th pattrn of th pric fluctuation an to improv th accuracy of pricting th trn of th stock markt. Among ths stuis, thr bnchmarks This rsarch work was partially support by th National Scinc Council of Taiwan unr contract NSC99-2221-E-110-048. Corrsponing author: cbyang@cs.nsysu.u.tw ar usually us. Th first is to prict whthr th trn of th stock markt is raising or falling. [5], [6], [9], [14], [16]. Th scon bnchmark is th iffrnc of prict inics an th ral ons. Th most commonly us masurmnts ar root man squar rror (RMSE) an man absolut prcntag rror (MAPE) [2], [7], [10], [12], [18]. Th thir bnchmark is to apply th machin larning tchniqus to min th traing stratgis from th historical ata, an th rturn got by applying ths stratgis to tra on stock is usually compar with th buy-an-hol stratgy [1], [3], [4], [13]. In this papr, our goal is to arn stabl rturn in Taiwan stock markt. Th traing stratgy is appli to Taiwan Stock Exchang Capitalization Wight Stock Inx (TAIEX) in th tsting prio. Th total traing prio is from 2000/9/14 to 2010/5/21, approximatly 10 yars in total. Th bst cumulativ rturn 166.57% occurs whn 545-ay training prio pairs with 365-ay tsting prio, which is much highr than th rturn of th buyan-hol stratgy 1.19%. Th rst of this papr is organiz as follows. W will introuc th gntic programming (GP) in Sction II. In Sction III, w will prsnt our mtho that th traing stratgis ar gnrat by GP. In Sction IV, w will show our xprimntal rsults. Finally, in Sction V, w will giv th conclusion an som futur works. II. PRELIMINARIES In this sction, w will giv an introuction of th gntic programming, which is th backgroun knowlg of this papr. Th gntic programming (GP), which is xtn from th gntic algorithm (GA), was propos by Koza at 1992 [8]. Th grat avantag of GP is that it can b appli in varitis of problms with som constraints. Th solutions of ths problms gnrat by GP ar rprsnt as formulas. Th rprsntation of th chromosom of GP is mor flxibl than GA. Th solutions of GA ar string structurs with fix lngth which n to b nco an to b co for answr transformation. Th tr structur of GP has ynamic xtnsibility. GP can pars th tr structur to gt th corrsponing solution. Thrfor, GP is mor suitabl for sarching traing stratgis. On traing stratgy is usually prouc by prfin functions, constants an variabls. Th volutions in GP ar summariz as follows. 1) Initialization: Th initial population is compos of iniviuals, which ar gnrat ranomly. Th structur of an iniviual is a tr. TAAI 2011, Novmbr 11-13, 2011, Chung-Li, Taiwan ISBN 978-986-87804-0-8 151
Procings of th 2011 Confrnc on Tchnologis an Applications of Artificial Intllignc (TAAI 2011) Ys Slct on iniviual Rprouction Start Ranomly gnrat initial population Assss fitnss of population Ar trmination critria satisfi? No Choos gntic opration Crossovr Slct two iniviuals Rturn bst iniviual Mutation Slct on iniviual Prform rprouction Prform crossovr Prform mutation Figur 1. Insrt offspring into nw population Is nw population full? En Th flow chart of GP. No Ys 2) Slction: To slct iniviuals with highr fitnss valus into th nw population is usually accomplish by using th roultt-whl mtho. 3) Rprouction: Rprouction is to copy th litist iniviual into th nw population. 4) Crossovr: Th most common approach for crossovr in GP is th subtr crossovr. Th intrnal nos ar usually slct as crossovr points. To prform th crossovr btwn two trs, ranom subtrs ar rspctivly slct from th fathr tr an th mothr tr. Thn, th fathr s subtr is rplac by th mothr s subtr, an th nw iniviual is th offspring. 5) Mutation: Mutation is appli to only on iniviual, an it incrass th ivrsity of th population. Th most common approach for mutation is th subtr mutation. In th subtr mutation, a mutation point (th root of a subtr) is ranomly slct from th iniviual. To prform th mutation, th subtr connct to th mutation point is rplac by a ranomly gnrat tr. Th nw iniviual is th rsult of mutation. In GP, th final answr is rprsnt by a formula rathr than som paramtrs. In othr wors, th solution spac of sarching is flxibl, an it also improvs th ncoing problm of GA. Figur 1 shows th flow chart of GP. A function no (or intrnal no) in th GP tr is usually an arithmtic oprator, a mathmatical function, or a Boolan oprator. Various problms can b solv with GP by signing suitabl function nos. Bfor w apply GP to th solution of a crtain problm, w hav to o th following works first. 1) To fin th st of trminal nos an function nos: On problm may n som spcific trminal nos an function nos, an th finitions of ths nos shoul satisfy th closur proprty whn th trs ar pars. In othr wors, w hav to chck whthr th trs can b pars for valuating or not. Som commonly us function nos ar givn as follows. a) arithmtic oprators : +,,,, tc. b) Boolan oprators : AND, OR, NOT, tc. c) comparison oprators : >,,, tc. ) logical oprators : if thn ls. Each trminal no (laf no) rprsnts a constant or a variabl for a spcifi problm. 2) To fin th fitnss function: Th fitnss scor of on chromosom is us to masur th goonss of th chromosom. W can liminat th chromosoms with low scors an rsrv th chromosoms with high scors. 3) To st paramtrs for GP: Som paramtrs of GP hav to b st bfor thy ar oprat. Th paramtrs inclu population siz, crossovr rat, crossovr mchanism, mutation rat, mutation mchanism, numbr of gnrations, an th maximum pth of th arithmtic tr. 4) To trmin th trminal conition: Th trminal conition gnrally pns on th gnrations, th typs of oprators, an th convrgnc of th fitnss scors. Whn GP trminats, th solution is rprsnt by th chromosom with th bst fitnss scor in th final gnration. III. STOCK INVESTMENTS WITH GENETIC PROGRAMMING In this sction, w propos a mol which is abl to gain stabl rturns on traing stock by using th gntic programming to sarch th stabl an profitabl traing stratgis. A. Flow Chart of Invstmnt Th flow chart for our mol is shown in Figur 2. In our mol, w us GP to train th stabl an profitabl traing stratgy in 3 historical prios which ar th most similar to th training prio of th targt stock, an thn w tra th stock by using th train stratgy in th tsting prio. Th historical prio starts from 1995/1/1 to th ay which is bfor th training prio. Th training prio an th tsting prio ar rolling upat until th n of th traing prio. Th sliing winow schm is shown in Figur 3. 152
Procings of th 2011 Confrnc on Tchnologis an Applications of Artificial Intllignc (TAAI 2011) Start St th training prio an tsting prio Sarch for thr historical prios which ar th most similar to th training prio by RMSE masurmnt. Fin th most profitabl traing stratgy for th thr historical prios with GP. t-n+1 Apply th traing stratgy to th tsting prio. Is th sift tsting prio ovr th traing prio? Figur 2. Training prio (t+p)-n+1 Ys En Th flow chart for invsting on stock. Training prio t (t+p*2)-n+1 Tsting prio t+p t+p Training prio Tsting prio t+p*2 t+p*2 Tsting prio No tim lin tim lin tim lin t+p*3 Figur 3. Th training prio an th tsting prio with th sliing winow schm. Hr, n, t, an p rprsnt th lngth (ay) of th training prio, th currnt at, an th lngth (ay) of th tsting prio, rspctivly. similar to th currnt training prio ar chosn from th historical ata by th masurmnt of th root man squar rror (RMSE). Hr, all ata sris ar form by th aily clos prics. Th quation of RMSE is givn as follows: n j=1 RMSE(X 1,X 2 )= (x 1,j x 2,j ) 2, (1) n whr X 1, X 2, x 1,j, x 2,j, an n rprsnt th ata sris of th first prio, th ata sris of th scon prio, th jth lmnt of th first prio, th jth lmnt of th scon prio, an th lngth of th prio, rspctivly. Aftr w fin th 3 historical prios with th lowst RMSE valus compar to th training prio, w xtn ths prios. That is, suppos that th lngths of th training an tsting prios ar 1 an 2, rspctivly. Th lngth of th historical prio w sarch is 1, an th lngth of th xtn prio is 1+2. Each stratgy gnrat by GP is us to tra th stock in th 3 xtn historical prios, thn w can gt 3 rturns with thir stanar viation. Th highr th avrag rturn ivi by its stanar viation is, th mor stabl an profitabl th traing stratgy is. Aftr gtting th bst traing stratgy, w apply it in th tsting prio. C. Gnrating th Traing Stratgy with th Gntic Programming To utiliz th gntic programming (GP), w hav to fin th function nos an th trminal nos first. Th function nos for our mtho consist of oprators >, <, =,,, logical an, logical or, +, -, an. Th trminal nos involv 6 basic information an 25 tchnical inicators of on stock, which ar opn prics, clos prics, highst prics, lowst prics, th traing volums, th amount of prics, MTM 5, OBV, DI, volum 5, volum 20, RSI 5, RSI 14, MA 10, MA 20, TAPI, PSY 14, WMS 5, WMS 9, BIAS 10, BIAS 14, BIAS 20, OSC 5, RSV 9, K 3, D 3, EMA 12, EMA 26, DIF, an MACD 9. W not ths 31 faturs as full faturs. Th constants for th trminal nos ar th numbrs gnrat ranomly btwn 1.0 an 1.0. In aition, w moify th lft subtr of th original arithmtic tr to a buy-tr, an th right subtr to a slltr. With this moification, th traing signal gnrat by two arithmtic trs on at t is givn as follows. B. Training Intrval Slction from Historical Data Lu t al. [12] an Yu t al. [18] prict th stock clos pric by fining th historical prio which is similar to th training prio. In this papr, th training prio is fin to b an intrval just bfor th currnt tsting prio. Th lngths of training an tsting prios n not b th sam. Th historical prio is slct from th intrval starting from th vry bginning to th ay just bfor th training prio. Th goal of historical prios is to hlp th mol construction of th training prio. In our mol, thr historical prios which ar th most IF (th valu of th buy-tr on at t> 0) AND (th valu of th sll-tr on at t< 0) THEN signal(t) TRUE ELSE IF (th valu of th buy-tr on at t< 0) AND (th valu of th sll-tr on at t> 0) THEN signal(t) FALSE ELSE signal(t) signal(t 1) END IF (2) Accoring to th traing signal, th action w shoul tak at at t is scrib as follows. 153
buying: If th signal of at t is TRUE an th signal of at (t-1) is FALSE, thn w buy th stock. slling: If th signal of at t is FALSE an th signal of at (t-1) is TRUE an w own th stock, thn w sll th stock. holing: If th signals of both ats (t-1) an t ar TRUE, thn w hol th stock an wait th signal to turn to slling. Similarly, if th signals of ats t an (t-1) ar both FALSE, thn w o nothing an wait th timing to buy. Whn GP voluts a traing stratgy in vry gnration, w can apply it to th 3 xtn historical prios. Thn, w gt thr rturns, whos avrag an stanar viation can b calculat. Our fitnss function of GP is to maximiz th cofficint of rturn variation which is th avrag rturn ivi by th stanar viation. In th n of volution, w obtain a traing stratgy which has th most stabl an profitabl rturn in th 3 xtn historical prios. Thn, w apply th stratgy in th tsting prio. Th training prio an th tsting prio ar rolling upat with th sliing winow schm. IV. EXPERIMENTAL RESULTS In this sction, w will first introuc th bnchmarks an th atast, an thn show our xprimntal rsults. A. Bnchmarks In this sction, w will introuc th masurmnts. Many masurmnts ar abl to valuat th prformanc of a traing mol, but thy usually us iffrnt units or currncis. To gt objctiv bnchmark rsults, w us th rturn on invstmnt (ROI), which is fin as ( final capital initial capital 1 100%.) W also compar our rsults with th buy-an-hol stratgy that th invstor buys on stock at th start of th traing prio, an slls th stock at th n of th traing prio. A goo traing mol is abl to arn high an stabl rturn. B. Data Collction an Prprocssing Our atast contains th basic information of Taiwan Stock Exchang Capitalization Wight Stock Inx (TAIEX), an th atast is ftch from Taiwan Economic Journal (TEJ) atabas, which was stablish in April of 1990. It provis th stock information, incluing th prics, tchnical inicators, an funamntal analysis of scuritis of Taiwan stock markt [15]. W assum that TAIEX is traabl. Our goal is to gain high an stabl rturn by traing TAIEX with its aily clos pric bing our traing targt. Th clos prics of TAIEX from 1995/1/1 to 2011/3/1 ar shown in Figur 4. In our xprimnts, th traing prio is from 2000/9/14 to 2010/5/21. Th rason w choos this prio is that th starting ay an th ning ay has almost th sam clos pric. In this prio, it is fair to compar our rsults with th buy-an-hol stratgy. /y Figur 4. Th clos prics of TAIEX from 1995/1/1 to 2011/3/1. C. Exprimntal rsults In all xprimnts, short-trm buying an slling is forbin. W prform fiv xprimnts scrib as follows. Exprimnt I: On arithmtic tr an th full fatur st ar us. Exprimnt II: Two arithmtic trs an th full fatur st ar us. Exprimnt III: W us two arithmtic trs an six slct faturs which ar frquntly us in th profitabl stratgis in Exprimnt II. Ths faturs ar RSI 5, PSY 14, WMS 5, WMS 9, DIF, an MACD 9. Exprimnt IV: W us two arithmtic trs an th full fatur st with 12 macroconomic inicators a, such as U.S. proucr pric inx, U.S. annual changs in consumr pric inx, Taiwan unmploymnt rat, tc. Exprimnt V: Two arithmtic trs an th full fatur st ar us. W sarch th historical ata to fin th thr prios which ar th most similar to th currnt training prio with th RMSE masurmnt. Thn, th most profitabl traing stratgy for ths thr prios ar train by GP. An finally, w apply th stratgy to th tsting prio. In all xprimnts, it is assum that TAIEX is traabl an only on unit is tra. Manwhil, w can sll only whn w hav on unit in han (bought bfor) Th traing f is assum to b 0.6% (th currnt f in Taiwan stock markt). W train th traing stratgy by using GP with training prios of various lngths, incluing 90, 180, 270, 365, 455, 545, 635, an 730 ays. An tsting prios of various lngths, incluing 90, 180, an 365 ays, with th sliing winow schm, ar tst. Thus, totally 24 cass ar prform in ach xprimnt. Th function nos inclu >, <, =,,, logical an, logical or, +, -, an. Th trminal nos involv 6 basic information an 25 tchnical inicators, an th constants ar ranom numbrs btwn 1.0 an 1.0. Th paramtrs of GP ar shown in Tabl I. In Exprimnt I, using only on arithmtic tr may gnrat traing signals which ar vry snsitiv to th fluctuation of th markt, an it may also caus many Procings of th 2011 Confrnc on Tchnologis an Applications of Artificial Intllignc (TAAI 2011) 154
Procings of th 2011 Confrnc on Tchnologis an Applications of Artificial Intllignc (TAAI 2011) Tabl I THE PARAMETERS OF THE GENETIC PROGRAMMING. Population siz 100 Numbr of gnrations 200 Initial mtho qual mix of Full an Grow mtho Slction mtho roultt whl Crossovr rat 90% Mutation rat 50% Maximum pth 3 Tabl II THE CUMULATIVE RETURNS FROM 2000/9/14 TO 2010/05/21 WITH TWO ARITHMETIC TREES FOR GP AND THREE HISTORICAL TRAINING PERIODS. /y Training \tsting prio 90 180 365 Avg. Stv. 90 61.27% 53.61% 68.44% 61.11% 7.41% 180 65.69% 66.76% 0.35% 44.27% 38.04% 270-8.64% -2.30% 109.28% 32.78% 66.33% 365-19.52% 4.26% 56.52% 13.75% 38.90% 455 68.88% 27.06% 75.71% 57.22% 26.34% 545 60.41% 126.72% 166.57% 117.90% 53.62% 635 73.61% 38.70% 145.58% 85.96% 54.50% 730 21.66% 78.56% 61.72% 53.98% 29.23% Avg. 40.42% 49.17% 85.52% Stv. 37.30% 42.21% 53.17% unncssary transactions, hnc it i not arn high rturn. In Exprimnts II, III, an IV, two arithmtic trs with iffrnt fatur sts ar us for training traing stratgis, but th training prios in ths xprimnts ar not highly rlat with th tsting prio, hnc it is har for GP to train a profitabl traing stratgis. Among th fiv xprimnts, th fifth is th most profitabl. Th cumulativ rturns of th xprimnt ar shown in Tabl II. As on can s, th cumulativ rturns of all cass ar almost positiv, it mans that our mtho has only small probability to los mony. In th xprimnt, whn th 545-ay training prio pairs with 365-ay tsting prio, w can gt th highst cumulativ rturn 166.57%, which is highr than th rturn of th buy-anhol stratgy 1.19%. W show th traing rcor in Figur 5 in 2001 an traing stratgis in Tabl III in th tn yars. In Figur 5, w can buy TAIEX at rlativly low pric an sll it at rlativly high pric in th bull markt, such as th 2n buying tim, 7th buying tim, 2n slling tim, an 7th slling tim. In th bar markt, w can sll th stock bfor th stock crashs, such as 2n, 3r, an 6th slling tim. It rvals th profitability of our mol. V. CONCLUSION In this papr, w propos a novl mol for invstmnt in Taiwan Stock Exchang Capitalization Wight Stock Inx (TAIEX). Our traing stratgis ar gnrat by two arithmtic trs in GP. Whn 545-ay training prio pairs with 365-ay tsting prio, th cumulativ rturn is 166.57%, highr than th buy-an-hol stratgy. In th futur, w will try to fin mor suitabl stratgis by sarching mor prios from th historical ata, an moify th valuating mtho for fining similar pattrns. Th longst common subsqunc or ynamic tim warping is on of th possibl ways to fin th most similar subsquncs in our training ata for GP. W will also apply th risk managmnt an th portfolio to th stock invstmnt. Figur 5. Th traing rcor from 2001/1/1 to 2001/12/31 with 545-ay training prio an 365-ay tsting prio in TAIEX. Hr, a vrtical soli lin rprsnts buying tim an a vrtical ott lin rprsnts slling tim. Tabl III THE TRADING STRATEGIES FROM 2000/9/14 TO 2010/5/21 WITH 545-DAY TRAINING PERIOD AND 365-DAY TESTING PERIOD IN TAIEX. tsting prio rturn traing arithmtic traing count trs stratgis 000914 010913 16.61% 9 buy rul sll rul RSV 9 (0.5 P SY 14 )AND(-0.1 <BIAS 14 ) 010914 020913 3.96% 11 buy rul (highp (-0.3)) (MA 14 ) sll rul MACD 9 >((D 3 )OR(MACD 9 )) 020914 030913 29.89% 18 buy rul MA 10 ((0.6)OR(highp)) sll rul RSV 9 < 0.3 OSC 5 030914 040912 12.33% 3 040913 050912 1.57% 20 050913 060912 1.12% 16 060913 070912 16.60% 21 070913 080911-6.11% 5 080912 090911 34.01% 17 090912 100521 4.48% 14 buy rul (BIAS 14 >MACD 9 ) MACD 9 sll rul (OBV avg.volum 20 )<avg.volum 20 buy rul (RSI 5 BIAS 20 ) 0.7 sll rul ((MA 14 )OR(MA 14 )) MA 20 buy rul DIF sll rul (BIAS 20 RSI 5 ) (PSY 14 + PSY 14 ) buy rul -0.6 (amoutp -0.1) sll rul (RSV 9 <MACD 9 )>PSY 14 buy rul BIAS 14 sll rul BIAS 20 buy rul (0.9 RSI 14 )+BIAS 14 sll rul -1.0 (highp > avg.volum 20 ) buy rul D 3 > WMS 5 sll rul (DIF MTM 5 ) (0.6 WMS 5 ) REFERENCES [1] P. F. Blanco, D. Sagi, an J.I.Halgo, Tchnical markt inicators optimization using volutionary algorithm, Proc. of th 2008 GECCO confrnc companion on Gntic an volutionary computation, Atlanta, USA, July 2008. [2] M. A. Boyacioglu an D. Avci, An aaptiv ntwork-bas fuzzy infrnc systm ANFIS for th priction of stock markt rturn: Th cas of th istanbul stock xchang, Exprt Systms with Applications, Vol. 37, pp. 7908 7912, 2010. [3] T. J. Chang, S. C. Yang, an K. J. Chang, Portfolio optimization problms in iffrnt risk masurs using gntic algorithm, Exprt Systms with Applications, Vol. 36, pp. 10529 10537, 2009. [4] J. S. Chn, J. L. Hou, S. M. Wu, an Y. W. C. Chin, Constructing invstmnt stratgy portfolios by combina- 155
Procings of th 2011 Confrnc on Tchnologis an Applications of Artificial Intllignc (TAAI 2011) tion gntic algorithms, Exprt Systms with Applications, Vol. 36, pp. 3824 3828, 2009. [5] D. Y. Chiu an P. J. Chn, Dynamically xploring intrnal mchanism of stock markt by fuzzy-bas support vctor machins with high imnsion input spac an gntic algorithm, Exprt Systms with Applications, Vol. 36, pp. 1240 1248, 2009. [6] R. Chouhry an K. Garg, A hybri machin larning systm for stock machin markt forcasting, Proc. of Worl Acamy of Scinc, Enginring an Tchnology, Vol. 39, pp. 315 318, Mar. 2008. [7] M. R. Hassan, B. Nath, an M. Kirly, A fusion mol of hmm, ann an ga for stock markt forcasting, Exprt Systm with Application, Vol. 33, pp. 171 180, 2007. [8] J. H. Hollan, Aaptation in natural an artificial systms: an introuction analysis with applications to biology, control, an artificial intllignc. Univrsity of Michigan Prss, 1975. [9] W. Huang, Y. Nakamori, an S. Y. Wang, Forcasting stock markt movmnt irction with support vctor machin, Computrs & Oprations Rsarch, Vol. 32, pp. 2513 2522, 2005. [10] H. Inc an T. B. Trafalis, Short trm forcasting with support vctor machins an application to stock pric priction, Intrnational Journal of Gnral Systms, Vol. 37, pp. 677 687, 2008. [11] K. Kwon an B. R. Moon, A hybri nurogntic approach for stock forcasting, IEEE Transactions on Nural Ntworks, Vol. 18(3), pp. 851 864, 2007. [12] Y. Lu, C. P. L, an C. C. Hung, A fuzzy tim srisbas nural ntwork approach to option pric forcasting, th 2n Asian Confrnc on Intllignt Information an Databas Systms, Vol. 5990, pp. 360 369, 2010. [13] J.-Y. Potvin, P. Soriano, an M. Vall, Gnrating traing ruls on th stock markts with gntic programming, Computrs & Oprations Rsarch, Vol. 31, pp. 1033 1047, 2004. [14] N. Powll, S. Y. Foo, an M. Wathrspoon, Suprvis an unsuprvis mthos for stock trn forcasting, Proc. th 40th Southastrn Symposium on Systm Thory, Nw Orlans, LA, USA, Mar. 2008. [15] Taiwan Economic Journal Co., Lt, TEJ. http://www.tj.com.tw/twsit/ Dfault.aspx, 1991. [16] C. F. Tsai an Y. C. Hsiao, Combining multipl fatur slction mthos for stock priction: Union, intrsction, an multi-intrsction approachs, Dcision Support Systms, Vol. 50, pp. 258 269, 2010. [17] T. J. Tsai, C. B. Yang, an Y. H. Png, Gntic algorithms for th invstmnt of th mutual fun with global trn inicator, Exprt Systms with Applications, Vol. 38(3), pp. 1697 1701, 2011. [18] T. H. K. Yu an K. H. Huang, A nural ntwork-bas fuzzy tim sris mol to improv forcasting, Exprt Systms with Applications, Vol. 37, pp. 3366 3372, 2010. [19] M. Zhang an W. Smart, Using gaussian istribution to construct fitnss functions in gntic programming for multiclass objct classification, Pattrn Rcognition Lttrs, Vol. 27, pp. 1266 1274, 2006. 156