Mining associations between trading volume volatilities and financial information volumes based on GARCH model and neural networks

Transcription

1 Proceedings of he 007 Inernaional Conference on Managemen Innovaion, Shangha China, June 4-6, 007 Mining associaions beween rading volume volailiies financial informaion volumes based on GARCH model neural neworks Nan L Jian Yang, Xun Liang Insiue of Comuer Science Technolog, Peking Univers China {linan, angian, liangxun}@ics.ku.edu.cn Absrac: There has been an increasing aenion on he influences online financial informaion has on he financial markes. In he meanwhile, he volaili of rading volumes, us as he volaili of sock reurns, has an insearable associaion wih financial risks. I has been considered ha here migh exis some direc or indirec correlaions beween online financial informaion volumes financial volailiies, hough corresonding quaniaive analses or emirical sudies are sill absen. In his aer, we inroduce a mahemaical model uilizing arificial neural neworks (ANNs) GARCH (Bollerslev, 986) model, in order o mine he associaions in beween. The rudimenar mahemaical basis is he GARCH model, while we inroduce he volume of financial informaion from he Inerne as an exogenous inu, in conuncion wih arificial neural neworks as he redicion ool. Since combining ANN GARCH o robe ino he correlaions beween he aforemenioned wo is somewha lef unouched, i s worh menioning ha no onl have we realized he redicion of he rading volume volailiies o an acceable exen; we also have quaniaivel analzed he model s forecasing abili for he volaili rends. Besides, we furher subsaniae he imac online financial informaion has on financial rading volume volailiies via a series of disurbance exerimens. Furhermore, we have resened a basic forecasing measure reling on he volaili-clusering feaure, roved ha our model significanl oulas his measure in forecasing volaili rend. Kewords: Inerne financial informaion; financial volaili; GARCH model; neural nework; financial forecasing; ime series. INTRODUCTION Due o is real-ime ineracion, exuberance a wide coverage, Inerne has graduall suerseded some radiional media o become one of he rimar channels eole acquire informaion. Consequenl, financial informaion aained from he Inerne las an imoran role wihin he financial markes. Liang (005) oined ou ha comared o oher media, Inerne enables eole o ge he mos u-o-dae comrehensive financial informaion. Noneheless, from he curren lieraure, alread-adoed exogenous inus for forecasing financial volailiies include consumable rices, ineres raes, foreign exchange raes, ec. (Cafolis, 996), whereas nobod has ever aken online financial informaion volume ino consideraion e. Thus does online financial informaion reall have an imac on financial volaili? ill he inroducion of online financial informaion volume hel imrove he accurac of forecasing? In his aer, we will give our answers o such quesions b resening a mahemaical mining model based on GARCH ANN. I s worh menioning ha here have alread exised some research works regarding he associaions beween financial markes Inerne financial news (uhrich e al., 998; Chuur Bhurun, 005; Cosanino, 997; Peramuneilleke Ramond, 00), whose commonal however, lies in ha he based heir researching on he naural language rocessing (NLP) echniques o mine he correlaions beween financial markes he frequencies of financial kewords occurred in financial news online. On he oher h, we ake an aroach mainl focused on he volume of online financial informaion, aricularl r o dig ino he associaions beween i he financial volailiies for he urose of forecasing. In he firs lace, wihin he financial field, redicion of he financial volailiies has alwas been aealing o academicians, invesors as well as raciioners. Since above all, forecasing volailiies serves as he fundamenal basis for ricing financial asses derivaives exemlified b ha financial volaili consiues an imoran arameer in he Black-Scholes model (Black Scholes, 973). I can also be illusraed b he rading of sraddle oions, which requires he buers o accurael redic he underling asse s volaili if he wan o gain a rofi. Besides, i has also been acknowledged ha here is a close correlaion beween financial volailiies risks, wih usuall he former as a reresenaive of he laer, resuling in ha o effecivel redic he financial volailiies becomes a main measure aken b orfolio holders o evade risks. ha s more, an accurae redicion ISBN

2 Proceedings of he 007 Inernaional Conference on Managemen Innovaion, Shangha China, June 4-6, 007 of financial volailiies will definiel serve as an effecive obsacle of financial crimes. Secondl, we base our mahemaical model on GARCH heor mainl due o he fac ha financial daa is a ical ime series exhibiing is own feaures, which enails a more suiable heoreical basis for mahemaical modelling. ihin he curren lieraure, several radiional ime series models saisical mehods have been adoed o forecas financial volailiies (Pang, 004), including auoregressive model, moving average model (Dicke e al., 986), logical model, long-run moving model, romwalking, ec. Noneheless, GARCH model aarenl oulas hese aroaches in modelling financial ime series since i s more caable o cach hose feaures as fa ail, volaili-clusering, asmmer, ime-varing variance, leverage effec, ec, herefore has been widel alied ino financial ime series invesigaion (Garcia e al., 005; Zheng e al., 005; Liu, 005). In he meanwhile, ANN has been adoed in his aer as he redicion ool. Before he alicaion of ANN ino he financial markes, eole mainl relied on some linear ools o esablish he redicion model, such as linear regression (Lai e al., 996). However, due o is sueriori in nonlinear learning modelling, ANN has rogressivel been alied ino financial forecasing b an increasing number of researchers (Freisleben Rier, 997). U ill now, invesigaion ino he correlaions beween financial volailiies online financial informaion based on a combinaion of GARCH ANN is sill absen. Our aroach is us aimed a romoing he accurac of financial forecasing wih he aid of hese wo mehodologies. As a maer of fac, he emirical sudies have subsaniaed ha our model is sufficien o rovide a saisfing redicion of he volaili rend is scalable enough o be alied ino differen socks or indices b aroriael modifing he arameers. The res ar of his aer is organized as follows. Secion briefl exlains he characerisics archiecure of our model, while secion 3 deails he underling heoreical mahemaical bases. How o uilize he ANN o imlemen a dnamic raining redicion is resened in secion 4 emirical sudies are covered in secion 5. In secion 6, an evenual conclusion is reached. OUR APPROACH In his aer, we haven aken he aroach, as he oher revious researchers did, o invesigae ino he volaili of financial asses values; on he oher h, we robe ino he volaili of financial rading volumes. This is mainl because we consider ha he flucuaion of rading volumes, us like ha of he asse values, vividl reflecs he aleraions of markes invesors behaviours. Therefore, effecivel forecasing he rading volume s volaili will be beneficial advisor o hose who are exosed o financial risks wish o somewha maser he develoing rend of rading volumes. The rimar subec in his aer is he correlaion beween Inerne financial informaion he rading volume volailiies, which is for he urose of imroving he redicing erformance of he laer. In order o achieve his goal, we inroduce he GARCH model as our heoreical basis, whose alicaion has sanned a wide range ino risk managemen, orfolio managemen, asse allocaion, oion ricing, ec. The rimar reasons ha have conribued o GARCH s sueriori over he oher mehodologies are in he firs lace, i is buil on advances in he undersings modeling of volailiies of he as; in he second h, i akes ino accoun some secific characerisics of financial ime series, such as excess kurosis, volaili clusering ime-varing condiional variances. I can be concluded ha GARCH is a referable alernaive o caure effecs exhibied b financial ime series. In addiion, GARCH model can be alied on an ime series ha has significanl exhibied GARCH effecs. There are examles such as Garcia e al. (005) Zheng e al. (005) who alied GARCH heor ino he redicion for elecrici rices, Liu (005) oherwise ino he Jaanese foreign exchange markes. In our aroach, we have subsaniaed ha he changing rae of financial rading volumes on a dail basis also exhibis GARCH effecs such as fa ail he volaili hereof is ersisen. Furhermore, we have roved ha he online financial informaion volume ime series also exhibis GARCH effecs using he GARCH oolbox rovided b MATLAB. Besides, ANN has been adoed ino our aroach as he self-learning redicion ool. So far, ANN has been widel sudied imlemened ino he financial domains (Cafolis, 996; Freisleben Rier, 997; Lai e al., 996; Kuan hie, 994; Tino e al., 00; Genca Min, 00). Noneheless, he curren lieraure is sill lack of aling ANN ino forecasing he volaili of sock marke rading volumes. In he meanwhile, here have exised some research workings ha conduc a comarison beween he redicion erformances of ANN GARCH (Freisleben Rier, 997; Tino e al., 00) or combine hese wo o redic he financial volailiies (Donaldson Kamsra, 997). However, as menioned reviousl, we are sill in lack of works ha ake he invesigaion ino he associaions beween financial rading volume volailiies online informaion volumes based on a conuncion of hese wo echniques. In his aer, we regard he online financial informaion volume as an imoran elemen ha influences he financial rading volumes, ake he endeavor o forecas he volaili of he laer one wih he aid of GARCH ANN. The basic archiecure of our mehodolog can be visualized in Figure. ISBN

3 Proceedings of he 007 Inernaional Conference on Managemen Innovaion, Shangha China, June 4-6, 007 Figure Changing raes of he rading volumes of NASDAQ index on a dail basis wihin he eriod from Oc h, 984 o Oc 6 h, 006 Figure Archiecure funcional ars of our aroach 3 GARCH METHODOLOGY AND MATHEMATICAL MODEL Tha we base our aroach on he GARCH model in his aer, as reviousl menioned, is rimaril because he secific feaures exhibied b financial ime series (Freisleben Rier, 997; Zhang Fan, 005; Liu, 005), which can be illusraed b fa ail, volaili clusering, ime-varing variance (Engle, 98), asmmer, non-linear ec. All hese feaures deermine ha radiional ime series models migh no be caable enough o accurael model financial ime series. In he meanwhile, GARCH model akes ino accoun he imevaring variance auo-regression (Engle, 98; Bollerslev, 986) as well as bases is mahemaical equaions on he informaion se derived from he immediae as, which consiues he sueriori of GARCH in modeling financial ime series. e suose ha he volaili of financial rading volumes exhibis similar characerisics as ha of sock rices, we furher subsaniae his suosiion via he ools rovided b MATLAB. Figure visualizes he ime series of he changing raes of he rading volumes of NASDAQ index on a dail basis wihin he eriod from Oc h, 984 o Oc 6 h, 006. I can be aarenl observed, from Figure, ha he changing raes on a dail basis of he rading volumes as well exhibi volaili-clusering feaure. Besides, a Kurosis value as.53 calculaed from his secific ime series also illusraes ha here exiss a fa ail effec of his ime series. To make i more enable, we ve also discovered obvious GARCH effecs exhibied b online financial informaion volume ime series via es exerimens conduced on more han 00 socks in he U.S. sock markes. As aforemenioned, he rincial subec being invesigaed in our aroach is he volaili of he dail changing raes of sock rading volumes, which enails a sound exression for he volaili. Corresonding o his, we define he variance of he rading volumes dail changing raes wihin a cerain eriod as he volaili. In aricular, for a secific sock, le v denoe is rading volume on da, hus he dail changing rae of he rading volumes can be denoed as v ln. () v If we define D as he widh of he calculaing window for he volail he volaili can be calculaed b comuing he variance of he wihin he (-D+) h he h da, as indicaed in where D ( i ) i0, () D D i0 D i. (3) Thus we achieve as he volaili of he rading volume s changing raes in his aer. Before we furher robe ino he GARCH mehodolog imlemened in our aroach, we firs ake a look a he original version of he GARCH model, which is comosed of he mahemaical equaions as, (4) where 0 >0,, ~ N (0, ), (5) i i, (6) i 0 0, i q reresens he dail sock reurn, reresens he informaion se available a ime denoes he disurbance, also known as he shock, forecas error, residual, innovaion, ec. (Freisleben Rier, 997; Engle, 98; Bollerslev, 986; Zhang Fan, 005), which o some exen reflecs he difference beween he acual reurn he execed one;, i.e. ISBN

4 Proceedings of he 007 Inernaional Conference on Managemen Innovaion, Shangha China, June 4-6, 007 he volail serves as he ime-varing variance of boh. According o he analses covered in he former ars of his aer, i is reasonable o relace he conained in hese equaions wih he dail changing raes of he rading volumes, in order o mine he associaions beween he rading volume volailiies he online financial informaion volumes. A close correlaion beween he financial volailiies he innovaion can be illusraed from equaions (4) o (6). As a maer of fac, how o aroriael correcl model he innovaion erm has a significan effec on he accurac of he volaili forecasing. ha GARCH has disclosed is ha, in all robabil is an undeermined funcion of hose exogenous inus which migh have an imac on he financial volailiies. Undeniabl, financial informaion has been aracing researchers raciioners aenion as being an imoran exogenous inu for redicing financial volaili. ha adds o raionali o regard financial informaion as one exogenous inu is ha GARCH model bases is condiional disribuion on he informaion se available a ime. Addiionall, Freisleben Rier (997) oined ou ha he arameer in equaion (6) deermines he exen of he immediae reacion on new evens in he marke, mosl in he form of financial news, of he sock reurn. Noneheless, due o he feasibili of he available echnologies, revious academicians were no able o conduc an in-deh comrehensive analsis of he financial informaion, due o he deendence uon manual selecion from a limied amoun of financial news. Forunael, he fas develomen of Inerne has enabled us o acquire he financial informaion ha we re ineresed from online in a mos real-ime exhausive fashion aferwards conduc a quaniaive analsis beween i he financial volaili. Considering hese facs, o designae he financial informaion volume as one variae of is usifiable. Emirical sudies o furher confirm his conclusion will be resened in secion 5. According o wha we have achieved so far, here is a good reason o formulize using he following wo equaions,, (7) ' ' f, ) g ( ), (8) ( where (7) is derived from (4), is suosed o be a consan (under he remise ha we assign a consan as he execed value for he dail changing rae of rading volumes), is he Inerne financial informaion volume on da. Combining hese wo equaions (7) (8), we can come o a conclusion ha he innovaion erm is a cerain funcion of boh he online financial informaion volume he dail changing rae of he rading volumes. Therefore we make a modificaion on he original GARCH model hus achieve a new ime series model exressed as, (9) 0 i ~ N(0, ), (0) i i i q r ( ) ( ) k k k ( k,() where, q, r in () reresen he hree ime lags in his model resecivel; he hree unknown funcions, namel he i, k reresen he undeermined nonlinear correlaions beween he volaili iself, he dail changing rae he exogenous inu, which is he online financial informaion volume. Equaions (9) o () consiue he rimar heoreical basis relied uon which we decide he inu ouu vecors of he ANN in our aroach. Miller (979) oined ou ha he residuals wihin he auo-regressive moving-average model do no exhibi significan auo-correlaions or ersisence, whereas he squared values of hem do. ha s more, GARCH model, exressed in (4) o (6), as well akes he squared residual as one of is inus. Consequenl, we make all he inus in () heir squared values. 4 ESTABLISHMENT OF THE NON-LINEAR PREDICTION MODEL USING NEURAL NETORKS Currenl, ANN has been ervasivel as well as successfull alied ino he financial fields. Good illusraions include he work done b Freisleben Rier (997), who uilized ANN o realize he esimaion of he arameers for he GARCH model, ha b Zhang, Liang Yang (006), who caialized ANN o imlemen he ricing for oions, ha b Tino, Schienkof Dorffner (00), who rediced he sock reurn volailiies based uon a recurren neural nework as well as imlemened a comarison o he GARCH model s erformance. In our aroach, we can no ge o know he exac exressions of he hree funcions conained in (), however he onl conclusion we are caable o obain is ha here migh come along some non-linear correlaions beween he volailiies, he dail changing raes he online financial informaion volumes. On he oher h, he adven of ANN has rovided an effecive ool for eole o invesigae ino he non-linear associaions beween differen daa ses. Via aroriae configuraions of he arameers hidden nodes number, ANN is sufficien o aroximae almos all forms of funcions (Cai Sh 003; Huang e al., 006; u e al., 006; Kuan hie, 994). In addiion, he works done b Cbenko (989), Funahashi (989), Hornik (99) Hornik e al. (989) also indicae ha ANNs wih sufficienl man hidden nodes roerl configured arameers can aroximae an arbirar funcion arbiraril well. Due o he fac ha financial daa is inherenl characerisic of being nois, sochasic non-saionar (Tino e al., 00), we ado a secial raining rocess, namel an online or a dnamic raining rocess, in order o reven he henomenon of over-fiing, which seriousl imedes he generali of he model. Because of ) ISBN

5 Proceedings of he 007 Inernaional Conference on Managemen Innovaion, Shangha China, June 4-6, 007 he sochasic naure of financial ime series, we selec he daa acquired wihin he eriod which is he closes o he curren ime oin as he raining aerns for ever raining eoch. In addiion, daa acquired wihin a ime which is oo remoe from he curren ime oin migh conain oeniall misleading informaion. In aricular, if we wan o realize he redicion for he volaili on da, rovided ha he size of he raining aerns amouns o C, we firs rain a neural nework via conducing suervised redicions for he volailiies from da -C o da -. A well-rained neural nework is hen used o forecas he volaili of he da aferwards. In a nushell, during he rocess of online or dnamic raining, he forecasing for he volaili on a cerain da is alwas based on a newl-rained neural nework using daa aained wihin he mos immediae as. The ANN adoed in our aroach is a hree-laer feedforward neural nework using differen variaions of back-roagaion as he raining algorihms, whose archiecure can be visualized in Figure 3. The non-linear correlaions beween he inu he ouu vecors are refleced via he non-linear ransfer funcion of he hidden laer, in aricular he logsig funcion. The secific algorihms used in our aroach conain he baesian regularizaion back-roagaion (Chan e al., 00; Ganca Min, 00), BFGS quasi-newon backroagaion (Hu e al., 006) he Levenberg- Marquard back-roagaion (Kanzow e al., 004). The former wo are able o effecivel imede he over-fiing effec while he hird is characerisic of fas convergence. q H- hose ranged from o r reresen he moving average ar. The size of he inu vecor amouns o +q+r, each of he inu vecors reresens he volailiies, squared dail changing raes squared online informaion volumes wihin he mos immediae as. Besides, here are H unis in he hidden laer he size of he ouu vecor is. Le C denoe he size of he raining aerns for one raining eoch, i.e. he neural nework for each raining eoch is rained based on he daa acquired from he as C das. In addiion, suose ha we use a marix ule <P, T> o demonsrae he raining aerns for one raining eoch, hus we have P T C C C C C Cq C C Cr C C C C C Cq C C Cr C C C C C Cq C C Cr 3 3 q 3 r C. (3) C C The rained neural nework is hen used o forecas he volaili on he da a comarison beween he forecas value he real value is also carried ou hereafer. ha s worh menioning is ha we name his forecasing rocess as he esing rocess. Likewise, we denoe he esing aerns b anoher marix ule <P, T > as ( ) r H inu laer hidden laer ouu laer Figure 3 Archiecure of he ANN in our aroach The, q, r indicaed in Figure 3 corresond o he ime lags of he volail he dail changing rae he online financial informaion volume, resecivel, while he reresens he forecasing value for he volaili on da. The inu elemens ranged from reresen he auo-regressive ar of he model while ISBN o

6 Proceedings of he 007 Inernaional Conference on Managemen Innovaion, Shangha China, June 4-6, 007 P' q r, (4) T ', (5) where T ss for he real volaili on he da, which is also he comaraive arge for he esing rocess. 5 EMPIRICAL STUDIES AND DISCUSSIONS The emirical sudies covered in his aer can rimaril be divided ino wo hases. During he firs hase, we uilize he ANN o carr ou he forecasing for he volailiies while recording he mean forecas errors he accuracies for he volaili rend forecasing. Cafolis (996) inroduced a crierion using he revious da s volaili o forecas ha of he curren one, which is based on he volaili-clusering feaure, in order o esablish a comaraive benchmark for his own redicive model. In his aer, we ado a similar aroach o imlemen a comarison. Considering ha currenl here is no acknowledged sard o rel on when i comes o he redicion of volaili rend, we again uilize he volaili-clusering feaure o imlemen he comarison regarding his. Secificall, we suose ha he volaili rend of he da - can be used o forecas ha of he da, hereafer subsaniae, via emirical sudies, ha our model can considerabl oula such kind of aroach in volaili rend forecasing. In he second hase, we conduc disurbance exerimens on hose well-rained neural neworks for he urose of observing o wha exen he change of each elemen in he inu vecor can cause a corresonding change on he ouu. Via his wa, we re able o erceive qualiaivel wheher he exogenous inu of he online financial informaion volume reall has an effec on he rading volume volaili. The widhs of he calculaing windows, namel he D, in boh hases are se o 0 das. In he work done b uhrich e al. (998), onl 5 webages are downloaded from indicaed news sources in he morning on he curren da for he urose of invesigaion, whereas in our aroach, we based our exerimens on he financial informaion acquired from Google Finance (h://finance.google.com), which collecs is financial news reors from more han 500 financial orals online. Moreover, we acquire our rading daa in he financial markes from Yahoo Finance (h://finance.ahoo.com). 5. Using ANN o forecas he dail rading volume volaili In he firs lace, all our exerimen daa are acquired from he finance secions of wo redominan orals, Google Yahoo. Secificall, he link for he financial informaion enr is h://finance.google.com, where we can aain he financial news wihin he as several monhs colleced from more han 500 websies online. The enr for he rading daa is h://finance.ahoo.com, where we can download he hisorical rices rading volumes of almos ever sock or index in he U.S. financial markes. Secondl, we inroduce a comaraive crierion o serve as a so called benchmark for our own aroach. As has been menioned reviousl, his crierion resembles he one used b Cafolis (996), boh of which rel on he basic raionale of volaili clusering. If we use o reresen he acual he forecas volaili on he da, resecivel, we are able o obain, (6) which is based on he hohesis ha we can use he volaili on he da - o forecas ha on he da. Similarl, if we le denoe he acual he forecas volaili rend on he da, resecivel, firs we assume ha, 0,, (7), hen we can also obain ha, (8) which is based on he hohesis ha we can use he volaili rend on he da - o forecas ha on he da. As aforemenioned, we have inroduced wo was o measure he forecasing erformance, namel he average forecas error e he volaili rend forecasing accurac raio. If we define e as he forecas error for he da, we have e, (9) e, (0) 0 e 0 ISBN

7 Proceedings of he 007 Inernaional Conference on Managemen Innovaion, Shangha China, June 4-6, 007 where 0 reresen he beginning ending da for he forecasing, resecivel. In addiion, we define he raio as he ercenage of he das on which he forecas volaili rend is equivalen o he real one. hen we conduc our exerimens, we acuall ake ino consideraion a lo of facors ha migh imose an influence on he ulimae forecasing erformance, including he widh of he calculaing window for he volail he secific sock, he values of he ime lags, he size of he raining aerns, ec., we herefore conduc a series of exerimens wih differen configuraions for hese facors. Conclusivel, we conduc our exerimens on wo indices, NASDAQ DO, wo socks, MSFT INTC, wih he ime san as from Jun 30 h, 006 o Se 8 h, 006, from Jun 9 h, 006 o Se 6 h, 006, from Jun 8 h, 006 o Se 6 h, 006 from Jul 3 rd, 006 o Se 8 h, 006, resecivel. The resuls of hese exerimens are shown in Table. Table The forecasing resuls for he dail volailiies using neural neworks. s/i in he firs row ss for sock/index, while N, D, M, I s for NASDAQ, DO, MSFT, INTC, resecivel. ANN here reresens he aroach we ake while benchmark reresens he comaraive crierion we inroduce based on volaili clusering. As aforemenioned, C reresens he size of he aerns, H he number of he hidden nodes, q, r he hree ime lags in equaion (). s/i model C H q r e (%) raio (%) N D M ANN benchmark ANN benchmark ANN benchmark ANN benchmark ANN benchmark ANN benchmark ANN benchmark ANN benchmark ANN benchmark ANN benchmark I ANN benchmark ANN benchmark ANN benchmark Disurbance exerimens conduced uon rained neural neworks ihin his hase of exerimens, we furher usif he correlaion beween online financial informaion volumes he financial rading volume volailiies b conducing disurbance exerimens on he rained neural neworks during he esing rocess. To accomlish his, we consecuivel adus each elemen of he inu vecor,,,,, q r [ ] from 75% o 5% of he original value based on a redeermined selengh, hereafer observe record he corresonding changing raes of he ouu incurred b he adusmen of he inu vecor. Le denoe he changing rae of he forecas volaili on da caused b adusing se-lenghs on he value of he i h elemen in he inu vecor, he average changing rae of he ouu caused b he above acion wihin he da 0 he da (refer o 5.), we have 0, () 0 where The. () in () reresens he changed forecas volaili when he i h elemen of he inu vecor has been modified b se-lenghs. Table demonsraes he values of we have acquired when conducing he exerimens on he index NASDAQ wihin he eriod from Jun 30 h, 006 o Se 8 h, 006. The secific configuraions regarding he arameers are =3, q=8, r=3, C=0 H=4. Table The disurbance exerimen resuls for he index NASDAQ wihin he eriod from Jun 30h, 006 o Se 8h, 006 wih he configuraion as =3, q=8, r=3, C=0 H=4. The rows in gre indicae he changing raes of he inu elemens. ISBN

8 Proceedings of he 007 Inernaional Conference on Managemen Innovaion, Shangha China, June 4-6, According o he resuls shown in Table, i is clearl demonsraed ha comared o he oher inu facors, such as he volailiies he dail changing raes during he immediae as, online financial informaion volume does have a cerain influence on he ouu, which can be considered as of he same magniude of significance wih he ohers. 5.3 Discussions ihin he rocess of conducing differen exerimens, we also have esablished our model uon he sock rice reurns, for he urose of invesigaing he correlaion beween he online financial informaion volume he sock reurn volaili. Noneheless, we ve discovered ha he forecasing erformance for he rading volume volaili considerabl oulas ha for he rice reurn volail if we ake online informaion volume as an exogenous inu. Therefore, we deem ha rading volume is more inclined o be affeced b online financial informaion. In addiion, we ve found ou ha he greaer he value of D is, he smaller he average forecas error becomes, which furher roves he volaili clusering feaure of financial ime series. Furhermore, an aarenl beer forecas erformance can be achieved if we square he moving average ar of he inu vecor, which consiues a roof for one of he GARCH heor s conclusions, i.e. here migh exis a significan correlaion beween he squared residuals of financial ime series. 6 CONCLUSION AND FUTURE ORKS In his aer, we have inroduced a mahemaical model based uon GARCH ANN used for he invesigaion of he correlaions beween financial rading volume volaili online informaion volume, in order o forecas he former. According o he exerimenal resuls, our model is caable o achieve an acceable forecasing erformance for he dail rading volume volaili an excellen one for he volaili rend comared o he aroach based on he volaili clusering. Regarding fuure works, we inend o make furher imrovemens on he raining algorihms adoed in our aroach. Since he hree algorihms adoed in our aer all have is own deficiencies such as he former wo suffer from he drawback of slow convergence while he hird an inclinaion of over-fiing. In addiion, we wish, in he fuure, o base our model on a more comrehensive se of online financial informaion, which migh san several ears in ime. ACKNOLEDGEMENT This research was suored b he Naional Naural Science Foundaion of China under Gran REFERENCES Cafolis, T. (996) Neural neworks models for he redicion of sock reurn volaili, IEEE Inernaional Conference on Neural Neworks 96, 3-6 June, Vol.4, Freisleben, B. Rier, K. (997) Volaili esimaion wih a neural nework, Proceedings of he IEEE/IAFE on Comuaional Inelligence for Financial Engineering (CIFEr) 97, 4-5 March, La H.Z.H., Cheung, Y.M. Xu L. (996) Trading mechanisms reurn volaili emirical invesigaion on shang hai sock exchange based on a neural nework model, Proceedings of he IEEE/IAFE 996 Conference on Comuaional Inelligence for Financial Engineering 96, NYC, USA, 4-6 March, ISBN

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