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The ndence tend memory, A 379 een Eff idence el Kaouther, and banks, résidence-2 E-mail: fl ecember 15 tp://dx.doi.o tal markets research sho ms to test th ary named H ducted on d o their leve results ob d to be assoc Analysis R / Asian ficiency on Dai , PhD Institute of 016 Tunis, flifelkaouthe 5, 2012 P org/10.5296 is very con owing that he existence Hurst expon daily data on els of devel btained allo ciated with S, Hurst ex n Journal of F y and P ly Data f Higher Com Tunisia er@yahoo.f Published: D /ajfa.v4i2.1 ntroversial, the pricing of the pers nent and the n stock retu lopment ov wed us to relatively th xponent, AR Finance & Ac ISSN 19 2012, Vol. www.macrothi Persiste a mmercial S fr December 1 1827 especially g was disto sistence effe e ARFIMA urns of 21 c ver the peri conclude hin stocks RFIMA mod ccounting 946-052X 4, No. 2 ink.org/ajfa nce: tudies 7, 2012 in these orted by ect using process. countries od from that the del 1. Intro Validat efficien assess t Accord events anticipa using so We can on certa long as In the sp - Unpre - Indepe - Havin normal to the n These c are norm existenc because driving refereed Howeve can be price qu memory impacts prices a term wh In gener memory them an 1 In his the by Brown, 2 The phen Joseph inte seven-year mean are ex series. oduction ed by thous nt capital m the securitie ing to the th and accurat ated events ome mathem n say that m ain informa the market peculation t edictable be endent, sinc ng a norma Gaussian l normal one. characteristi mal and wi ce of smal e rational ag prices to th d and corres er, an impe more or les uickly rega y2 this me s on profits and the fund hen the pric ral the hypo y (total inde nd therefore esis entitled Theor a biologist), whic nomenon of long erprets Pharaoh's d drought to seven xtremely long. Th sands empir markets requ es traded on heory of eff tely reflect are integrat matical mod markets are e ation are un authorities theory of B fore the imp ce no one ca al distributio aw. There i ics refer em ithout mem l or low a gents, calle heir equilib sponds to th erfect marke ss correlated ins its equi eans that th s, interest damental va ce returns to othesis of ef ependence o e we cannot ry of speculation, ch is the basis of memory is also k dream: he saw se n years good harv he presence of lon rical testing uires that a n the market ficiency, fin the expect ted into exis del. efficient wh nable to infl can preven achelier1, th plementatio an use the p on, that is is no exces mpirically to ory. This m autocorrelati ed in the jar brium: "Mea he theory of et may hav d. Low auto ilibrium val he price sl rates....Lon alue. These o the standar fficiency im of returns) w predict futu , backed March 29 most pricing mod known as Joseph even lean cows se est (Mignon (199 ng memory in tim 380 g on all fina market is e t at any time nancial mar tations expr sting course hen investor fluence the nt and suppr he differenc on of the eve past to make to say that sive deviati o uncorrelat means that t ion in the rgon of Fam an reverting f random wa e a memory ocorrelation lue. Conver owly integ ng memory differences rd equilibriu mplies that th which mean ure returns to 9, 1900, he introd dels in finance, in effect. (Mandelb even large monito 98), p.191). This m me series, refers t Asian ancial mark efficient wh e is reflected rkets incorp ressed abou es, and it wo rs with insi price of sec ress insider t ces between ent. e future prof t the distrib ion from th ted price ser the action o series of p ma, knowle g behavior" alk and mar y effect. Em ns mean a s rsely, high grates inform reflects la persist and um. he return ser s the absenc o from past duced the use of th ncluding the Blac rot and Wallis 19 or and Joseph con means that the pe o lasting consequ n Journal of F kets in the w hen all relev d in the pric orate the co ut future eve ould be usel de informat curities, wh trading. n Pt and Pt-1 fits. bution of de e mean. Th ries. Stock m of arbitrageu prices is ra edgeable pro . The mark rtingale. mpirically, t hort memor autocorrelat mation on asting devia d cannot be ries are char ce of serial c returns. The he Brownian mov ck-Scholes (1973) 68). It refers to a ncludes that this w eriods when the se uences but not a p Finance & Ac ISSN 19 2012, Vol. www.macrothi world, the th vant inform ce of securit onsequences ents. All kn less to try to tion or a m hich will be noted t are eviations fo he deviation market fluc urs is effec apidly disap ofessionals, ket is efficie the series o ry. In this c ations reflec the fundam ations betw reduced in racterized b correlation b e controver vement in finance ). a passage in the B was a planned ser eries is above (or permanent shock ccounting 946-052X 4, No. 2 ink.org/ajfa heory of mation to ties. s of past nown or o predict monopoly e true as e: ollows a n returns ctuations tive, the ppearing , end by ent, well of prices case, the ct a long mentals, ween the the long by a zero between sy about e (discovered Bible where ries of r below) its to the said this is profitab simultan Thus, th finance Several were us fact that highligh Fox an Jacobse Finally, market The obj sample importa between sample UK, the South A emergin In what long me R/S and present 2. Liter The ph astronom depende (1951, (1978), been th Diebold Rudebu structur The inte from m FIGAR the dev process that the pr bility (low neously adv he ability to , both from l statistical t sed. Indeed, t the S& P5 hts the depe d Farahman en (1996) st , Golaka an using daily jective of th of 21 stock ance in the e n long mem includes th e Japan, and Africa, Egy ng powers o t follows we emory, we w d the ARFI the results. rature Revi henomenon mer Newco ence structu 1957), Man the search he subject o d and Rud usch (1991) re interest ra erest in rese modeling the RCH (fractio velopment o ses, they are roponents o dependence vocate the a predict futu an academ tools for th , the study o 500 can be c endencies lo nd (1999) tudied the lo nd Nath (200 y NIFTY ind he paper is k markets w economy, as mory in stoc he developed d the USA, ypt, Saudi A of Turkey, I e will expos will then se IMA model iew of long m omb and th ure of long ndelbrot an for depend of many co debusch (19 ) on consum ates or LO ( earch on lo e volatility onally see B of these var e relatively of efficienc e where de absence of lo ure perform ic or practic he developm of Hsieh (19 considered f ong-term ret studied the ong-term de 01) attempt dices. to test stoc with a wider s an attempt ck returns an d stock mar it also inclu Arabia, Sou Indonesia, B se, first, a li et out, in th l, then we memory app he chemist g-term beca nd Wallis ( dence struct ontributions 989) and S mption, She (1991) on th ng memory of the serie Bollerslev a rious resear rare in the 381 cy seem to ependence b ong memor mance from p cal point of ment of chao 991) in the following a turns of the e returns of ependencies ted to test th ck index ret developme t to provide nd the level rkets of US udes, in add uth Korea, Brazil, Mexi iterature rev he second se will show peared in t Student. T ame import (1968), Ma tures in lon . Among th Sowell (19 ea (1991) a he stock ma y is further es through A and Mikkel rch studies literature. B Asian o accept th between ob ry in these s past one is o f view. os theory on U.S. marke random wa Dow Jones f major ma s indices of he presence turns for lo nt spectrum e further inte l of stock m SA, the Fran dition to the Argentina, ico, China, view of rese ection, the c the empiric he year 18 The fact th tant researc ndelbrot (1 g-term econ hese studies 992) on the and Backus arket. highlighted ARFIMA p lsen (1996) of the fore Baillie (199 n Journal of F e predictab bservations ame series. observed to b n economic t raises man lk, the same Industrial. O arket indice seven indus of long me ng memory m in terms o ernational e market devel nce, the Ger e emerging m Australia, India and R earches mad concept of H cal evidenc 895 from o hat time ser ch topic in 972) and M nomic and s may be m e real prod s and Zin ( d by recent process, lead integrated ecast series 96), Doukha Finance & Ac ISSN 19 2012, Vol. www.macrothi bility of sh of short-te be a crucial c and financ ny doubts a e way Peter Opong, Mu es of Engla strialized co emory in th y using data of size, liqui evidence on lopment. W rmany the I markets of those of th Russia . de on the co Hurst expon ce. Finally, observations ries may e n economic McLeod an financial se mentioned t duct, Dieb (1993) on t developmen ding to the GARCH). through A an et al. (20 ccounting 946-052X 4, No. 2 ink.org/ajfa hort-term erm) but l issue in cial data about the rs (1994) ulholland, and, and ountries. he Indian a from a idity and n the link While the Italy, the Tunisia, he seven oncept of nent, the we will s of the exhibit a s. Hurst nd Hipel eries has those of old and the term nts back process Despite ARFIMA 003) and Robinso integrat Davidso nonline includin of exch markets Timotej analysis to perfo suggest Czech R of LRD time w represen David, showing evidenc of the volatilit dissimil manage We pro indices Averag David G country period f present 3. Meth To dete Mandel standard floods. a- Hurs The in hydrolo could e capacity on (1994, 2 tion. on and Tera earity of tim ng for exam hange rates s (Willinger j Jagric, Bo s of long-ra orm an anal t that we ca Republic, H D (Poland an window, th ntative for t McMillan, g that Afric ce of long m UK and U ty is mixed. lar across m ement strate opose to co through m e) and the w G. McMilla y indices cla from Janua in long mem hodology ect the dep lbrot sugge d deviation st exponent nvention of ogical series exhibit the l y by the sta 2003) provid asvirta (200 me series. mple: financ (Ferrara an r et al (1999 oris Podobn ange depend lysis of LRD an divide the Hungary, Ru nd Slovakia he results the markets Pako and can marke memory in v USA show . These resu markets and egies. ntinue the modeling A work of Tim an, Pako Th assified into ary 2000 to mory time s pendence o ests using t ) that was o t f Hurst is s. This is fr long memor andard devia de an overv 02), in turn Since then ce on a serie nd Guégan 9)). nik, Marko dence (LRD D in the cap e stock mar ussia, and S a). Addition show som in transitio Thupayaga ets (largely) volatility is short mem ults show th this may ha work on lo ARFIMA ( motej Jagric upayagale, o three grou December series. of long-term the statistic originally d the study from his stu ry process. ation of T s 382 view of the n, they studi n, this conc es of inflati (2001)) an Kolanovic D) based on pital market rkets into tw Slovenia), a nally, if the me addition on economie ale, (2009) ) display a very mixed mory in retu hat the behav ave implica ong memory (Auto Regr c, Boris Po (2009) by e ups accordin 2010. Such m or the p c R/S also developed b y of long-t udy of the i The empir successive d Asian processes o ied the non cept has be ion rates (B nd price ser (2005) in t the Hurst e ts of six tran wo groups: and markets Hurst expo nal propert es. in their ar predictable d. In compa urns while vior of equi ations for po y with a stu ressive Fra dobnik and expanding t ng to their l h a model a presence of called (res y Hurst (19 term statist ideal capac rical law of discharges o n Journal of F of long mem n-stationary, een applied aillie et al ( ries of shar heir paper, exponent. A nsition econ markets wi s with no or onent is esti ties, which rticle they f e componen arison, resul evidence o ity market r ortfolio dive udy of the actionally I d Marko Ko the sample b evels of dev aims to refl f long mem scaled Ran 951) at its a tical depen ity of a wa f Hurst is by of a river; H Finance & Ac ISSN 19 2012, Vol. www.macrothi mory and fr , long mem d in variou (1996)), on res traded presents a An estimator nomies. Th ith strong L r only a we imated on a h we belie funds some nt in return lts from the of long mem returns and r ersification dynamics Integrated olanovic (20 by the choi velopment lect the phe mory pheno nge or Ran analysis on ndence on ater tank th y dividing Hurst found ccounting 946-052X 4, No. 2 ink.org/ajfa ractional mory and s fields, a series in stock wavelet r is used e results LRD (the eak form a sliding eve are e results ns; while e control mory in risks are and risk of stock Moving 005) and ce of 21 over the enomena omenon, nge over the Nile various at Hurst the tank that this ratio is and 1. I behaved proport b- Resc The sta from its the aver With R The ran study, H constan The Hu used to R/S ~ T Hurst's 0 if H > d on the val rocess has n e positive an of a long m ce of Josep Asian called Hurs r, Hurst sho e capacity r "TH Law". partial sums . Thus, a tim tten: min ∑X X ⁄ atistic R/S i ike TH, wh is given by articularly i dence struct s asymptoti rrelation me past observa ½ When H lues of H an no depende nd decrease memory proc ph long ter n Journal of F st exponent ould have fo of the stan s of deviatio me series X X X⁄ is always n ere H is a : interesting i ture. ically propo easure of lo ations and f ~1, CH then nd CH. nce on long e very rapid cess, we can rm. This is Finance & Ac ISSN 19 2012, Vol. www.macrothi usually be found that th andard devi ons of a tim Xt, t = 1 ..... non-negative mean of 0. insofar as th ortional to T ong-term CH future obse n increases. g-term, this dly when th an say here called per ccounting 946-052X 4, No. 2 ink.org/ajfa etween 0 his ratio iation is me series T, XT is e. In his .73. The he value TH with 0 H linked ervations We can s type of he delay that the rsistence phenom probabi - If 0 < correlat of decli long-ter Therefo measure that the reason t c- Lo's The stat it is ver theoreti As a so tests the The mo The we The mo include Concern with: (KT) is φ is the Subsequ menon in ca ility that it i < H < ½, tion is nega ine. This is rm depende ore, the Hu e of the inte e statistic R that Lo (199 modified r tistical R/S ry sensitive ical distribu lution to the e null hypot odified R/S, Q S q ights wj (q) odified R/S s not only th ning the cho the integer estimator o uently wj (q ase "if the s is also on th we are tal ative this is a particula ency." urst exponen ensity of lon R/S does not 91) develop rescaled ran (rescaled r to the depe ution is unkn ese problem thesis of sho denoted Qm RS q 1T X ) have been statistic di he standard oice of q, Aq part of KT. of the autoc q) become: series has b he rise next p lking about explained b ar form of lo nt, which i ng-term dep t determine ped the mod nge statisti ange) introd endence of nown. ms, Lo (199 ort memory mT is written1S q ma X 2T suggested b iffers from d deviation o Andrews (19K ou orrelation c ω 384 been on the period." t anti-persis by rising ph ong memor is determin pendence in e whether (H dified R/S st ic (1991) duced by H short-term 1) develope y against the n: ax X 2T ω q by Newey a the R/S on of the series 991)) providu K 3T2 coefficient o ω 1 jK Asian e rise the pr stent proce hases which ry, which w ned from an n a time seri H) is statist tatistic. Hurst in 195 and also it i ed the modif e alternative X m X and West (1 nly by its tr s but also th des the folloT 2 φ1 φ of order 1. jK n Journal of F revious peri ss that is t tend to be f was named " nalysis of t ies. But the ically signi 1 has a maj is not a stat fied R/S sta e of long me in X X X 987). aditional de he weighted owing rule: Finance & Ac ISSN 19 2012, Vol. www.macrothi iod, there i to say that followed by "anti-persis the R/S pro e major draw ificant, it is or drawbac tistical test atistic from emory. X X enominator d autocovari ccounting 946-052X 4, No. 2 ink.org/ajfa s a high the CH y phases tence of ovides a wback is for this ck is that since its where it since it ances. Lo (199 number with the From h robustn weak de distingu d- The ARFIM These m are a ge integer. Recall t nonstati (I (d)), known Thus, th infinite memory existenc non-inte memory series, short-te long-ter on a sin a series The sim discrete Hosking notewor d = H – Therefo paramet - If 0 autocor 91) defined r of observa e values tab his article “L ness of the m ependence, uish short m ARFIMA MA models models have eneralizatio . that the ARM ionary so it therefore t as ARIMA he presence memory, an y. These tw ce of a para eger coeffi y process. T because it erm and on rm moveme ngle parame of long-ter mplest ARF e time: it is d g (1981), G rthy relation –1/2 ore, it is po ter “d”. 0. Ne ed value of pplying the with the crit e 1,620 1,7 mong the tw : LQ 45, SS he memory is confirms of a short-t haracteristic can be rati y efficient. P bitraged aw idities that Asian hoice of the (Xi, Xj) an a value too e will be s to study eff rrelated, thu opposite. It nary and im x 2, where w e null hypot idering the H from the a m the relatio ng to the m e presence evertheless, H is signif method of tical values 47 at the re wenty-one e SE Compos detected fr what we h erm memor c of efficie ionalized fo Prices tend t way. Thin m perpetuate n Journal of F e distance e d the value small may et as the sta ficiency. Fo us justifying reveals the mportant too we took the thesis of ran e different t application onship: d method R/S, of long me the traditio ficantly diff R/S amend given by L spective thr exhibit long site, Tunind rom the trad ave previou ry in the ret nt markets or developed to reflect al markets, on information Finance & Ac ISSN 19 2012, Vol. www.macrothi to the exte es of the cor lead to us i andard devi or if, in rel g the effici types of lin ol in the ana e values of m ndom walk, trends of the meth H . all series e emory beca onal statistic ferent or no ded, which p Lo (1991), w reshold of 1 g term depe dex, EGX, T ditional ana usly mentio turn series, at the exp d stock ma ll publicly a the other h nal inefficie ccounting 946-052X 4, No. 2 ink.org/ajfa nt that a rrelation integrals iation of lation to iency of near and alysis of m going , the test hod R/S, See the exhibit a ause the c of R/S ot to 1/2. provides which in 10% and endence: Tadawul alysis of oned, the thus we pense of rkets on available hand, are ency and Inappro adequat creditor develop In addit of impo speciali encoura markets b- Stud For the between the stud table in The tab be asso long me stock m 6. Conc A mark returns is impo market presenc which d sustaina The pro only six market can infe for the short-te seems t markets The per time req market informa time. W opriate infor te regulator rs were foun pment. tion, the pre ortant insti ized broker age specula s from their dy of persis e sake of ri n detection dy period in n appendix 3 ble shows th ciated with emory may markets work clusion ket is inform since all in ssible to ma price and it ce of long m decays slow able betwee ocedure of t x rounds am indexes LQ er a violatio other serie erm autocor to be close s that the tre rsistence co quired for t where inf ation is also We are far fr rmation acq ry environm nd to be str esence of pr itutional asp s, tend to b ative activit r fundament stence over igor we wi of long-ter n each index 3. hat the owne stock mark y be linked ks. mationally formation, k ake abnorm ts fundamen memory in wly when en market pr the heuristic mong the tw Q 45, SSE C on of the as es there wa rrelation, m ely linked to end is up. ompletely d the integrati formation o very slow om ideal m quisition and ment, especi rongly asso rice manipu pects in re be typical c ties and m tals and thei periods wi ill try to sh rm persisten x bullish an ership of lo ket indicatin to particula efficient if known or a mal profits by ntal value. B that persist the delay i rice and its c R / S amen enty-one ex Composite, sumption of as evidence more it was o countries destroys the ion of infor fits very s w, but mostl arket define 392 d dissemina ially in rela ciated with ulations, use elation to l characteristi may explain ir slow adju ith differen how in this nce and the nd bearish p ong-term dep ng an upwar ar character it is impos anticipated, y speculatin But this def tence is cha increases an fundamenta nded, which xhibit long t Tunindex, f weak form e of a shor s observed s whose lev e hypothesi rmation in t slowly. In ly because ed by the pr Asian ation about ation to pro h low levels e of inside in listing requ ics of thin m n the depar ustment to n nt trends s paragraph market tren periods, the pendence o rd trend, a p ristics of th ssible to pr is already i ng on the di finition of e aracterized b nd this lea al value. h provides u term depend EGX , Tad m of efficien rt memory that the ch vel of devel is of marke the price. A a market of overreac roponents o n Journal of F firms issuin operty rights of financia nformation uirements an markets. Th ture of sto new informa h if there is nd, for this results are n market in phenomeno he environm redict future ncorporated fference be efficiency is by an autoc ads to the e us with stati dence: the f awul and M ncy in these that is to haracteristic lopment is et efficiency A persistent antipersist ctions that f the rationa Finance & Ac ISSN 19 2012, Vol. www.macrothi ng equities s and prote al and stock and the ina and the abs hese charac ock prices ation. s some con s reason we summarize ndex returns on that sugg ment in whi e returns fr d in the pric etween the o s challenge correlation existence o istical V sho following re Merval there e markets. W say, a pres c of long m relatively l y since it s market wo tant integra are correct ality of inve ccounting 946-052X 4, No. 2 ink.org/ajfa , lack of ection of k market dequacy sence of cteristics in these nnection divided ed in the s tend to gests that ich each rom past ce. So, it observed d by the function of a gap ows that eturns of efore we Whereas sence of memory low and signals a uld be a ation of ed, over estors. Howeve exponen replicat Referen Andrew Matrix Backus structur http://dx Baillie, Journal Bernste Portfoli Bollersl volatilit David G Studies http://dx Davidso Journal http://dx Diebold Journal http://dx Diebold Index: http://dx Doukha Depend Dufréno Applica http://dx Frieder, Journal http://dx er the analy nt suspect b ted using LO nces ws, Donald W Estimation. , D.K., & S re of inte x.doi.org/10 R.T. (199 of Econom ein, Peter L io Managem lev T., & M ty. Journal G. McMilla in x.doi.org/10 on, J., & T l x.doi.org/10 d, F.X., & G l o x.doi.org/10 d, F.X., & A real x.doi.org/10 an, P., Oppe dence. Birkh ot G., & M ations to M x.doi.org/10 , L., & Subr l of x.doi.org/10 ysis conduct bias caused O statistics t W K. (1991 . Econometr .E. Zin. (19 rest rates. 0.2307/2077 96). Long m metrics 73, 5 . (1999). 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K 15-1 Brand Perce Quantita 01745 Asian odology allo t term depe nd Autocorr iety, 59(3). ation uncer , Credit a d fractional 10.1016/030 icient Mark 10.3905/jpm and pricing The efficien Finance, ong Memory mory and p conomics, sting output Monetary ). Theory an opments in N Kluwer Acad eptions and ative A n Journal of F owed for det endence. Th relation Con tainty: Evid and Banki l integration 04-4076(95) ket Hypothe m.1999.390 long memo ncy of Afric 26(4 y and Nonl 110(2), ersistence i 24, t with the C Economic nd Applicat Nonlinear C demic Publ the Market nalysis, Finance & Ac ISSN 19 2012, Vol. www.macrothi termining th his study sh nsistent Cov dence from ing, 25, 6 n in econo )01732-1 esis. The Jo 0965 ory in stock can equity m 4), 2 linear Time 1 in aggregate , 1 Composite cs, 24, 1 tions of Lon Cointegrati lishers, 299 t for Commo 40(1), ccounting 946-052X 4, No. 2 ink.org/ajfa he Hurst hould be variance the term 681-700. ometrics. urnal of k market markets. 275-292. e Series. 105-437. e output. 189-209. Leading 189-209. ng-range ion With 9 pages. on Stock. 57-86. Geweke series m Geweke series http://dx Hosking http://dx Hsieh, D of Finan Hurst, H Society Jacobse 93-417. Lo, A.W http://dx LO, An Econom Malkiel Econom Malkiel The Fin MAND covarian Mandel Researc McLeod reassess http://dx Mignon Paris. Mignon NATH, UTIICM e J., & Port models. The e J., & S. P models. x.doi.org/10 g, J.R.M x.doi.org/10 D. (1991). C nce, 46, 183 H.E. (1951) of Civil En en, B. (1996 . http://dx.d W. (1991). L x.doi.org/10 ndrew W. ( mics. Second l, Burton G mic Perspec l, Burton G nancial Revi DELBROT, nce to R/S a lbrot, B.B., ch, 4, 909-9 d, A.I., & sment of x.doi.org/10 n V. (1998). n, V. (1997) , Golaka C. M Conferen ter-Hudak S ory Related Porter-Huda Journa 0.1111/j.146 . (1981). 0.1093/biom Chaos and N 39-1877. ht ). Long-term gineers, 11 6). Long term doi.org/10.10 Long-term 0.2307/2938 (2008). Eff d ed. Londo G. (2003). T ctives, 17(1) G. (2005). R iew, 40(1), B.B. (1972 analysis. An & Wallis, J 918. http://d K.W. Hip the Hurst 0.1029/WR . Marchés fi ). Long-term (2001). Lo nce Paper. S. (1990). T d Fields, 86, ak. (1983). T al of 67-9892.19 Fraction met/68.1.165 Nonlinear D tp://dx.doi.o m storage c 6, 770-799. m dependen 016/S0927- memory in 8368 ficient Mark on: Palgrave The Efficien , 59-82. http Reflections o 1-9. http://d 2). Statistic nnals of Eco J. (1968). N dx.doi.org/10 pel (1978). phenomen 014i003p00 inanciers et m memory a ong Memor 394 The estimati , 87-104. The estimat Time 83.tb00371 nal differ 5 Dynamics: A org/10.1111 capacity of . nce in stock -5398(96)00 n stock mark rkets Hypot e Macmillan nt Market H p://dx.doi.o on the Effic dx.doi.org/1 cal methodo onomic and . Joseph and 0.1029/WR Preservatio non. Wate 0491 modélisatio and chaos. S ry and India Asian ion and app tion and app Series .x rencing. B Applications 1/j.1540-62 reservoirs. returns. Jou 0009-6 ket prices. E thesis. The n. Hypothesis a org/10.1257/ cient Marke 10.1111/j.07 ology for n d Social Mea d operationa R004i005p00 on of the r er Resourc on des renta Springer Ve an Stock M n Journal of F plication of plication of Analysis, Biometrika, s to Financia 61.1991.tb0 Transaction urnal of Emp Econometri New Palgr and Its Criti /089533003 et Hypothes 732-8516.20 non-periodic asurement, al hydrology 0909 rescaled adj ces Resear abilités bour erlag. Market-An E Finance & Ac ISSN 19 2012, Vol. www.macrothi f long-memo f long memo 4, 2 , 68, 1 al Markets. 04646.x ns of the A pirical Fina ica, 59, 127 grave Dictio tics. The Jo 3321164958 sis: 30 Year 005.00090.x c cycles: f 1, 259-290. gy. Water Re djusted rang rch, 14, 4 rsières. Eco Empirical Ev ccounting 946-052X 4, No. 2 ink.org/ajfa ory time ory time 221-238. 165-176. Journal merican ance, 33, 79-1313. onary of urnal of 8 rs Later. x from the . esources ge, I: A 491-508. onomica, vidence. Newey, Heteros 703-708 Olsen ( Analyst Opong, Equity 267-282 Peters, Econom Robinso Long http://dx Robinso Sixth W Scheink Univers Shea, G interest http://dx Timotej Hypoth 43(4), 7 Willing depende , Whitney skedasticity 8. http://dx. (1998). Beh ts Journal, 5 K.K., Mulh Indicies: A 2. http://dx. Edgar E. (1 mics. New Y on, P. M., & Memory x.doi.org/10 on, P.M. (1 World Congr kman, J., & sity. G.S. (1991). rate x.doi.org/10 j Jagric, Bo hesis Hold?: 79-103. ger, Taqqu, ence. Finan K; West, y and Autoc doi.org/10.2 havioral fin 54(02), 10-8 holland, G., An Applicati doi.org/10. 1994). Frac York: John W & M. Henry y. Journ 0.1016/S030 994). Time ress. http://d & Xiong, W . Uncertaint term 0.1007/BF0 oris Podobn : Evidence ,M., & Te nce and Stoc & Kenne correlation C 2307/19136 nance and Ib 8. http://dx.d , Fox, A.F., ion of Hurs 1016/S0927 ctal Market Wiley & So y. (2003). H nal of 04-4076(02 e series with dx.doi.org/1 W. (2003). ty and impl structure. 01206277 nik, & Ma from Six T everovsky, chastics, 3, 395 eth D (198 Consistent C 610 b implicati doi.org/10.2 & Farahma st and BDS 7-5398(99)0 Analysis: A ons. Higher Orde Econom 2)00208-7 h strong de 10.1017/CC Overconfid lied varianc Empiric arko Kolano Transition E V. (1999) 1-13. http:/ Asian 87). A Sim Covariance ons for sto 2469/faj.v54 and, K. (199 S Tests. Jou 00004-3 Applying Ch r Kernel Se etrics, ependence. A COL052144 dence and S ce bounds i cal Eco ovic. (2005 Economies. . Stock m //dx.doi.org/ n Journal of F mple, Posit Matrix. Ec ck, price V 4.n2.2161 99). The Beh urnal of Emp haos Theory emiparametr Volume, Advances in 4594.002 Speculative n long-mem onomics, 5). Does th Eastern Eu arket price /10.1007/s0 Finance & Ac ISSN 19 2012, Vol. www.macrothi tive Semi- conometrica Volatility. F havior of So mpirical Fin y to Investm ric M-estim 114(1), n Econome e Bubles. P mory model 16, 2 he Efficient uropean Eco es and lon 0078000500 ccounting 946-052X 4, No. 2 ink.org/ajfa definite, a, 55(3), Financial ome UK nance, 6, ment and mation of 1-27. etrics, 1, rinceton ls of the 287-312. Market onomics, g range 049 Append CAC SP5 FTSE MIBT S$P/T NIKKE DA LQ- ISE-1 BOVE IPC SSE Com NIFT MICE TUNIN EGX KOS FTSE TADAW MERV SP/AS dix 1. Calcu Sk C 40 0.394 00 -0.094 E100 0.069 TEL -0.609 TSX 0.255 EI225 0.555 X 0.741 -45 1.173 100 1.173 ESPA 1.173 C 0.373 mposite 1.566 TY 0.35 EX 0.35 NDEX 0.35 X 30 0.309 SPI -0.23 JSE 0.741 WUL 0.275 VAL 0.701 SX50 0.275 ulation of s k Ku 4002 2.10322 4044 2.30954 9159 2.02373 9381 2.57556 5913 1.92178 5232 2.23985 1152 2.45005 3229 3.64680 3229 3.64680 3229 3.64680 3146 1.59505 6885 5.22842 994 1.63265 994 1.63265 994 1.63265 9711 1.75299 3072 1.81978 1152 2.45005 5576 2.15130 1316 2.46221 5576 2.15130 statistics JB 7 165.3771 6 58.9987 2 112.5762 6 161.14 1 162.0988 7 203.5808 7 276.5251 5 708.4385 5 708.4385 5 708.4385 5 290.8353 6 1739.25 4 272.4151 4 272.4151 4 272.4151 4 218.1046 4 192.0314 7 276.5251 3 115.6757 3 264.9612 3 115.6757 396 augmented ADF test -0.883028 - -1.125635 -0.581993 -1.028095 - -0.712938 - -0.221833 - 2.412442 -0.756041 - -0.756041 - -0.756041 - 1.813961 0 -0.675308 - 0.471062 - 0.471062 - 0.471062 - 0.08139 0.38657 - 2.412442 2.408518 - -0.424588 2.408518 - Asian Phillips Perron test KPS -1.909149 0.93 -1.97652 0.5 -2.05624 1.24 -1.138692 0.38 -1.145514 3.65 -2.067614 0.67 1.439008 5.47 -1.563469 1.58 -1.563469 1.58 -1.563469 1.58 0.519614 6.0 -1.296607 2.39 -0.775398 5.0 -0.775398 5.0 -0.775398 5.0 -0.05649 5.46 -1.347061 4.59 1.439008 5.47 -1.415932 5.3 1.064622 3.78 -1.412094 5.3 n Journal of F SS test White t 33378 49.645 17874 162.66 45823 70.647 89724 30.619 55343 46.713 74326 68.027 71842 1.3567 88478 8.8954 88478 8.8954 88478 8.8954 02364 7.6290 99185 51.487 14026 15.368 14026 3.8568 14026 10.306 61516 14.959 93266 25.165 71842 15.73 36574 6.0848 82724 87.923 36574 6.0848 Finance & Ac ISSN 19 2012, Vol. www.macrothi test BP 519 93.505 621 90.096 741 91.362 981 52.727 394 77.706 753 88.534 799 70.828 463 88.982 463 88.982 463 88.982 063 88.926 741 53.727 807 83.986 88 89.902 639 91.008 95 88.037 599 94.214 33 95.749 847 67.116 398 96.715 847 67.116 ccounting 946-052X 4, No. 2 ink.org/ajfa Corrected BP 0.924 0.904 0.918 0.696 0.825 0.903 0.747 0.865 0.865 0.865 0.91 0.541 0.894 0.925 0.917 0.913 0.918 0.928 0.715 0.95 0.715 Append dix 2．BDS S S test CAC 40 SP500 FTSE100 MIBTEL S$P/TSX NIKKEI225 DAX LQ-45 ISE-100 BOVESPA IPC SSE Composite NIFTY MICEX TUNINDEX EGX 30 KOSPI FTSE JSE TADAWUL MERVAL SP/ASX50 m=2 0.199275 0.194668 0.199484 0.200159 0.199943 0.199491 0.199230 0.204226 0.200639 0.201991 0.205602 0.201384 0.204708 0.202683 0.206120 0.202295 0.201379 0.202732 0.206939 0.205602 0.198840 397 m=3 0.339375 0. 0.331305 0. 0.339653 0. 0.340773 0. 0.340754 0. 0.339799 0. 0.338960 0. 0.347457 0. 0.341248 0. 0.343534 0. 0.349702 0. 0.342999 0. 0.347868 0. 0.345584 0. 0.350577 0. 0.344421 0. 0.343122 0. 0.344788 0. 0.350932 0. 0.349702 0. 0.339053 0. Asian m=4 m= .437110 0.504 .426298 0.491 .437364 0.505 .439051 0.507 .439325 0.508 .437821 0.505 .436134 0.503 .447681 0.517 .439326 0.507 .442407 0.511 .450469 0.520 .441986 0.510 .447624 0.516 .446030 0.516 .451900 0.522 .444074 0.513 .442448 0.511 .444075 0.513 .450755 0.519 .450469 0.520 .436813 0.504 n Journal of F =5 m=6 4935 0.55165 1704 0.53625 5101 0.55168 7463 0.55479 8052 0.55578 5855 0.55281 3358 0.54952 7762 0.56667 7518 0.55463 1357 0.55923 0933 0.57015 0891 0.55864 6912 0.56503 6349 0.56541 2912 0.57268 3492 0.56162 1916 0.56036 3062 0.56090 9802 0.56741 0933 0.57015 4648 0.55139 Finance & Ac ISSN 19 2012, Vol. www.macrothi 55 58 80 96 81 10 20 79 35 35 55 40 31 13 89 26 66 07 14 55 90 ccounting 946-052X 4, No. 2 ink.org/ajfa Calcula Append ation of the R CAC SP5 FTSE MIBT S$P/T NIKKE DA ISE- LQ- BOVE IP SSE Com NIF MIC TUNIN EGX KOS FTSE TADA MERV SP/AS dix 3． Ca D S$ MI R/S statistic Hur C 40 0.835 500 0.543 E100 0.535 TEL 0.598 TSX 0.577 EI225 0.553 AX 0.554 -100 0.547 -45 0.604 ESPA 0.575 C 0.561 mposite 0.619 TY 0.582 CEX 0.573 NDEX 0.653 X 30 0.590 SPI 0.564 E JSE 0.545 AWUL 0.648 VAL 0.600 SX50 0.538 alculation o P DAX P/TSX IBTEL and Hurst e The analysis R rst d 308 0.335308 747 0.043747 220 0.035220 891 0.098891 033 0.077033 416 0.053416 691 0.054691 952 0.047952 082 0.104082 024 0.075024 213 0.061213 408 0.119408 119 0.082119 438 0.073438 710 0.153710 355 0.090355 964 0.064964 904 0.045904 590 0.148590 424 0.100424 832 0.038832 of the Hurs Th Period Hurst 1 0.566 2 0.563 3 0.578 4 0.571 1 0.587 2 0.573 3 0.560 4 0.591 5 0.573 1 0.564 2 0.571 398 exponent R / S Cm 0.591752 0 0.062523 0 0.050037 0 0.146933 0 0.112701 0 0.076861 0 0.078767 0 0.068735 0 0.155217 0 0.109607 0 0.088564 0 0.180024 0 0.120574 0 0.107169 0 0.237492 0 0.133441 0 0.094239 0 0.065704 0 0.228740 0 0.149375 0 0.055308 0 st exponent he analysis R / S d C 0.066 0.0 0.063 0.0 0.078 0.1 0.071 0.1 0.087 0.1 0.073 0.1 0.060 0.0 0.091 0.1 0.073 0.1 0.064 0.0 0.071 0.1 Asian The analy Hurst d 0.441819 -0.05 0.537867 0.037 0.541490 0.04 0.561448 0.06 0.555388 0.05 0.534178 0.034 0.555212 0.05 0.528830 0.02 0.578024 0.07 0.530557 0.030 0.546901 0.046 0.566038 0.066 0.553105 0.053 0.536975 0.036 0.600180 0.100 0.572732 0.072 0.528225 0.02 0.510559 0.010 0.574739 0.074 0.564870 0.064 0.542355 0.042 t on returns The an Cm Hurst 096 0.563 092 0.516 114 0.521 103 0.457 128 0.548 107 0.517 086 0.509 134 0.519 106 0.563 092 0.514 103 0.451 n Journal of F ysis R / S modifie d Cm 8181 -0.07748 7867 0.05389 1490 0.05920 1448 0.08891 5388 0.07980 4178 0.04852 5212 0.07954 8830 0.04077 8024 0.11423 0557 0.04327 6901 0.06717 6038 0.09586 3105 0.07639 6975 0.05259 0180 0.14898 2732 0.10608 8225 0.03990 0559 0.01474 4739 0.10916 4870 0.09409 2355 0.06047 s alysis R / S mod d Cm 0.063 0.092 0.016 0.022 0.021 0.030 -0.043 -0.058 0.048 0.070 0.017 0.024 0.009 0.012 0.019 0.027 0.063 0.091 0.014 0.020 -0.049 -0.066 Finance & Ac ISSN 19 2012, Vol. www.macrothi ed V 89 0.63 98 1.35 03 1.39 19 1.61 09 1.55 21 1.31 45 1.55 76 1.27 31 1.85 71 1.28 79 1.45 69 1.69 97 1.52 95 1.34 84 2.21 86 1.77 04 1.25 45 1.09 68 1.82 96 1.67 74 1.40 dified V 1.75 1.13 1.21 0.7 1.55 1.17 1.08 1.2 1.75 1.15 0.6 ccounting 946-052X 4, No. 2 ink.org/ajfa S FT CA NIK FTS N K TUN TAD SP/ EG SP500 TSE100 AC 40 KKEI225 SE JSE Nerval KOSPI NINDEX DAWUL /ASX50 GX 30 3 0.575 4 0.571 1 0.565 2 0.560 3 0.575 4 0.573 1 0.565 2 0.561 3 0.575 4 0.573 1 0.568 2 0.563 3 0.572 4 0.575 1 0.565 2 0.561 3 0.577 4 0.571 1 0.557 2 0.582 3 0.593 4 0.565 5 0.566 1 0.559 2 0.584 3 0.570 1 0.559 2 0.580 3 0.573 1 0.565 2 0.559 1 0.558 2 0.578 3 0.587 4 0.583 5 0.569 1 0.558 2 0.582 3 0.575 1 0.566 2 0.565 3 0.609 4 0.571 399 0.075 0.1 0.071 0.1 0.065 0.0 0.060 0.0 0.075 0.1 0.073 0.1 0.065 0.0 0.061 0.0 0.075 0.1 0.073 0.1 0.068 0.0 0.063 0.0 0.072 0.1 0.075 0.1 0.065 0.0 0.061 0.0 0.077 0.1 0.071 0.1 0.057 0.0 0.082 0.1 0.093 0.1 0.065 0.0 0.066 0.0 0.059 0.0 0.084 0.1 0.070 0.1 0.059 0.0 0.080 0.1 0.073 0.1 0.065 0.0 0.059 0.0 0.058 0.0 0.078 0.1 0.087 0.1 0.083 0.1 0.069 0.1 0.058 0.0 0.082 0.1 0.075 0.1 0.066 0.0 0.065 0.0 0.109 0.1 0.071 0.1 Asian 109 0.766 103 0.523 094 0.451 086 0.397 110 0.419 106 0.572 094 0.421 089 0.592 110 0.539 106 0.604 099 0.441 091 0.467 104 0.437 109 0.446 094 0.510 089 0.514 113 0.501 103 0.572 082 0.367 120 0.532 138 0.522 094 0.531 096 0.599 085 0.542 123 0.539 101 0.523 085 0.368 117 0.533 107 0.622 094 0.544 085 0.615 084 0.525 114 0.527 128 0.549 123 0.510 101 0.696 084 0.456 120 0.530 109 0.522 096 0.528 094 0.526 162 0.581 103 0.393 n Journal of F 0.266 0.445 0.023 0.032 -0.049 -0.066 -0.103 -0.133 -0.081 -0.107 0.072 0.105 -0.079 -0.103 0.592 1.272 0.539 1.112 0.604 1.309 -0.059 -0.079 -0.033 -0.045 -0.063 -0.083 -0.054 -0.072 0.010 0.014 0.014 0.019 0.001 0.001 0.072 0.105 -0.133 -0.168 0.032 0.045 0.022 0.031 0.031 0.044 0.099 0.147 0.042 0.059 0.039 0.055 0.023 0.032 -0.132 -0.167 0.033 0.047 0.122 0.184 0.044 0.063 0.115 0.172 0.025 0.035 0.027 0.038 0.049 0.071 0.010 0.014 0.196 0.312 -0.044 -0.060 0.030 0.042 0.022 0.031 0.028 0.039 0.026 0.036 0.081 0.119 -0.107 -0.138 Finance & Ac ISSN 19 2012, Vol. www.macrothi 1.2 1.27 0.7 0.5 0.55 1.6 0.5 1.25 1.15 1.22 0.6 0.77 0.58 0.65 1.1 1.13 1.01 1.9 0.5 1.25 1.15 1.22 1.9 1.3 1.35 1.17 0.4 1.29 2.3 1.37 2.22 1.19 1.29 1.52 1.09 5.1 0.7 1.3 1.2 1.23 1.18 2.07 0.4 ccounting 946-052X 4, No. 2 ink.org/ajfa BOV N IS SSE C L M Downtr Uptrend VESPA NIFTY IPC SE-100 Composite LQ-45 MICEX rend d 5 0.591 6 0.586 1 0.554 2 0.591 3 0.571 1 0.559 2 0.581 3 0.577 4 0.616 1 0.555 2 0.577 3 0.573 1 0.572 2 0.560 3 0.598 4 0.580 5 0.580 6 0.573 1 0.582 2 0.563 3 0.571 4 0.587 5 0.573 1 0.559 2 0.588 3 0.571 1 0.558 2 0.601 3 0.573 400 0.091 0.1 0.086 0.1 0.054 0.0 0.091 0.1 0.071 0.1 0.059 0.0 0.081 0.1 0.077 0.1 0.116 0.1 0.055 0.0 0.077 0.1 0.073 0.1 0.072 0.1 0.060 0.0 0.098 0.1 0.080 0.1 0.080 0.1 0.073 0.1 0.082 0.1 0.063 0.0 0.071 0.1 0.087 0.1 0.073 0.1 0.059 0.0 0.088 0.1 0.071 0.1 0.058 0.0 0.101 0.1 0.073 0.1 Asian 134 0.462 126 0.529 078 0.513 134 0.392 103 0.516 085 0.524 119 0.541 112 0.531 175 0.518 079 0.512 113 0.517 106 0.524 106 0.513 086 0.525 146 0.522 118 0.516 117 0.523 107 0.531 120 0.336 091 0.521 103 0.512 128 0.488 107 0.525 085 0.540 130 0.522 103 0.523 084 0.546 150 0.287 107 0.552 n Journal of F -0.038 -0.052 0.029 0.041 0.013 0.019 -0.108 -0.139 0.016 0.022 0.024 0.034 0.041 0.058 0.031 0.043 0.018 0.025 0.012 0.016 0.017 0.023 0.024 0.034 0.013 0.019 0.025 0.036 0.022 0.031 0.016 0.023 0.023 0.032 0.031 0.043 -0.164 -0.204 0.021 0.029 0.012 0.017 -0.012 -0.017 0.025 0.036 0.040 0.057 0.022 0.031 0.023 0.033 0.046 0.066 -0.213 -0.256 0.052 0.075 Finance & Ac ISSN 19 2012, Vol. www.macrothi 0.7 1.27 1.14 0.3 1.18 1.23 1.5 1.32 1.19 1.11 1.19 1.27 1.11 1.17 1.19 1.13 1.22 1.27 0.3 1.17 1.09 0.9 1.21 1.3 1.19 1.18 1.27 0.2 1.4 ccounting 946-052X 4, No. 2 ink.org/ajfa