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Numerical Algorithms Group Title: selp mfaox Eeht esUs nfoo i atg tanlaciaDin ilincpMinpaAniF :yrammuS atad gnisu yb atad laicnanif htiw sledom lacitamehtam gnidliub sredisnoc elcitra sihT mgietnnemIinecdinnemrhnan gueanetai drtlitsasneah,qwu a gclo uocn i derhdsssk i .so n treesc anb eau sef .tsylana laicnanif eht ot elbaliava seuqinhcet eht ot noitidda lu dradnats eht naht atad lacirotsih erom eriuqer ot dnet seuqinhcet gninim atad eht ,revewoH modeatcnlnihaoesdnesfu , e rn aelt wordkcbisaef,n f iciutnlott e rpret. sihT elcitra sredisnoc gnidliub lacitamehtam sledom htiw laicnanif atad yb gnisu atad gninim . seuqinhcet In general, data mining methods such as neural networks and decision trees can be a usef lu noitiddao t eht seuqinhcet elbaliava ot eht laicnanif .tsylana ,revewoH eht atad gninim seuqinhcet dnet ote riuqer more historical data than the standard models and, in the case of neural networks, can be difficult to .terpretni Stockm arketr eturnsa ruof fo eno otni llaf ot thguoht eb nac atad setar egnahcxe ycnerruc ngierof dn .swollof sa seirogetac .1 eulav xedni tsewol ,eulav xedni tsehgih ,esolc ta eulav xedni ,nepo ta eulav xedni :seires emit eviF .emulov gnidart dna .2 Fundamentafla ctores. :g .t,h ngierof ,secidni noitcudorp lairtsudni ,xedni selas liater ,dlog fo ecirp e .setar egnahcxe ycnerruc .3 Laggedr eturnsf romt het imes erieso fi nterest. .4 Technicafla ctorvsa :r iabletsh aatr feu nctionosof n meo rtei msee riese,. g.m,o vinagv erages. Thes tan darda pproacht om odelings tockm arketr eturnso re xchanger atesi st om odelt heu nivariate tsiemrewi aieutsth o regress(imaAvonRevd) ai vnegr t(armMgaAoAedcd d) eaee tnr le sr.m ainn e appropriatneu mbeolrfa gfsoAa rRnA dR MmAo delbsa seoednx perienc emit eht gnizylana yb dna e seriedsa tSai .m ilarlya,an p propriatneu mbeorrf e gimefso SrE TA(Rs elf - dna )RA noitisnart gniticxe STAR( smootht ransitionA R)m odelsc anb ed eterminedT. h esem odelsa red eterministici nt hes ense am esu ot tpmetta yeht taht thematiceaqlu atidotenoss c ritpbhreeo cetshgsae tn eratttehissem e er ie s. .ytilibaterpretni rieht ni seil sledom eseht fo egatnavda ehT nac ti taht esnes eht ni elbixelf si taht ledom a tpoda ot si ,gninim atad morf nward ,hcaorppa rehtonA approximate non era sledom hcuS .ycarucca hgih htiw snoitcnuf fo ssalc ediw a - parametrici nt hes ense .atad eht dna ledom dettif a fo seulav retemarap eht neewteb pihsnoitaler tcerid a eb ton deen ereht taht aTdhvea nmtuoasiosdgianfueen c clsglh u de: .1 tiliba ehT .snoitcnuf xelpmoc ylhgih ledom ot y .2 .e.i( atad rehto edulcni ot ,erofereht ,dna ledom eht ni selbairav fo rebmun hgih a esu ot ytiliba ehT data.series time lagged to addition in factors) technical and fundamental non fo egatnavdasid ehT - parametricm odel .terpretni ot ysae ton era yeht taht si s the adjusting By network. neural a is choice of model the data, series time mining data of case the In numbeorff r epea rameterass sociatewdi tmaho delta,r adecro ntrolist fsl exibilitOyf .t enc,r oss - oitadilav dloh ro ,n - oudta tai,us s etddo e terminsaeu itablvea lufeo trh neu mbeorff r epea rameters contnaeiauni rnenaed lt wosrtkr ucTntheueur rneae.lt womrockso tm monuflsiiyenn d a ncial itlum a si snoitacilppa -al neddih elgnis a htiw )PLM( nortpecrep reyal .sedon fo rey © T heN umericalA lgorithmsG roup 1 Numerical Algorithms Group Thep roblemo fp redictings tockm arketr eturnso re xchanger atesa tt ime 1+t eiata chsae srbt ec an regressiooncr l assificatiopnr oblWemh .e reast her egressionp roblemf ore xchanger ated atai nvolves ht ,etar egnahcxe lautca eht gniledom egnahcxe eht rehtehw gnitciderp sevlovni melborp noitacifissalc e rahtiaens c reasdoeerdc reased. Applicationtsh aitn volvmeo delinrge turnfsr otmh set ocmka rkeitn cludpeo rtfolimoa nagemenatn d .)woleb ees( serutuf gnidart PLM noisser g:eerlpmaxe rop tfolio management ot desu eb nac snoitciderp hcuS .seulav nruter )war( eht gnitciderp sevlovni esac noisserger ehT manageap ortfolioo fns tocksa sf ollows. Supposteh ahti storicadla tfao (Nnr>Ns ) t ockasr ues etdfo i mNtu lti - A .snortpecrep reyal fo dne eht t reare MLPs the week each - s’Z ynapmoc esoppus ,elpmaxe roF .atad lacirotsih tsetal eht edulcni ot dettif pensifouhbnnaem dsea nn apgoiarn tgf o$lo1mif0io 0l lisoinnD ceec emb1e9ur9s 3im nugl ti - reyal perceptronsT. h ef undm onitorsap oolo f1 ,000U .S.s tockso naw eeklyb asisF. o re acho ft heses tocks therei saM LPw hichm odelst hef uturep erformanceo ft hes tocka saf unctiono ft hes tock’se xposuret o changeprice weekly its of estimate an gives and factors, technical and fundamental 40 coTmhpea n y . .snruter detciderp ot yletanoitroporp dnuf eht setacolla dna skcots n pot eht fo oiloftrop a stceles neht MLP classification example: trading futures Asa ne xampleo fad atam iningc lassifier,c onsidert hep roblemo ft radingaf utureo fs toacpAtkr iocBne .krowten laruen a gnisu yb C etad seirogetac owt fo eno otni deifissalc era atad ,pets emit hcae tA .deraperp si atad lacirotsih eht ,yltsriF :C etad no B ecirp ta A kcots lles ro yub ot elbatiforp saw ti rehtehw ot gnidrocca .1 :gnoL .C etad no kcots eht yub .2 C.date on stock the sell Short: ta noitisop elbatiforp a tciderp ot desu eb nac ledom eht ,atad lacirotsih siht htiw ledom a dettif gnivaH etadpu si ledom eht pets emit hcae fo dne eht tA .)keew ro yad txen eht ,.g.e( 1+t emit eht edulcni ot d .atad lacirotsih wen eht nevig )trohs ro gnol rehtie( noitisop elbatiforp a ni eb dluohs redart eht ,sevirra C etad emit eht yB currentm arketv alueo fs tockA . sgenliudrarT Tradinrgu lecsabd nee terminefdr odma twaic taah t egorical hcuS .llaf ro esir ,lles ro yub ,.g.e ,emoctuo ruletsa kteh feo romsaf e otcf o nditionaslt atementasn adan c tione,. g., IFC ONDITION1A NDC ONDITION2 T HENA CTION acirotsih etairporppa na neviG .ledom eert noisiced dettif a gniweiv yb dnuof eb nac dna siht ,tes atad l .saedi dna selur wen etareneg ro ,tsixe ot thguoht elur a etadilav rehtie ot desu eb dluoc hcaorppa fo eno no tset a si eert eht ni edon lanretni hcaE .atad lacirotsih gnisu dettif si noisiced a taht esoppuS tciderp ot desu selbairav eht suounitnoc sekat ,1X yas ,elbairav eht fI .atad lacirotsih eht ni emoctuo eht :rehtie si tset siht ,seulav ,)EULAV < 1X( ro )EULAV => 1X( © T heN umericalA lgorithmsG roup 2 Numerical Algorithms Group ,2X yas ,elbairav eht fI .eert noisiced eht stif taht mhtirogla eht yb denimreted era EULAV dna 1X erehw cant ake onoedmf i scretvea luest,h itse sitos n oef : {(X2=i )},f ori= 1 ,2 ,m , suhT .lles ro yub ,.g.e ,snoitca eht niatnoc sedon faeL .mhtirogla gnittif eht yb nesohc era i dna 2X erehw tes a evig lliw edon fael hcae ot toor eht morf eert eht nwod gnicart o fr ules. gniwollof eht fo ytidilav eht tset ot tliub eert noisiced a dna detcelloc eb dluoc atad lacirotsih ,elpmaxe roF :elur “Whent he1 0 -03 eht evoba sessorc egareva gnivom yad - segareva gnivom htob dna egareva gnivom yad ianrcer ettaiismsiei n tg , .”yub o hcao rtpnpeanopmoC Analystss eekingn ewi nsightsf romm assived atabaseso ft ickd ataa nds imilarm arket informationc an gniniM ataD GAN gnisu yb snoitacilppa gninim atad dezimotsuc fo tnempoleved rieht etarelecca won Componentasbs u ildinbgl ocks expCeocMmatiprenoedin Dneagnt tas NAG Thea pptlhiec iartf ioorn s. er ot dedeen morf stsylana evitatitnauq eerf ot - eht gnilbane ,senituor gninim atad cisab tnevni hcuS .tsoc rewol ta dna ylkciuq erom snoitacilppa gninim atad dezilaiceps fo tnempoleved evitsuahxe wen gningised ni egatnavda evititepmoc a smrif evig ot detcepxe si sesabatad laicnanif fo noitarolpxe misddpiaerssrocsidoevuvtace ttrisiv,ne g - oiloftrop ezimixam ot setuor ralimis gniyfitnedi ni dna ,sgnicirp returns. iniM ataD yolpme nac enO ngC omponentsf ore achs tageo ft hem odelingp rocess – noitaraperp atad sisylana tnenopmoc elpicnirp( noitamrofsnart atad ,)noitareneg selbairav ymmud dna noiteled esiw esac( k( gnidliub ledom dna ,)gnilacs atad dna - meansa ndh ierarchicalc lustering;k - aen noisiced ;srobhgien tser itlum ;sisylana eert - .)noisserger elpitlum lareneg ;noisserger citsigol ;skrowten laruen nortpecrep reyal dradnats gnisu sngised noitacilppa nwo rieht ni stnenopmoc eseht esu nac srepoleved noitacilppA .sloot tnempoleved xidneppA of terms .1 gniretsulC . .noitarolpxe atad ro noitcuder atad rehtie rof desu eb nac taht euqinhcet gninim atad ralupop A (a)k - meansc lusteringT: h ec lusteringt echniquek nowna sk - meauinscstsel o du stdearit naat o knownn umbero fg roups.T hism ethod of number the lower to i.e. reduction. data for used be can dataF. o re xample,i fas eto f N rebmun a htiw deretsulc si atad M ( )N < M o fc lusterc enters,t he M models.prediction or classification either build to used be then can centers cluster Hie(b) rarchicacll usteriHnig e:r archicacll usteriniugss etedox plortehn eu mbeocrfl ustertsh aotc cur its of group a to datum each assigns clustering hierarchical of method One data. of set a in naturally ylno litnu spuorg segrem yllatnemercni neht dna nwo eht yb detaerc snrettaP .sniamer puorg eno eht rof etairporppa era spuorg ynam woh ediced neht ohw sresu yb dezylana era spuorg fo gnigrem dataU. n likek - sets.dastmaa llert ol imiitnefhdiaoic sprgl pmhuraltsmotyhteai ieacvsrnhe is n g, .2 Classification . Classificapttrhiiokeasocn os socneofseflf swT it aoasnhg sl eonosld fi netoa nesowtg d. ia a n tga minintge chniquecsabu nes efdoc rl assification. © T heN umericalA lgorithmsG roup 3 Numerical Algorithms Group i tilps hcae erehw ,atad no stilps etairavinu fo tes a setaluclac eert noisiced A :eert noisiceD )a( sa a ,edon fael hcae ot eert noisiced a fo edon toor eht morf gnicart yB .elbairav a fo eulav eht no tset derived.be can rules of set hcus ,yranib si esnopser emoctuo eht nehw desu eb nac noisserger citsigol A :noisserger citsigoL )b( as yes o r on F. lliw ro tcudorp ralucitrap a yub remotsuc eht lliw :eb thgim emoctuo eht ,elpmaxe ro eht ot rewsna sey a fo ytilibaborp eht setaler noisserger citsigoL .mialc a ekam tneilc ecnarusni na .selbairav yrotanalpxe fo rebmun a fo seulav .3 noitciderP . tciderP .elbairav suounitnoc a rof eulav a gnitaluclac fo ssecorp eht si noi .4 noitciderp ro noitacifissalC . eicftfluohoasrTelse hrlsmbde oidime wfanpoc iitirdancaneenga ogdl tr isi c otni on. (a)k - nearenseti ghbGoirdv saae:t n u tmkh,e - a srobhgien tseraen lgorithmf indsi ts k closest hivsoarttfreosha itatrofedeenahvuifoiat tdbeerc rvtt oh lsrnaa ahamfeeeasl le e g urmiee bn e rs interesto r,f orc lassification,t hem odalc lassT. h em easureo fc losenessc anb ee ithert he2 - norm ro )ecnatsid naedilcuE( 1 eht - norm. itluM )b( - itlum A :skrowten laruen nortpecrep reyal - non a si ledom )PLM( nortpecrep reyal - raenil eerht A .etamixorppa nac ti snoitcnuf fo sepyt eht fo esnes eht ni elbixelf ylhgih si taht ledom - reyal pecca taht reyal tupni na fo stsisnoc PLM .reyal tuptuo na dna sedon fo reyal neddih a ,seulav atad st non a ylppa nac sreyal tuptuo dna neddih eht ni edon hcaE - linetalrriaa nn esafro rtmoa tion evah snoitarugifnoc desu ylnommoC .reyal suoiverp eht ni sedon ta seulav eht fo noitanibmoc citsigol .reyal tuptuo eht ta snoitcnuf raenil ro citsigol dna reyal neddih eht ni snoitcnuf yrotanalpxe fo noitanibmoc raenil a si taht ledom a dliub ot desu euqinhcet A :noisserger raeniL )c( variables( orf unctionst hereof)T. h ep arametersi nt hem odelc anb e ssap eno ylno gnisu dnuof sets.datal arge rfesogurlri ietnsamesbaailkroei n dn agt a, thteh rough yB lledgnaL nehpetS lledgnaL nehpetS ediwdlrow eht fo puorG noitasilausiV dna sisylanA ataD eht fo rebmem a si .D.hP componentscreates which (NAG), Group Algorithms Numerical eht fo tsom yb desu erawtfos rehto dna .moc.gan@ksedofni ot dedrawrof eb nac snoitseuQ .dlrow eht ni sesuoh ecnanif rojam dehsilbup yllanigirO yb ,sweN gnireenignE laicnaniF yraurbeF .)moc.swenef.www( 2002 Numerical Algorithms Group www.nag.com [email protected] © T heN umericalA lgorithmsG roup 4