Econometric model used in the capital market analysis

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1 Theorecal ad Appled Ecoomcs Volume XXI (014), No. 10(599), pp Fe al Ecoomerc model used he capal marke aalyss Mădăla Gabrela ANGHEL ARTIFEX Uversy of Buchares, Romaa Absrac. I he frame of hs arcle, by applyg he lear regresso model, we proceed o he aalyss of he exsg depedece bewee he value recorded by he Buchares Exchage Tradg dex (meag he overall evoluo of he capal marke Romaa) ad ha of he sock exchage capalzao. The applcao of hs ecoomerc model provdes o he capa vesors a seres of ecessary formao mea o fx her behavour durg he forhcomg perods. Keywords: regresso model, capalzao, BET dex, sascal ess, he leas squares mehod. JEL Classfcao: G10, G14, C58. REL Classfcao: 11B.

2 60 Mădăla Gabrela Aghel 1. Iroduco The facal markes ad, maly, he sock exchage markes, are complex srucures where a very large umber of ecoomc ees are acg wshg, frs ad foremos, o ge a prof as hgh as possble. I hs respec, he moder facal markes are dsgushg hemselves by a very cospcuous dyamcs of he vesme acvy ad parcularly as far as he porfolo vesmes are cocered. I hs coex, s requred ha sascal-mahemacal models are formulaes, as suppor for modellg he ma processes occurrg o hese markes as well as o allow a easer maageme of all he acves volved by he vesme acvy. A sgfca aspec whe aalysg he performaces of he capal marke s gve by he esablshme of he exsg correlaos bewee he varous dcaors ad/or dces hs oe.. Leraure revew The frs ecoomerc models whch could be appled o he facal markes, geerally speakg ad, parcularly, o he capal marke, have bee coceved durg he secod half of he XX ceury. Ths s he perod whe sarg from he exsg heorecal models, he frs models wh src applcao he facal ad capal vesme domas have bee coceved ad mplemeed. Ths kd of ecoomerc models ca be foud ou he works of cera wellkow specalss he feld, such as: A. Goldberg (Ecoomerc heory 1964), H. Thel (Prcples of ecoomercs 1971), L. Kle (A exbook of ecoomercs 1974) ec. By he years 1990 ad he begg of he years 000, he ecoomerc models mea o he facal ad bakg aalyss reached a ew sage of developme whch allowed hem o be mached wh he ew requremes of he capal marke. I hs respec, o oe he effors pad by researchers such T. Mlles (The ecoomerc modellg of facal me seres 1993), E. Berd (The pracce of ecoomercs: classc ad coemporary 1991), W. Gree (Ecoomerc aalyss 000), F. Debld (Elemes of forecasg 00) or C. Doughery (Iroduco o ecoomercs 007), He, Chagl; Slveoe, Aaa; Terasvra, Tmo (Parameerzg Ucodoal Skewess Models for Facal Tme Seres 008). The ecoomerc model of regresso ad he acual possbles o use for ecoomc aalyss kep o beg permaely aalysed durg he prevous ceury, a seres of referece works for hs doma o be meoed such as hose sged by Frakl Graybll (A roduco o lear sascal models 1961),

3 Ecoomerc model used he capal marke aalyss 61 Peer Spre (Models regresso ad relaed opcs 1969), Davd Belsley, Edw Kuh ş Roy Welsh (Regresso dagoscs 1977), Damodar Gujara (Basc ecoomercs 005) or Gregory Chow (Ecoomercs 1983). 3. The smple regresso model From a heorecal po of vew, he smple regresso model s defed hrough a mahemacal relao bul up o he bass of he ecoomc heory whch assumes ha he ecoomc pheomeo, as a effec, s he oucome of he cumulaed aco of wo caegores of facors (Doughery, 008): a ma, deerma facor; all he oher facors whch ca be cosdered as o esseal, of casual or cosa aco, varable of he ecoomc effec pheomeo. Cosequely, by way of absracg, hese oes are o ake o accou for he amed aalyss, her effec beg coceraed he resdual varable. From a mahemacal po of vew, he smple regresso model mples a drec relao bewee wo varables, of whch oe s cosdered as a facoral oe (causal or explcave) whle he secod oe, s a resulg oe. Such a ecoomerc model ca be rascrbed, a mahemacal for, as follows (Adre, Bourboas, 008): Y = f(x) + ε. Ou of he caegory of he u-facoral regresso models he larges ulzao he ecoomc aalyses goes o he lear model. I he case of hs model, he relao bewee he resulg (Y) ad he facoral varable (X) ca be syhezed hrough a fuco of he form (Voeagu, Ţţa, 007): where: y he resulg characersc (explaed); x he facoral characersc (explcave, causal); ε he resdual varable. I he suao ha he lear depedece s foud aga as a resul of makg rasformaos o he wo varables, we shall say ha he regresso model s a lear oe as agas s parameers. For sace, he model Y = b + alx s o-lear as agas he facoral varable bu s a lear model as agas he wo parameers. O he corary, he regresso model Y = b + l ax s lear as agas he facoral varable, bu s o lear as agas he wo parameers a ş b, bu as agas b ad la. 61

4 6 Mădăla Gabrela Aghel From a heorecal po of vew, mus be meoed ha here are varous ufacoral o-lear models, whch are learzed hrough rasformaos appled o he varables of he regresso model. Ths caegory of o-lear models rasformed o lear models ca clude he followg (Gujara, 005) urs o a lear model by logarhmc procedure appled o he wo erms of he equaly above: log log log O he bass of hs rasformao, we ge as resul a lear model as agas he varables logy ad logx. The expoeal model or he log model defed by he relao: y = a + b x s learzed by logarhmc procedure, resulg he lear model: log log log A seres of o-lear models cao be wre he form of lear models by applyg cera elemeary rasformaos. I oher suaos, here are dffere echques of esmaos whch are appled order o esmae he parameers. As hey cao be learzed hrough elemeary rasformaos, he esmao of he parameers s made hrough umercal mehods (Aghelache, Aghelache, 009). I order o ge correcly esmaes resuls ou of applyg he lear regresso model s ecessary o defe a se of sadard hypoheses for he model ou of he geeral populao. These hypoheses are formulaed as follows (Aghelache, 013): I 1 : he daa seres are o affeced by measureme errors; I : he resdual varable has a zero mea; I 3 : he dsperso of he resdual varable s vara me, meag ha ges he homoscedascy propery; I 4 : he resduum are o self-correlaed; I 5 : he facoral (explcave) varable s o correlaed wh he resdual varable; I 6 : he model s errors are ormally dsrbued accordg o a co-dsrbuo of a zero mea ad a dsperso σ ( 0, ). I order o es hese hypoheses he sascal ess are appled. The esmao of he lear regresso model s made o he bass of he daa seres for he wo characerscs. From he mahemacal po of vew, hese seres are represeed by he colum vecors of he varables x ad y :

5 Ecoomerc model used he capal marke aalyss 63 Whe defg he lear regresso, he above meoed hypoheses are ake o cosderao. Cosderg he relao y = a * b x s o oce ha he esmaed value of he resulg varable, of he esmaors of he model parameers ad her properes deped o he characerscs of he depede varable ad he properes of he resdual varable (Aghelache e al., 010). I order o esmae he parameers of he lear model of regresso, we ca use he leas squares mehod. I hs case, he values of he resulg characersc are esmaed by usg he relao: where â ad are he esmaors of he parameers of he regresso le. The real values of he resulg characersc are equal o he esmao we ge wh he help of he regresso model, correced wh he resdual error, amely: The esmao of he parameers s based o he codo ha he sum of he squares of he dffereces bewee he real value ad he esmaed oe hrough he regresso model s a mmum oe (Aghelache, 013): 1 ŷ ) m (y αˆ βˆ x ) 1 F( αˆ,βˆ) m(y aˆ, aˆ, m e m yˆ ax ˆ aˆ, aˆ, m. The opmum codos lead o he followg sysem of equaos: aˆ, aˆ, aˆ yˆ ax ˆ yˆ ax ˆ 0 x 0 I order o esablsh he wo esmaors he lear sysem of equaos s solved: b ˆ aˆ x x aˆ y x y. 63

6 64 Mădăla Gabrela Aghel The compug relaos of he wo, â ad, are comg ou of he seleme of he lear sysem of equaos: â x x x y y x x The coeffce of he regresso le slope s obaed ou of he relao (Aghelache, 013): x y xy x xy y 1 1 aˆ. x x x x 1 1 w x x 1 x x. The formula for calculag he esmaor of he loose erm of he regresso le s se up by solvg he equaos sysem or by cosderg he fac ha he regresso le s passg hrough he cere of he pos cloud, amely: The mehod of he leas squares holds cera drawbacks as o s ulzao esmag he parameers of he lear regresso model, as follows: I does o provde accepable oucomes f he formulaed hypoheses are o sasfed: If og by, he esmaors se up o he bass of he seres (x, y ), 1, ad by, hose evaluaed hrough he values seres (x, y ), 1,1, s resulg ha bewee he wo pars of esmaors here s o a smple relao of recurrece: The esmaors are affeced case ha he daa seres s showg major chages, he form of breaks of level. I order o faclae he ulzao of he regresso models for ecoomc ad facal aalyses, specfc sascal ess have bee creaed whch aferwards

7 Ecoomerc model used he capal marke aalyss 65 have bee cluded specalzed formacs packages. For sace, he Evews programme whch allows geg ecoomerc models of qualy wh a mmum effor from he sde of he user of such a sofware soluo (Adre, 008). 4. The applcao of he regresso model o he capal marke Romaa I order o ake advaage of he submed heorecal aspecs, we used he regresso ecoomerc model mea o evaluae he relao bewee he value recorded by he BET dex ad he value of he sock exchage capalzao. The aalyss of he Buchares Sock Exchage ca be acheved hrough he suppor of a complex sysem of dces. Amog hem, a sgfca role as o geerae a rue mage o he performaces of he major sock exchage suo from Romaa s played by he BET dex (Buchares Exchage Tradg) (Aghel, 008). The BET dex has bee lauched o Sepember 19 h, 1997 ad represes he referece dex of he capal marke our coury. BET s a prces dex weghed by he free-floa capalzao (free-floa of a compay cluded he srucure of he BET dex represes he umber of shares ssued crculao whch are avalable for rasacos o he publc), whch s reflecg he overall edecy of he eques ssued by he frs e compaes, classfed depedg o her lqudy (Aghelache, 009). Thus, he prces recorded durg every sesso of rasacos are repored a he correspodg prces recorded durg he rasacos sesso of referece, by applyg he followg calculao relao hs respec (Buchares Sock Exchage BET dex maual): p, q, Ff R c, BET BET p, q, Ff R c, where: BET T value of BET dex a he curre mome, T; BET T-1 value of BET dex a he prevous mome, T-1; p,t prce correspodg o he eques of he compay by he curre mome T; p,t-1 closg prce correspodg o he eques of he compay by he mome T-1; q,t umber of eques by he curre mome T; Ff free floa facor correspodg o he compay from he dex beg calculaed wh wo dgs, bearg oe of he followg values: {0,1; 0,; 0,3; 0,4; 0,5; 0,6; 0,7; 0,8; 0,9; 1}; R represeao facor a maxmum 0% of he wegh of he compoes of he dex cos, correspodg o he eques of he compay ; s calculaes wh hree dgs ad belogs o (0,1]; 65

8 66 Mădăla Gabrela Aghel c,t correco facor of he prce correspodg o he eques of he compay; a he mome T, he days of operaoal revso; s calculaed wh sx dgs; c,t-1 correco facor of he prce correspodg o he eques of he compay; a he mome T-1, he days of operaoal revso; s calculaed wh sx dgs; N umber of compaes cluded he dex. Oe of he facors of sgfca fluece o he value of he BET dex s gve by he sock exchage capalzao. Ths oe represes a dcaor of oe sock exchage poeal reflecg he marke value of he lsed compaes, whch ca be esablshed as a sum of he producs bewee he umber of shares ssued by each of he lsed compaes ad he correspodg marke prce (Aghel, 013). I order o aalyse he exsg relao bewee he values recorded by he Buchares Exchage Tradg dex ad he sock exchage capalzao value, boh sascal-mahemacal models ad, maly, regresso ecoomerc models ca be used. I hs respec, we submed o he aalyss a seres of daa (daly frequecy) cocerg he BET dex value ad he sock exchage capalzao for he year 01. (366 caledar days/ 50 acual rasacg sessos he daa beg used are daly surveys over a me horzo bewee Jauary 1 s 01 ad December 31 s 01, respecvely 50 surveys, excepg week-ed days ad legal holdays). As a frs sage of he aalyss of he cosdered seres of daa, we used he formacs package Evews order o geerae a seres of sascal ass ypcal for each oe of he wo dcaors ake o accou: he BET dex value ad he sock exchage capalzao value. The sascal ess appled o he seres of daa referrg o he BET dex evoluo durg he aalysed perod evdeced he fac ha average value of hs dex cous for 4, le. Meame, s o oce ha he dsrbuo of hs seres of daa do o correspod exacly o he ormal dsrbuo, a suao whch, however, should be o cosdered as very grave as s ypcal o mos of he daa seres he facal doma. I he case of he aalyss of he seres of daa referrg o he evoluo of he sock exchage capalzao, s o sae ou ha hs dcaor s recordg a average value of 84, mllo le, he dsrbuo of he recorded values beg also dffere from he ormal dsrbuo.

9 Ecoomerc model used he capal marke aalyss Seres: CAPITALIZARE Sample 1/04/01 1/8/01 Observaos 50 Mea 8.41e+10 Meda 8.54e+10 Maxmum 9.85e+10 Mmum 6.93e+10 Sd. Dev. 6.5e+09 Skewess Kuross e e e e e e+10 I order o se up he ype of regresso model o be ulzed for esablshg he depedece bewee he BET dex value ad he value of he sock exchage capalzao, he wo seres of daa have bee represeed as a pos graph o whch he regresso le has bee also ploed. 1.0E E+10 9.E+10 Jarque-Bera Probably CAPITALIZARE 8.8E E E E+10 7.E E+10 4,00 4,400 4,600 4,800 5,000 5,00 5,400 BET Ou of he aalyss of he above graph, we sae ou ha here s coeco of lear ype bewee he wo varables. Ths depedece ca be syhecally showed up by meas of a ecoomerc model ypcal for he smple lear regresso, amely: BET = α + β * CAPITALIZATIO + ε where: BET BET dex value (he depede varable); CAP value of Buchares Sock Exchage capalzao (he depede varable); 67

10 68 Mădăla Gabrela Aghel α, β he parameers of he lear regresso model; ε he resdual value of he regresso model. Based o he prevous meoed elemes, wh he help of he formacs package, he parameers of he prevously submed regresso model have bee esmaed, hrough he mehod of he leas squares. Depede Varable: BET Mehod: Leas Squares Dae: 11/0/13 Tme: 18:51 Sample (adjused): 1/04/01 1/18/01 Icluded observaos: 45 afer adjusmes Varable Coeffce Sd. Error -Sasc Prob. C CAPITALIZARE 3.4E E R-squared Mea depede var Adjused R-squared S.D. depede var S.E. of regresso Akake fo crero Sum squared resd Schwarz crero Log lkelhood Haa-Qu crer F-sasc Durb-Waso sa Prob(F-sasc) Esmao Commad: ========================= LS BET C CAPITALIZARE Esmao Equao: ========================= BET = C(1) + C()*CAPITALIZARE Subsued Coeffces: ========================= BET = e-08*CAPITALIZARE Based o he prevously submed daa, he values of he wo parameers of he regresso model, α ad β, are se up as follows: α = 141,13 β 3,4 10 The regresso model defg he relao bewee he BET dex ad he value of he sock exchage capalzao s rascrbed as follows: BET 141,13 0, CAPITALIZARE

11 Ecoomerc model used he capal marke aalyss 69 The value beg recorded by Prob (0.0000) evdeces he fac ha he varable s sgfca from sascal po of vew. The coeco bewee he BET dex value ad ha of he sock exchage capalzao s a drec oe whch ca be explaed as follows: by a crease of 1% of he capalzao value, he BET dex value s recordg a crease % oly. Boh R-squared (R ) ad he Adjused R-squared (R adjused) show he exe o whch he depede varable s explaed by he depede varable. The recorded values are comprsed bewee 0 ad 1. The dfferece bewee he wo coeffces cosss of he fac ha Adjused R-squared s preseg, from sascal po of vew, a more sgfca resul sce s sacog he cluso of depede varable of a low relevace for explag he depede varable. I he suao here submed, he value recorded by R-squared shows ha a proporo of 53.59% of he BET dex value s explaed by he value of he capalzao, he dfferece up o 100% represeg he fluece of oher facors o cluded o he prese mode (a raher low fluece). A comparso made bewee he model se up for he values recorded by he wo dcaors durg he year 01 ad hose for he years 010, respecvely 007 (whch made he objec of prevous aalyses) evdeced he fac ha he sgfcace of he sock exchage capalzao for seg up he BET dex value dmshed sgfcaly. Ths suao ca be explaed by gog deeply o he effecs of he ecoomc ad facal crss whch led o he occurrece of rapd ad dffcul o acpae aleraos of he facors whch are fluecg he acvy of he ma compaes quoed o he capal marke from our coury ad, mplcly, he evoluo of he major specfc dcaors of he Buchares Sock Exchage. The coeco bewee he BET dex value ad ha of he sock exchage capalzao ca be explaed as follows: for he crease of 1% of he capalzao value, he BET dex value s recordg a crease of % oly. The valdy of he aalysed regresso model ca be suded by meas of he ess mplemeed he formacs package Evews. Thus, based o he values of he es R-squared ad of he es F-sasc (whch value of s exceedg he referece level of he ables) we ca sae ou ha he model descrbg he relao bewee he sock exchage capalzao ad he value of he ma sock exchage dex of he Romaa capal marke s a correc oe. 5. Coclusos The smple lear regresso model submed above s cofrmg, o he bass of he real daa recorded o he Romaa capal marke, he allegaos from he specalzed leraure accordg o whch hs ype of ecoomerc model ca be successfully ulzed order o defe ad sysemze a mahemacal form he 69

12 70 Mădăla Gabrela Aghel exsg relaos bewee he varous facal dcaors specfc o he sock exchage sysem. The regresso models allow he defcao of cera fucoal depedeces bewee he varous compoes of he capal marke, whch provdes he real possbly o forecas he pheomea submed o he aalyss over a large esablshed me horzo. The smple lear regresso model ca be ulzed wh good resuls oher aalyses cocerg he evoluo of he facal marke. Refereces Adre, T., Bourboas, R. (008). Ecoomercs, Ecoomca Publshg House, Buchares Adre, T., Sacu, S., Iacob, A.I. (008). Iroduco Ecoomercs usg Evews, Ecoomca Publshg House, Buchares Aghel, M.G. (008). Usg he Regresso Model he Aalyss of he Capal Marke, Romaa Sascal Revew, Suppleme Romaa he Process of Europea Iegrao, ssue 1 Aghel, M.G. (013). Models for he Maageme ad Aalyss of Porfolos, Ecoomca Publshg House, Buchares Aghelache C. (013). Elemes of Theorecal Ecoomercs, Arfex Publshg House, Buchares Aghelache C., Aghelache G.V. (009). Ulzao of he ecoomerc models he aalyss of he asses raes, Mealurga Ieraoal Vol. XIV, Specal Issue 9, F.M.R. Scefc Aghelache, C., Mar, D. ad Barbu, C.M. (010). Esmao of he regresso fucos rasformao, Mealurga Ieraoal, Vol. XV, ssue. 1 Aghelache, G.V. (009). Capal Marke a Europea Coex, Ecoomca Publshg House, Buchares Doughery, C. (008). Iroduco o ecoomercs. Fourh edo, Oxford Uversy Press Gujara, D. (005). Basc Ecoomercs, The McGraw-Hll Compaes Voeagu, V., Ţţa, E. (007), Theory ad Pracce Ecoomercs, Meeor Press Publshg House, Buchares Wooldrge, J. (006). Iroducory ecoomercs. A moder approach, d edo, MIT Press (Buchares Sock Exchage)

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