016 Jon Inrnaonal Confrnc on Arfcal Inllgnc and Copur Engnrng (AICE 016) and Inrnaonal Confrnc on Nwork and Councaon Scury (NCS 016) ISBN: 978-1-60595-36-5 AdaBoos Arfcal Nural Nwork for Sock Mark Prdcng Xao-Mng BAI 1,a, Chng-Zhang WANG,b,* 1 Inforaon School, Capal Unvrsy of Econocs and Busnss, Bjng, Chna School of Sascs and Mahacs, Cnral Unvrsy of Fnanc and Econocs, Bjng, Chna a xbag@gal.co, b xbaczwang@163.co *Corrspondng auhor Kywords: AdaBoos, Arfcal Nural Nwork, Sock Indx Movn. Absrac. In hs work, w propos a nw drcon of sock ndx ovn prdcon algorh, cond h Ada-ANN forcasng odl, whch xplos AdaBoos hory and ANN o fulfll h prdcng ask. ANNs ar ployd as h wak forcasng achns o consruc on srong forcasr. Tchncal ndcaors fro Chns sock ark and nrnaonal sock arks such as S&P 500, NSADAQ, and DJIA ar slcd as h prdcng ndpndn varabls for h prod undr nvsgaon. Nurcal rsuls ar copard and analyzd bwn srong forcasng achn and h wak on. Exprnal rsuls show ha h Ada-ANN odl works br han s rval for prdcng drcon of sock ndx ovn. Inroducon Sock prc ndx ovn s a prary facor ha nvsors hav o consdr durng h procss of fnancal dcson akng. Cor of sock ndx ovn prdcon s o forcas h clos prc on h nd pon of h prod. Rsarch sch basd on chncal ndcaors analyss assus ha bhavor of sock has h propry of prdcably on h bass of s prforanc n h pas and all ffcv facors ar rflcd by h sock prc. By analyzng chncal ndcaors of prvous sock prc, on could oban poran nforaon whch could b xplord o forcas h followng sock prc [1]. Sock ark prdcon was don on ISE by ANN n []. Prdcon rsuls of dffrn classc approachs and ANN wr xand and hy found ANN was supror o ohr hods. ANN odls wr xand n prdcon of h followng day ndx drcon n [3]. ANN odl and lnar rgrsson odl wr xplord o forcas rgng sock ark n [4]. Fnancal ndcaors ncludng h clos prc, h hghs prc, h lows prc, wr slcd as ndpndn varabls for ANN npu o forcas h drcon of ISE Naonal-100 n [5]. Prdcng prforanc of ANN and SVM wr sudd for prdcng drcon of sock prc ndx ovn on ISE n [6]. Tn chncal ndcaors wr slcd and ulzd for prdcon. Sudy rsuls showd ha ANN was sgnfcanly br han SVM. ANN was ulzd o forcas sock ark ndx ovn on ISE n [7]. Forcasng prforanc was assssd n dffrn prod of. Thy confrd ha ANN go hgh prcnag of corrcly forcasd sgns. ANN was ngrad wh ahurscs o forcas sock prc on Turksh Sock ark n [8]. In h sudy, 45 chncal ndcaors, such as h clos prc, MACD, h hghs prc, wr slcd as h npu o ANN. I assrd ha HS basd ANN odl dd br han ohr odls o b copard. ANN was adopd o forcas sock prc ndx on Tawan Sock Exchang n [9]. I was sad ha volals aong h daa was conssn wh ARCH parns. ANN xd wh ARCH could nhanc prc prdcon. ANN and prncpal coponn analyss hods wr xand n [10] for prdcng h sock prc on Thran Sock Exchang. I clad ha prncpal coponn analyss could forcas h sock prc accuraly accordng o wny accounng varabls. Th sudy showd ha ANN odl was supror o ohr hods. On h bass of accounng raos, [11] copard nural nwork for forcasng sock rurns on Canadan sock ark wh ohr wo hods,
ordnary las squars and logsc rgrsson chnqus. Rsuls ndcad ha nural nworks ouprford h ohr ons. Volaly of sock prc on Kora Sock Exchang was sudd n [1]. ANN was cobnd wh srs parns o forcas h volaly of sock prc. Rsuls assrd h suprory of ANN ovr s rvals. Th forcasng prforanc of ARIMA and ANN odl wr xand basd on h sock daa fro Nw York Sock Exchang n [13]. Rsuls rvald h suprory of ANN odl ovr ARIMA odl. In ordr o prdc h axu and nu day sock prcs of Brazlan powr dsrbuon copans, ANN was ployd o do ha n [14]. I rvald ha ANN wh on hddn layr and fv hddn nurons achvd h bs rsuls. Durng h procss of larnng, h valus of nal wghs of an ANN odl ar usually s a rando. Rsuls of on ANN odl for classfyng or prdcng ay xhb hgh volaly. Addonally, ANN s pron o local opu durng h ranng procss whch ay rsul n bad or unsasfacory classfcaon or prdcon rsuls. Whl accordng o h hory of boosng [15], ruls of hub, or wak classfrs, can b cobnd o for hghly accura cobnd classfrs. And wak-larnrs can b ployd o dscovr hs spl ruls whch ak h cobnd algorh wdly applcabl. Insprd by h da, w ap o consruc a boosng prdcor n hs papr for sock prc forcasng. ANN odls ar ployd as h wak prdcors o for h cobnd srong on. W laboraly dsgn h boosng ruls and propos a boosng prdcon algorh basd on ANN for sock prc forcasng. Our work anly focuss on consrucng a srong prdcor usng ulpl ANN odls, whch s dffrn fro os of prvous works for sock ark forcasng concnrang on opzng parars and archcur of on sngl ANN. Rsarch Mhodology Accordng o h hory of conocs, h drcon of h sock ndx ovn s dfnd by h followng forula: Drcon sgn( P P ) (1) End Pon Sar Pon Whr PEnd Pon rfrs o h sock ndx prc of h nd pon ovr h prod, P Sar Pon rprsns h sock ndx prc of h sar pon ovr h prod. For daly drcon prdcon, P End Pon s oday's sock ndx clos prc and P Sar Pon pon s prvous day's sock ndx clos prc. Targ populaon of hs rsarch conans sock ndx prcs nforaon on Shangha Sock Exchang ovr a prod fro Jan. 011 o Mar. 016. Sock prcs nforaon fro nrnaonal sock arks, such as S&P 500, NSADAQ, and DJIA, and forgn xchang ras o US dollar ovr h sa prod of ar also consdrd. Tchncal Indcaors 38 chncal ndcaors of sock ark ar slcd as h ndpndn varabls, s n Tabl 1, and ar ulzd as h npu o our Ada-ANN odl o forcas h drcon of sock ndx ovn.
Tabl 1. Tchncal ndcaors of sock ark. 1: Today's opn prc 0: Slow sochasc %D : Prvous opn prc 1: Wlla's %R 3: Prvous hghs prc : Bollngr ddl band 4: Prvous lows prc 3: Bollngr hghr band 5: Prvous clos prc 4: Bollngr lowr band 6: Today's opn prc of S&P 500 5: 5-day spl ovng avrag of clos prc 7: Prvous opn prc of S&P 500 6: 5-day xponnal ovng avrag of clos prc 8: Prvous clos prc of S&P 500 7: 5-day rangular ovng avrag of clos prc 9: Exchang ras o US dollar 8: 6-day spl ovng avrag of clos prc 10: Today's opn prc of NSADAQ 9: 6-day xponnal ovng avrag of clos prc 11: Prvous opn prc of NSADAQ 30: 6-day rangular ovng avrag of clos prc 1: Prvous clos prc of NSADAQ 31: 10-day spl ovng avrag of clos prc 13: Today's opn prc of DJIA 3: 10-day xponnal ovng avrag of clos prc Tabl 1. Tchncal ndcaors of sock ark (Con.). 14: Prvous opn prc of DJIA 33: 10-day rangular ovng avrag of clos prc 15: Prvous clos prc of DJIA 34: 0-day spl ovng avrag of clos prc 16: Monu clos prc 35: 0-day xponnal ovng avrag of clos prc 17: Fas sochasc %K 36: 0-day rangular ovng avrag of clos prc 18: Fas sochasc %D 37: Clos prc ovng avrag convrgnc/dvrgnc 19: Slow sochasc %K 38: Accuulaon/dsrbuon oscllaor AdaBoos Thorcal frawork of boosng for achn larnng s PAC (probably approxaly corrc) larnng odl. In ordr o solv los of praccal dffculs ncounrd by h arlr boosng algorhs, AdaBoos algorh was proposd on h bass of boosng n [16]. Suppos ranng s s Sran ( x1, y1),,( x, y). Whr ( x, y)( 1,, ) rprsn ranng sapls. x X s h ndpndn varabl and X dnos h doan spac. y Y s h rspons varabl and Y rprsns h valu doan. For bnary classfcaon probl, s assud ha Y 1, 1. Wak larnng algorh s calld ravly by AdaBoos for round T. Whl a dsrbuon or s of wghs ovr S ran should b anand durng h procss. L D ( ) dno h wgh of h dsrbuon on sapl a round ( 1,, T). In h procss of raon, D ( ) wll b ncrasd a h followng round for sclassfd sapls whch forcd h followng wak larnr o pay or anon o h hard sapls. Durng ach raon, h opal "wak hypohss" rprsnd by h : X Y s acqurd wh rspc o h dsrbuon D. Error of h wak larnng algorh s forulad as: Pr [ h ( x ) y ] D ( ) () ~ D h : ( x) y Havng go h wak hypohss, h fnal hypohss H(x) can b oband usng h wghd ajory vo srags: T H( x) sgn( h( x)) (3) 1 ANN Gnrally, ANN s a nonlnar sys whch s consrucd by a s of nrconncd nurons[17]. A ullayr prcpon (MLP) s a fdforward ANN whch s ford by ulpl layrs of nods n
a drcd annr. Nods of ach layr n MLP ar fully conncd o hos of h nx followng layr. Evry nod xcp for h ons of npu layr has a nonlnar acvaon funcon. Error backpropagaon sragy whch blongs o suprvsd larnng chnqu s ulzd by MLP for larnng procss. Archcur of a MLP wh on hddn layr s llusrad n Fg. 1. Fgur 1. Thr-layr MLP archcur. For ach nod xcp for h ons of npu layr, l u dnos h suaon npu of nod, hn: j 1 j j (4) u w x b Whr b s h bas of h nod, w j s h wgh of ANN. L f rprsns h acvaon funcon of ANN whch s usually a nonlnar funcon such as: f( x) anh( x) x x x x (5) By h acvaon opraon, h oupu of h nod s: o f( u ) anh( u ) u u u u (6) Gvn ranng parn ( x1,, xp; y), suppos h oupu of ANN s y. Th rror backpropagaon chnqu updas h wghs w j of ANN by opzng h followng rror-nrgy funcon[34]: 1 : ( ) y y (7) Ada-ANN Forcasng Modl In hs sudy, w rprsn h ncras and dcras of h sock ndx ovn as 1 and 1 rspcvly. As ANN algorh xhbs hgh prforanc on h ask of sock ark forcasng, s ployd as h wak larnng algorh n our AdaBoo forcasng odl. Th psudocod of our Ada-ANN forcasng odl s llusrad n Tabl.
Tabl. Ada-ANN algorh. Inpu: Tranng sapl s S ( x, y ),,( x, y ) ; ran 1 1 Maxu raon nubr: T; Hddn layr sz of ANN: N; Tran pochs of ANN: M T Oupu: Th fnal hypohss: H( x) sgn( ( )) 1 n x 1 1: Inalz wgh of sapl: D1 () ( 1,, ) : For 1,, T 3: For 1,, M 4: Inalz wghs of ANN randoly: w j 5: Copu h rror-nrgy funcon wh rspc o dsrbuon D : 1 : ( y y) 6: Do whl ( ) 7: Copu gradn of wh rspc o w j : : 8: Upda wghs of ANN: wj wj wj 9: Copu h rror-ngrgy funcon 10: EndDo 11: EndFor 1: Oban h opal wak hypohss h( x): n ( x) and s rror: w j Pr ~ D[ n ( ) ] x y 1 1 13: Copu ln( ) 14: Upda wgh of sapl: D(), f ( ) ; n x y D 1() ( Z s a noralzaon facor) Z, ls. 15: EndFor Rsuls and dscussons Prcs nforaon rlad o h drcon of sock ndx ovn forcasng on Shangha Sock Exchang and nrnaonal sock arks s ulzd o carry ou xprns. W xrac h daa ovr h prod of fro 01/10/011 o 03/0/016. Daa on sock-ark-clos da s xcludd. Daa xracd fro 01/10/011 o 08/04/015 s ployd as h ranng s. Th rs s usd as h sng s. Sapl sz of h ranng s s 1100, and ha of h sng s s 147. Dscrpv sascs of h ranng and s daass ar llusrad n Tabl 3. Tabl 3. Dscrpv sascs of h ranng and s daass. Daas Incras Dcras Toal Tranng 51 579 1100 Ts 7 75 147 Su 593 654 147 Th Ada-ANN forcasng odl s proposd o prdc h sock ndx ovn. To ach MLP, hr groups of xprns ar conducd wh rspc o h hddn layr sz s s o 0, 5 and 30 rspcvly. Durng h procss of larnng, vry MLP odl wll b rand for any s o fnd
h opal wak hypohss. Th ranng pochs s s o 0. In AdaBoos algorh, hr ar svral wak larnrs. In hs work, h nubr of wak larnrs s s o 10. To vrfy h prforanc of our forcasng odl, prdcon accuracy on hr groups of hddn layr sz ar calculad and rpord. A h sa, prdcng rsuls of sngl ANN odl on h sa s s for h hr groups of xprns ar also rcordd. Th sngl ANN forcasng odl usd n our work has h sa archcur wh ha usd as h wak larnr n h Ada-ANN forcasng odl. For ach group of xprns, h sngl ANN forcasng odl s sd and h rsuls ar ulzd as h bnchark. Accuracy coparsons undr h sa condons ar suarzd n Tabl 4. Tabl 4. Accuracy coparson. Prdcon Accuracy(%) Modl Group 1 Group Group 3 Ada-ANN 76.87 77.55 68.71 ANN 7.11 74.15 63.7 As h xprnal rsuls shown, our Ada-ANN forcasng odl ouprfors h sngl ANN prdcng odl n rs of h sascal accuracy crra. In addon, hs wo forcasng odls ar all vrfd on h sa s daa s. Sascal rsuls can b consdrd as h ru ndcors of h prdcng prforanc. Fro h rsuls of h hr groups of xprns, on can s ha h prdcng prforanc of our Ada-ANN odl s supror o ha of h sngl ANN odl for h drcon of sock ndx ovn forcasng ask. Anohr pon dsrvd o b nocd s ha h archcur of ANN has pac on h prforanc of h prdcng odl consrucd by. Sascal rsuls of h hr groups of xprns show ha boh our Ada-ANN forcasng odl and h sngl ANN on has go h bs prforanc n group. Tha s o say, for hr-layr ANN wh 38 npus and on oupu, h bs rsul s oband wh h hddn layr sz bn s o 5. Th bs rsul of our forcasng odl s 77.55%, whl ha of sngl ANN s 74.15%. In slar work, h bs rsuls ar rpord as 60.81% n [3], 57.80% n [4], 74.51% n [5] and 76.70% n [7]. Our forcasng odl has go h bs rsul. Conclusons To assss h prdcably of Chns sock ark, 38 chncal ndcaors ar xracd fro Shangha Sock Exchang and ohr nrnaonal sock arks. A nw forcasng odl s proposd whch ploys MLP as h wak larnrs along wh h da of AdaBoos o for h srong prdcor. To vrfy h ffcvnss and prforanc of h proposd odl on h ask of prdcng drcon of sock ndx ovn, xprns ar conducd n hs work. Sascal analyss ndca ha h drcon of sock ndx ovn on Shangha Sock Exchang can b prdcd prcsly. Coparav analyss of sascal xprnal rsuls show ha h Ada-ANN forcasng odl has suprory ovr s rvals. I can prov h accuracy ffcvly. Rfrncs [1] H. Mhanna, Sock prc prdcon by usng unobsrvd coponns odl and rando volals (M.S. Thss), Facauly of Engnrng, Unvrsy of Scnc and Culur, 01. [] B. Egl, M. Ozuran, B. Badur, Sock ark prdcon usng arfcal nural nworks, Procdngs of h 3rd Hawa Inrnaonal Confrnc on Busnss, (003) 1-8. [3] A.I. Dlr, Prdcng drcon of s naonal-100 ndx wh back propagaon rand nural nwork, Journal of Isanbul Sock Exchang, 7 (5-6)(003): 65-81.
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