A Time Series Forecasting Model Using Group Method Of Data Handling (GMDH)

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1 Tme Seres orecsng odel Usng Group ehod O Hndlng GH Ruhdh Smsudn eprmen o Sowre ngneerng cul o ompuer Scence nd Inormon Ssem Unvers Technolog o ls 7- ruhdh@um.m Pueh Sd eprmen o Sowre ngneerng cul o ompuer Scence nd Inormon Ssem Unvers Technolog o ls 7- pueh@um.m STRT The ccurc o me seres orecsng s undmenl o mn decsons processes. orecsng cn sss he orgnon o mke beer plnnng nd decson mkng. The selecon o orecsng model s he mporn crer h wll nluence o he orecsng ccurc. Hence n order o cer hese chllenges hs sud proposes new me seres orecsng model b usng he Group ehod o HndlngGH echnque. Ths model s n enhncemen o convenonl GH model h wll mprove he predcon ccurc o he rdonl GH model. The benchmrked nd non-benchmrked d re used n hs sud. The benchmrked d re ve well-known d ses h lws hndled n rel le me seres pplcon. enwhle he non-benchmrked re rce eld d obned rom ud grculurl evelopmen uhor Kedh ls. The prelmnr sud ws done b comprng he enhnced GH Kondo model wh he convenonl GH neurl nework nd RI model. rom he epermenl resuls comprng he perormnce o our models we cn conclude h enhncemen o GH model Kondo model n mn cses s more compeen n modelng nd orecsng me seres hn he oher models. egores nd Subec escrpors : I.. [odel evelopmen]:odelng mehodologes; I.. [Problem Solvng onrol ehods nd Serch]: Heursc mehods Generl Terms permenon. Kewords Group ehod o Hndlng GH Neurl Nework RI rce eld orecsng me seres.. INTROUTION The grculurl secor hs conrbued sgncnl o he growh nd developmen o he lsn econom even hough he lsn econom hs undergone sgncn srucurl chnges over he ls our decdes. or he rs hree decdes snce ndependence grculure ws he mn conrbuor o he nonl econom. Rce eld producon s mong he op pror under he grculurl secor becuse o he globl ood crss h eced o our counr n 7. ccordng o bdullh hmd dw hs openng remrks he openng o he nsers' eeng on ood Secur nonl rce producon wll be rsed o mee up o % o he counr s needs b [].To cheve hs he Governmen hs lloced n ddonl R.bl o boos grculurl producon. The Thrd grculure Polc 99- ws esblshed o mee les 7% o ls s demnd % ncrese over he rgeed %. The remnng % comes rom mpored rce mnl rom Thlnd Venm nd hn[]. Hence rsng level o nonl rce sel-sucenc hs become sregc ssue n he grculurl nsr o ls. The bl o orecs he uure enbles he rm mngers o ke he mos ppropre decson n ncpon o h uure. Predcng he uure s mporn or he orgnon o pln he necessr polces or gend. orecsng cn sss he orgnon o mke beer plnnng nd decson mkng. Thereore he selecon o orecsng model s he mporn crer h wll nluence o he orecsng ccurc. The ccurc o me seres orecsng s undmenl o mn decsons processes nd hence he reserch or mprovng he eecveness o orecsng models hs never been sopped [][]. The RI model s one o he mos populr models n rdonl me-seres orecsng nd oen used s benchmrk model o compre wh oher models. However he RI model s onl clss o lner model nd hus cn onl cpure lner eure o d me seres. onsequenl los o reserches

2 hd red o ppl he rcl nellgen echnques o mprove he ccurc o he me seres orecsng ssues such s rcl Neurl Nework [][][][][7][9] Group ehod o Hndlng GH[][7][9][][][]. Hence n order o cer hese chllenges hs sud proposes new me seres orecsng model usng Group ehod o Hndlng GH echnque. Ths model s n enhncemen o convenonl GH model h wll mprove he predcon ccurc o he rdonl GH model.. OJTIVS The mor gol o me seres orecsng s o ge he bes ccurc model n order o mke good decson n he orgnon. Ths reserch s ocusng on he eors o mprovng he ccurc o orecsng mehods. s menoned bove so compung echnques or rcl nellgence hve been eensvel suded nd used n me seres orecsng. One o he echnque s Group ehod o Hndlng GH. GH s heursc sel-orgnng modelng mehod whch re genered dpvel rom d n he orm o neworks o cve neurons n repeve generon o populons o compeng models o growng comple correspondng vldon nd selecon model unl n opml comple model h s no oo smple nd no oo comple hve been reled. The mn de o GH s o buld n nlcl uncon n eedorwrd nework bsed on qudrc node rnser uncon whose coecens re obned usng regresson echnque []. In c rel GH lgorhm n whch he model coecens re esmed b mens o he les squre mehod. Hence he gol o hs sud s o ccurel develop me seres orecsng model usng he Group ehod o Hndlng GH. The ollowng obecves s consdered n order o cheve he gol o hs sud:. To enhnce new desgn rchecure o GH model n order o enrch nd mprove he predcon ccurc... To compre he perormnce o he new GH model wh he benchmrked ndvdul models such s RI NN nd convenonl GH To mplemen he new hbrd GH model wh he benchmrked d such s hemcl process concenron redng:ever hour hemcl process vscos redng: ever hour I common sock closng prces Wol s Sunspos Numbers Inernonl rlne pssengers nd non-benchmrked d such s rce eld d. THOOLOGY mehod o desgnng n enhnced o group mehod o d hndlng GH orecsng model consss our phses nmel he d collecon pre-processng desgn he rchecure o GH model nd compre he new model wh ohers prevous model. The del o hese phse re descrbe s below: Phse : ollecon There re wo pe o d hve been used n hs sud whch re unbenchmrked nd benchmrked d. The unbenchmrked d re colleced rom ud grculurl evelopmen uhor U Kedh ls rngng rom 99 o. These me seres come rom deren locon nd hve deren sscl chrcerscs. The ohers d consss he benchmrked d seres re emploed b Hnsen e l. 99 nd Hmceb e l. 9. These d re uled o orecs hrough n pplcon med o hndled rel le me seres. There re ve well-known d ses - he chemcl process concenron redng d he I common sock closng prces he chemcl process emperure redng he Wol s sunspo d nd he nernonl rlne pssengers re used n hs sud o demonsre he eecveness o he hbrd model. These me seres come rom deren res nd hve deren sscl chrcerscs. The hve been wdel suded n he sscl s well s he NN lerure. ll seres were clssed no our mn cegores h encompss he mor o he me seres pes nmel sesonl nd rended sesonl rended nd nonlner. Phse : Pre-Procesng ll dses re scled durng he d preprocessng phse. The wo mn dvnges o sclng re o vod rbues n greer numerc rnges rom domnng hose n smller numerc rnges nd o preven numercl dcules durng he clculon []. Generll ech d cn be lnerl scled o he [] rnge usng he ollowng ormul m.. where nd represen he normled nd orgnl d; nd m represen he mmum vlues mong he orgnl d. Then he scled or normled d s dvded no rnng nd esng. The rnng d se connng he rs % vlues nd he ls % wll be he esng d se. The rnng d wll become he npu o he model rchecure. enwhle he esng dse wll be used o vlde he predcve model. Phse : esgn he rchecure o GH model The desgn sep o he rchecure o GH model s s ollows: N n [Sep ]: onsder neurons n he rs ler rom o npu vecor X... n where n s he number o npus. Le s n s. So hs [Sep ]: Se X N k k N... vrbles X... new vrbles n he d se or ll ndependen n. onsruc he prl qudrc polnomls

3 k. k.. I n rom sep hen s. Then he prl qudrc polnomls re: sed on Kondo he ol equon o he model s ncresed ccordng o eq.. Thus he model become robus nd su o ppl n deren pe o d. r r k... <r<n Then he ddonl equon become: 9 7 In convenonl GH models mn resercher consdered he prl qudrc polnomls s he rnser uncon. However here re mn pes o rnser uncons h re vlble n he enhnced GH. Kondo [] nd Prk e l. [] showed h emplong heerogeneous rnser uncon whn model gves beer resuls rher hn use uns us o sngle rnser uncon. Hbrd rnser uncon produce more ccure resul hn sngle rnser uncon. In hs sud pes o rnser uncon re used nd shown n he Tble. The rnser uncon polnomls wh r nodes npus hve been mplemened n hs model. These were mplemened no us o mprove he ccurc o he lgorhm bu lso o show h vrous lernves cn be ncorpored no one nework. Tble : The Trnser uncon or r node npus Tpe Nme Trnser uncon Polnoml PLY k k Sgmod NN ep / k k ponenl R ep k k or ech rnser uncon wll produce en deren equon reer o k. So or rnser uncon he ol equon h wll be produced s deren equon. k [Sep ]: sme he coecens o he. The coecens o he re deermned b les squred errors S n he orm o X Y X X T where }... { s he vecor o unknown coecens s he vecor o oupu s vlue rom observon nd T }... { Y m m m m m m X [Sep ]: hoose he bes vrbles nd elmne he wekes vrble. The selecon crer o he bes vrbles s bsed on some perormnce nde men squre error bsolue or relve error h epresses how he vlues ollow he epermenl oupu. In some mehod columns o re replced b he rened columns o where m s he ol number o he rened columns. In oher versons he bes neuron o hese m neurons s dded o columns o orm new se o he npu vrbles. m n... m... n... [Sep ]: Ths sep s o es wheher he se o equons o he model cn be urher mproved. The lowes vlue o he men squre error obned n he curren ler s compred wh he smlles vlue obned he prevous ones. I n mprovemen s cheved one

4 goes bck nd repes seps nd oherwse he eron ermned nd relon o he nework hs been compleed. The conguron o he convenonl GH srucure s shown n gure. {... } se o negers. or emple he rs locon n 99 s wren s me he second locon n 99 s me nd so on. The me seres plo s gven n gure. s Ler Inpu Vrbles s Ler p q p nd ler or hgher q Trnser uncon nd ler or hgher Z p q p q p q Z p q p q p q... hemcl process concenron redng or ever hour: ver neresng problem s he predcon o d h re no genered rom mhemcl epresson nd hus governed b prculr deermnsm. or hs purpose we used nurl phenomenon he chemcl process concenron redng or ever hour hs ol o 97 d. The rs 7 d prs o he seres were used s rnng d whle he remnng % o he d where used o vlde he model dened. g. shows chrceron o hs me seres. Ths seres hs been nlsed b o e l [] nd dened hvng n RI model.. I common sock closng prces: Ths me seres s rel seres o he dl d rom 7 9 o November 9. The d shows brek n he ls hrd o he seres nd no obvous rend or sesonl. Ths seres hs been nlsed b Hmceb e l. 9 nd s dened s hvng n RI. gure shows hs me seres. gure : srucure o convenonl GH Phse : ompre he resul o GH model wh oher model er he resul s obned rom phse hen he resul wll be compred wh he oher prevous model such s convenonl GH Neurl Nework nd RI model.. mprcl Resul There re wo pe o d hve been used n hs sud whch re unbenchmrked nd benchmrked d. oh o hese d wll be dvded no rnng se connng he rs % vlues nd es se wh he ls %. Onl he rnng se s used or model selecon nd prmeer opmon beng he es se used o compre he proposed pproch wh oher models. Inormon regrdng he seres dsrbued mong he rnng nd orecsng ses re gven n Tble. Tble : The seres d h re used o compre orecs mehods Seres Trnng Se orecsng Se Rce Yelds hemcl process concenron redng:ever hour I common sock closng prces hemcl process vscos redng: ever hour Wol s Sunspos Numbers Inernonl rlne pssengers 7. hemcl process vscos redng or ever hour: Ths seres hs d nd lso hs been nlsed b o e. l. 99 nd Hmceb e l. 9 nd s dened s hvng n RI. gure shows hs me seres.. Wol s Sunspos Numbers: The sunspo d conns he nnul number o sunspos rom 77 o 9 gvng ol o observons. The sud o sunspo cv hs prccl mpornce o geophscss envronmen scenss nd clmologss. The plo o hs me seres see g. suggess h here s cclcl pern wh he men ccle o bou ers. Ths seres lso hs been nlsed b o nd Jenkns nd s dened s hvng n R model o e. l. [] nd Hmceb e l. 9. : Inernonl rlne pssengers: The seres s n emple o me seres d wh cler rend nd mulplcve sesonl. The d conns he monhl pssengers rom 99 o 9 hs d. The d hs long served s benchmrk nd hs been well suded n sscl lerure. o e l. [] show h he seres s dened s hvng n. Rce Yelds 7 Rce Yelds. Rce Yelds. The rce elds d conns he elds d rom 99 o gvng ol o observons. Gven se o observons mde unorml spced me nervls he locons o rce eld re rescled o he me s becomes he Inde

5 gure : Seres Rce Yelds 7. hemcl oncenron Sunspor 7 Inde 9 7. Inde gure : Seres Woler Sunspos Numbers gure : Seres hemcl process concenron redngever hour rlnes Pssenger IPrces 7 9 Inde gure 7: Seres : Inernonl rlne pssengers Inde gure : Seres I common sock closng prces. In hs secon we provde severl numercl emple o evlue he dvnges nd he eecveness o he KONO pproch. The perormnces o he ech model or boh he rnng d nd orecsng d re evlued nd s seleced ccordng o he men bsolue error nd roo-men-squre error RS whch re wdel used or evlung resuls o me seres orecsng. The nd RS re dened s hemcl Vscos Inde 7 79 N ˆ N where nd re he observed nd he orecsed rce elds ŷ he me. The crerons o udge or he bes gure : Seres hemcl process vscos redng: ever hour RS N ŷ N model re relvel smll o nd RS n he modelng nd orecsng.. ng RI models o he d Through he erve model buldng process o dencon esmon nd dgnosc checkng. Severl models were dened nd he sscl resuls durng rnng nd orecsng re compred nd he crerons o udge or he bes model re

6 deermned bsed on nd S. Two sscl uncons re used or he grphcl dencon o R model usng he o Jenkns mehodolog he uocorrelon uncon nd he prl uocorrelon uncon P. Tble lss he possble R srucures o some rel d seres er beng properl derenced wh or whou sesonl componens. These models hve lso been used b mn reserchers such s o e l. [] nd Hmceb e l. 9. Tble : omprsons o RI models sscl resuls Seres RI Trnng orecsng odel RS RS ng neurl nework models o he d One o he ke sks n me seres orecsng s he selecon o he npu vrbles nd he number o neurons n he hdden ler. or he NN models here s no ssemc pproch whch cn be ollowed.the unversl ppromon heorem shows h neurl nework wh sngle hdden ler wh sucenl lrge number o neurons cn n prncple rele n gve se o npus o se o oupus o n rbrr degree o ccurc. s resul he NN desgned n hs sud re equpped wh one sngle hdden ler. The deermnon o he number o neurons n he hdden ler s more r hn scence. eermnng he se o he nework he number o neurons hs mporn consequences or s perormnce. Too smll nework m no rech n ccepble level o ccurc. Too mn neurons m resul n n nbl or he nework o generle m roe lern he rnng perns. Snce he number o npus vres dependng on he npu deermnon mehod used s no possble o use he sme nework rchecure or ech model. In hs sud he number npus I nd were used or ll d se. To help vod he overng problem some reserchers hve provded emprcl rules o resrc he number o hdden nodes. To selec n ppropre rchecure he gudelnes usng I proposed b er Wong I proposed b Tng & shwck [] nd I/ proposed b Kng []. The nework ws rned or epochs usng he bckpropgon lgorhm wh lernng re o. nd momenum coecen o.9. The neworks h elded he bes resuls or he orecsng se were seleced s he bes NN or he correspondng seres. The bes NN srucures nd he bes resuls or he rnng nd orecs re shown n Tble. Seres Number o neurons Trnng orecs Inpu Hdden Oupu RS RS ng GH nd KONO models o he d The GH nd KONO models re pcll composed o lers o nodes. In desgnng hese models one mus deermne he ollowng vrbles: he number o npu nodes he number o hdden lers nd he number o oupu. The selecon o he number o npu corresponds o he number o vrbles pl mporn roles or mn successul pplcons o hese model. The ssue o deermnng he opml number o npu nodes s crucl e complced one. There s no heor h cn used o gude he selecon he number o npu. In hs sud he nd re lso used s he number o npu nodes. Tble nd Tble shows he comprson o modelng/orecsng precson mong he wo deren pproches bsed on wo sscl mesures. Tble : Perormnce o GH Seres Number o Trnng orecsng Inpu Ler RS RS Tble : Perormnce o KONO pproch Seres Number o Trnng orecsng Inpu Ler RS RS or comprson purpose he rnng nd he orecs perormnce o KONO were compred wh he RI NN nd GH model. Tble shows he comprson o modelng/orecsng precson mong he wo pproches bsed on wo sscl mesures. The resuls show he KONO models n mn cses s more compeen n modelng nd orecsng me seres hn he oher models. The RI model hs good perormnce or he wo seres nd or esng. Tble.: omprson o Neurl Nework odel Tble : omprve perormnce o he KONO RI NN nd GH or S Seres

7 Tesng orecs -ng RS Seres RI NN GH KONO RI NN GH KONO oncluson orecsng s n mporn problem h spns mn elds ncludng busness nd ndusr governmen economcs envronmenl scences medcne socl scence polcs nd nnce. The reson h orecsng s so mporn s h predcon o uure evens s crcl npu no mn pes o plnnng nd decson mkng. In hs sud we conduced he epermen whch nvolves wo pe o d benchmrked d nd non-benchmrked d. The non-benchmrked d obned rom ud grculurl evelopmen uhor Kedh ls rngng rom 99 o. These me seres come rom deren locon nd hve deren sscl chrcerscs. The ohers d consss he benchmrk d seres emploed b Hnsen e l. 99 nd Hmceb e l. 9 re uled o orecs hrough n pplcon med o hndled rel le me seres. There re ve well-known d ses - he chemcl process concenron redng d he I common sock closng prces he chemcl process emperure redng he Wol s sunspo d nd he nernonl rlne pssengers re used n hs sud o demonsre he eecveness o he model. The resuls re compred wh hose he RI NN nd GH. rom he epermenl resuls comprng he perormnce o s models we cn conclude h KONO models n mn cses s more compeen n modelng nd orecsng me seres hn he oher models. KNOWLGNTS Our hnks o SIGHI or llowng us o mod emples he hd developed nd So ompung Reserch Group SRG or supporng he commens nd de o hs sud. 7 RRN [] bdullh hmd dw. 9. ls ms To Increse Rce Producon. ernm. [] o GP Jenkns G. 99. Tme Seres nlss: orecsng nd onrol Prence Hll PTR Upper Sddle Rver NJ. [] rlow S.J. 9. Sel-orgnng ehod n odelng:gh Tpe lgorhm rcel ekker Inc. [] Hsu.W. hng. nd Ln.J.. prccl gude o suppor vecor clsscon. vlble : hp:// [] Klnr. rdln H. nd Nrmn-ZdehN. 9. n Invesgon on he Su N SPT correlon usng GH pe neurl neworks nd genec lgorhms. ngneerng Geolog :-. [] Kng S. n nvesgon o he Use o eedorwrd Neurl Nework or orecsng. Ph.. Thess Ken Se Unvers 99. [7] Kondo T. nd Ueno J. 9. edcl Imge Recognon o bdomnl ul-orgns b R GH-pe Neurl Nework. Inernonl Journl o Innovve ompung Inormon nd onrol. :9-9. [] L K.K. Yu L. Wng S. & Hung W.. Hbrdng ponenl Smoohng nd Neurl Nework or nncl Tme Seres Predcon. IS Pr IV LNS 99: 9-. [9] Oh S.K. Pedrc W. nd Roh S...Genecll opmed u polnoml neurl neworks wh u sebsed polnoml neurons Inorm. Sc. 7 : 9 9. [] Onwubolu G... esgn o hbrd derenl evoluon nd group mehod o d hndlng neworks or modelng nd predcon. Inormon Scence. 7:- [] Prk H.S. Pedrc W. nd Oh S.K. 7. voluonr desgn o hbrd sel-orgnng u polnoml neurl neworks wh he d o normon grnulon per Ss. ppl. :. [] Sd P. kr. Kmrudn S.S. & Jr.N.. Inellgen ecson Suppor Ssem or Rce Yeld Predcon n Precson rmng. IRP Repor. [] Tng Z. & shwck P.. eedorwrd Neurl Nes s odels or Tme Seres orecsng. ORS Journl on ompung :7-99. [] Wong.S. Tme Seres orecsng Usng ckpropgon Neurl Nework. Neurocompung : [] Wongseree N. hrnn. Vchumros K. Wnchgoon P. nd uchroen S. 7. Thlssem clsscon b neurl neworks nd genec progrmmng Inorm. Sc. 77 :77 7. [] Wu Jr. S. Hn J nnmbhol S. nd rn S. rcl Neurl Neworks or orecsng Wershed Runo nd Srem lows Journl o Hdrologc ngneerng -. [7] Zhng G. Puwo.. & Hu.Y.. orecsng wh rcl neurl neworks: The se o he r. :- [] Zhng G.P.. Tme Seres orecsng Usng Hbrd RI nd Neurl Nework odel. Neurocompung : 9-7. [9] Zou H.. X G.P. Yng.T. & Wng H.Y. 7. n Invesgon nd omprson o rcl Neurl Nework

8 nd Tme Seres odels or hnese ood Grn Prce orecsng. Neurocompung 7: