CHOOSING THE BEST PERFORMING GARCH MODEL FOR SRI LANKA STOCK MARKET BY NON-PARAMETRIC SPECIFICATION TEST

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1 Journal of Daa Scence 3(5), CHOOSING THE BEST PERFORMING GARCH MODEL FOR SRI LANKA STOCK MARKET BY NON-PARAMETRIC SPECIFICATION TEST Aboobacker Jahufer Souh Easern Unversy of Sr Lanka Absrac:Ths paper examnes he performance of dfferen knd of GARCH models wh Gaussan, Suden- and generalzed error dsrbuon for Colombo Sock Exchange (CSE), n Sr Lanka Analyzng he daly closng prce ndex of CSE from January, 7 o March, 3 I was found ha he Asymmerc GARCH models gve beer resul han symmerc GARCH model Accordng o dsrbuonal assumpon hese models under Suden- as well as generalzed error provded beer f han normal dsrbuonal assumpon The Non-Paramerc Specfcaon es sugges ha he GARCH, EGARCH, TARCH and APARCH models wh Suden- dsrbuonal assumpon are he mos successful model for CSE Key words: GARCH Model, Asymmerc GARCH Model, Generalzed Error Densy, Colombo Sock Exchange, Non Paramerc Specfcaon Tes Inroducon The varous well-known characerscs are common o many fnancal me seres Volaly cluserng s ofen observed (e large changes end o be followed by large changes and small changes end o be followed by small changes; Mandelbro (963) for early evdence) Second, fnancal me seres ofen exhb lepokuross, meanng ha he dsrbuon of her reurns s fa-aled see Fama (965) Moreover, he so-called leverage effec, frs noed n Black (976), refers o he fac ha changes n sock prces end o be negavely correlaed wh changes n volaly Engle (98) proposed o model me-varyng condonal varance wh he Auo Regressve Condonal Heeroskedascy (ARCH) processes ha used pas dsurbances o model he varance of he seres Early emprcal evdence showed ha hgh ARCH order has o be seleced n order o cach he dynamc of he condonal varance The Generalzed ARCH (GARCH) model of Bollerslev (986) was an answer o hs ssue I was based on an nfne ARCH specfcaon and allows reducng he number of esmaed parameers from o only Boh models allow akng he frs wo characerscs no accoun bu her dsrbuon s symmerc and fa als herefore, Correspondng auhor

2 458 CHOOSING THE BEST PERFORMING GARCH MODEL FOR SRI LANKA STOCK MARKET BY NON-PARAMETRIC SPECIFICATION TEST o model he hrd sylzed fac, namely he leverage effec To solve hs problem, many nonlnear exensons of he GARCH models have been proposed Among he mos wdely spread are he Exponenal GARCH (EGARCH) of Nelson (99), The Threshold GARCH (TGARCH) model of Zakoan (994), Glosen e al (993) and he Asymmerc Power ARCH (APARCH) of Dng e al (993) Unforunaely, GARCH models ofen do no fully capure he hck als propery of hgh frequency fnancal me seres Ths has naurally led o he use of non-normal dsrbuons o beer model hs excess kuross Bollerslev (986), Balle and Bollerslev (989), Kaser (996) and Bene, e al () among ohers used Suden- dsrbuon whle Nelson (99) and Kaser (996) suggesed he Generalzed Error Dsrbuon (GED) Oher proposons nclude mxure dsrbuons such as he normal-lognormal (Hseh 989 or he Bernoull-normal Vlaar and Palm 993) Peers () n hs workng paper showed he forecasng performance of dfferen knds of asymmerc GARCH model wh normal, Suden- and skewed Suden- dsrbuonal assumpon for wo maor European sock ndces Forecasng condonal varance wh asymmerc GARCH models has been suded n several papers Pagan and Schwer (99), Bralsford and Faff (996), Fransese e al (998), Loudon e al () On he oher hand, comparng normal densy wh non-normal ones also has been explored n many occasons Hseh (989), Balle and Bollerslev (989), Peers () and Lamber and Lauren () Marcucc (3) compared a number of dfferen GARCH models n erms of her ably o descrbe and forecas he behavor of volaly of fnancal me seres He esmaed assumng boh Gaussan nnovaons and fa-aled dsrbuons, such as suden- and Generalzed Error dsrbuon Hong and L (4) suded he Nonparamerc Specfcaon Tess of Dscree Tme Spo Ineres Rae Models n Chna They examned a wde varey of popular spo rae models n Chna, ncludng he sngle-facor dffuson models, GARCH models, Markov regmeswchng models and ump-dffuson models and he specfcaon of hese models Hong and L (5) conduced a sudy on Nonparamerc Specfcaon Tes for Connuous- Tme Models wh Applcaons o Spo Ineres Raes Bara (4) examned he me varyng paern of sock reurn volaly n Indan sock marke In hs sudy he daly closng ndex of CSE n Sr Lanka s used The srucure of he assgnmen s as follows: Secon presens he dfferen GARCH models used n hs sudy, denses are descrbed n Secon 3 and Secon 4 presen non-paramerc specfcaon es, Secon 5 repors he emprcal fndngs whle Secon 6 presen he conclusons Models of he Sudy y Le us consder a unvarae me seres If s he nformaon se (e all he nformaon avalable) a me, we can defne s funconal form as: y E[ ] () y

3 Aboobacker Jahufer 459 E[] where denoes he condonal expecaon operaor and E[ ] unpredcable par), wh and s, E[ ] s s he dsurbance erm (or The erm n Eq () s he nnovaon of he process The condonal expecaon s he expecaon condonal o all pas nformaon avalable a me Condonal Heeroscedasc (ARCH) process of Engle (98) s any z { The Auoregressve } of he form () z E[ ] where s ndependenly and dencally dsrbued (d) process,, Var[ z ] and where s a me-varyng posve and measurable funcon of he nformaon se a me By defnon, s serally uncorrelaed wh mean zero bu s condonal varance equals o and herefore, may change over me, conrary o wha s assumed n OLS esmaons Specfcally he ARCH (q) model s gven by q (3) The models consdered n hs paper are all ARCH-ype They dffer on he funconal form of bu he basc logc s he same GARCH Model The GARCH model of Bollerslev (986) can be expressed as q p (4) Usng he lag or backshf operaor L, he GARCH (p, q) model s L) ( L) (5) ( q p ( L ) L L wh ql ( L) L L and pl Based on Eq (5), s sraghforward o show ha he GARCH model s based on an nfne ARCH specfcaon If all he roos of he polynomal ( L) of Eq (5) le ousde he un crcle, we have [ ( L)] ( L)[ ( L)] or equvalenly z

4 46 CHOOSING THE BEST PERFORMING GARCH MODEL FOR SRI LANKA STOCK MARKET BY NON-PARAMETRIC SPECIFICATION TEST p, whch may be seen as an ARCH( ) process snce he condonal varance lnearly depends on all prevous squared resduals EGARCH Model The EGARCH or Exponenal GARCH model was proposed by Nelson (99) The specfcaon for condonal varance s: log( q p r k ) log( ) k (6) k k The lef hand sde of Eq (6) s he log of he condonal varance Ths mples ha he leverage effec s exponenal raher han quadrac and ha forecass of he condonal varance are guaraneed o be non-negave The presence of he leverage effecs can be esed by he hypohess 3 TGARCH Model The mpac s asymmerc f TARCH or Threshold ARCH and Threshold GARCH were nroduced ndependenly by Zakoan (994) and Glosen e al (993) The generalzed specfcaon for he condonal varance s gven by: q p r (7) where, f or, oherwse In hs model and have dfferenal effecs on he condonal varance; has an mpac of, whle has an mpac of If, ncreases volaly and we say ha here s a leverage effec for he h order If he news mpac s asymmerc 4 APARCH Model Taylor (986) and Schwer (99) nroduced he sandard devaon GARCH model where he sandard devaon s modeled raher han he varance Dng, e al (993) nroduced he Asymmerc Power ARCH model The APARCH (p, q) model can be expressed as: k k k k

5 p Aboobacker Jahufer 46 q (8) (,,, p),(,,, q) where,,, and Ths model s que neresng snce couples he flexbly of a varyng exponen wh he asymmery coeffcen (o ake he leverage effec no accoun) Moreover, he APARCH model ncludes seven oher ARCH exensons as a specal case:, (,, p) ) ARCH when (,, p) and, (,, p) ) GARCH when, (,, p) ) Taylor (986) / Schwer (99) GARCH when v) GJR when, v) TARCH when (,, p) v) NARCH when (,, p) and v) The log-arch of Geweke (986) and Penula (986), whenever 3 Dsrbuonal Assumpons I may be expeced ha excess kuross and skewness dsplayed by he resduals of condonal heeroscedascy model wll be reduced f a more approprae dsrbuon s used In hs sudy, hree dsrbuons such as Gaussan, Suden- and Generalzed Error are consdered Gven a dsrbuonal assumpon, ARCH models are ypcally esmaed by he mehod of maxmum lkelhood 3 Gaussan The Normal dsrbuon s by far he mos wdely used dsrbuon when esmang and forecasng GARCH models If we express he mean equaon as n Eq () and z, he log-lkelhood funcon of he sandard normal dsrbuon s gven by T L T ln( ) ln( z ) (9) where T s he number of observaons 3 Suden -Dsrbuon For he Suden- dsrbuon, he log-lkelhood conrbuons are of he form:

6 46 CHOOSING THE BEST PERFORMING GARCH MODEL FOR SRI LANKA STOCK MARKET BY NON-PARAMETRIC SPECIFICATION TEST L T ln ln 5ln 5 T z ln( ) ( )ln () where s he degree of freedom and s he gamma funcon When, we have he normal dsrbuon So ha he lower he faer he als 33 Generalzed Error () For he GED, we have: L T ln / r 3 3/ rr / 5ln( r / 3/ rz ) () / r where he al parameer r The GED s a normal dsrbuon f r, and fa-aled f r 4 Non Paramerc Specfcaon Tes Recenly Hong and L (5) proposed wo new nonparamerc ranson densy-based specfcaon ess for connuous-me seres models These ess share he appealng feaures of boh A-Sahala (996) and Gallan and Tauchen (996) nonparamerc approaches and have many addonal nce properes Frs, unlke A-Sahala (996) margnal densy-based es, he ess are based on he ranson densy whch capures he full dynamcs of a connuous-me process Second, o acheve robusness o perssen dependence, he daa s ransformed va a dynamc probably negral ransform usng he model ranson densy whch s well known n sascs (eg, Rosenbla 95) and s more recenly used o evaluae ou-of-sample densy forecass n dscree-me analyss (eg Debold, e al 998, Hong e al 4) The ransformed sequence s d U[,] under correc model specfcaon rrespecve of he dependence srucure of he orgnal daa Thrd, o elmnae he well-known boundary bas of kernel esmaors as documened n Chapman and Pearson (), a boundary-modfed kernel s nroduced Fourh, o reduce he mpac of parameer esmaon uncerany, a es based on he Hollnger merc s proposed Ffh, he regulary condons for asympoc analyss are based on he model ranson densy raher han he sochasc dfferenal equaon of he underlyng process As a consequence, he ess are applcable o a vas varey of connuous-me and dscree-me dynamc models such as GARCH/sochasc volaly models, regme-swchng models, ump-dffuson models and mul-facor dffuson models The nonparamerc

7 Aboobacker Jahufer 463 specfcaon es proposed recenly by Hong and L (5) o evaluae dfferen spo rae models Assumng he underlyng process {X} follows he followng daa generang process: dx X, ) d ( X, ) dw () ( (, ) where X (, ) and X W are he drf and dffuson funcons respecvely and p (, /, ) s a sandard Brownan moon Le x y s be he rue ranson densy of he dffuson process X X x ha s he condonal densy of ( X y s / s ), For a gven ( X,, ) par of drf and dffuson models and a ceran famly of ranson denses p( x, / y, s, ) s characerzed If a model s correcly specfed, here exss some sasfyng p ( x, / y, s, ) (, /, ) p x y s almos everywhere for some To es n such a hypohess, Hong and L (5) frs ransform he dscrezed daa va a probably negral ransform and defne hs dscree ransformed sequence by X (,, ) X X Z ( ) p[ x, / X,( ), ]dx,,,, n (3) ( ) If he model s correcly specfed, he exss some such ha p [ x, / X ( ),( ), ] p[ x, / X ( ),( ) ] almos surely for all > Z Z Consequenly, he ransformed seres ( ) n s d U[,] under correc Z specfcaon I can be called ha ( ) n generalzed resduals of he model p( x, / y, s, ) Here, d U[,] propery capures wo mporan aspecs of model specfcaon, d characerze he correc specfcaon of model dynamcs and U[,] characerze correc specfcaon of he model margnal dsrbuon The es ha wheher Z n ( ) follows d U[,] s no a rval ask because s a on hypohess The wellknown Kolmogorov-Smrnov es checks U[,] under he d assumpon raher han es d and U[,] only I would mss he alernaves whose margnal dsrbuon s unform bu no d To make such on hypohess ess, Hong and L (5) develop wo nonparamerc ess of d U[,] gˆ ( z, ) by comparng a kernel esmaor z gˆ ( z, ) for he on densy z of { Z, Z } wh uny, he produc of wo U[,] denses The kernel on densy esmaor s for any neger

8 464 CHOOSING THE BEST PERFORMING GARCH MODEL FOR SRI LANKA STOCK MARKET BY NON-PARAMETRIC SPECIFICATION TEST gˆ ( z n, z ) ( n ) K h ( z, Zˆ ) K h ( z, Zˆ ) (4) where, K h ( x, y ) h h h x y k( ) / k( u )du,x[,h ) h ( x / h ) x y k( ), x [ h, h] h x y ( x ) / h k( ) / k( u )du,x[ h, ] h And he kernel k () s a bounded symmerc probably densy wh suppor [,] so ha k( u) du, uk( u) du u k( u) du, and one choce s he quarc kernel: n 5 k( u) ( u ) X ( u ) (5) 6 ( u ) u where s he ndcaor funcon, akng value f and zero, oherwse Zˆ Z ( ˆ) and ˆ ˆ / 6 s a - conssen esmaor for h Sz n, where s he sample Z sandard devaon of n gˆ ( z, ) The frs ess s based on a quadrac form beween z and, he produc of wo U[,] denses, n Mˆ ( ) [ gˆ ( z, z ) dz dz (6) ] and he frs es sasc s a properly cenered and scaled verson of M ( ) : / Qˆ ( ) [( n ) hmˆ ( ) A ] V, (7) h / where he non-sochasc cenerng and scale facors b A h ( h ) k ( u) du kb ( u) dudb, (8) [ [ k( u v) k( v)] du] V (9) ˆ Ŝ z and k () k() / b b k( v) dv

9 Aboobacker Jahufer 465 Under correc model specfcaon, (Hong and L 5, Theorem ) has shown ha Qˆ ( ) N(,) n dsrbuon and under model msspecfcaon, n probably { Z, Z } U[,] Q ˆ( ) Whenever are no ndependen or (Hong and L 5, Theorem 3) The quadrac form es Q ˆ( ) hough convenen and que accurae when he rue parameer was known mgh be adversely affeced by any mprecse esmae for ˆ n fne samples To allevae hs problem hey proposed a second es based on he square Hellnger merc, Mˆ ( ) [ gˆ ( z, z ) dz dz () ] s gˆ ( z, ) whch s a quadrac form beween z and h / / The assocaed es sasc Hˆ ( ) [4( n ) hmˆ ( ) A ] V, () A h V where and are as n Eq (8) and Eq (9) Under correc model specfcaon hs es has he same asympoc dsrbuon as Q ˆ( ) and s asympocally equvalen o Q ˆ( ) n he sense ha Q ˆ( ) Hˆ ( ) n probably Under model msspecfcaon we also have H ˆ ( ) { Z, Z } as n whenever are no ndependen or U[,] I can be summarzed he omnbus evaluaon procedures followng Hong and L (5): () esmae he parameers of dscree spo rae models usng maxmum lkelhood esmaon (MLE) mehod o yeld a n { Zˆ Z ( ˆ)}, where kernel on densy esmaor n -conssen esmaor ˆ ; () compue he model generalzed resdual ( ) Z s gven n Eq (3); () compue he boundary- modfed ( z, z ) n Eq (4) for a pre-specfed lag, usng a kernel n gˆ ˆ / 6 Eq (5) and he bandwdh h Sz n, where s he sample sandard devaon of he model Zˆ generalzed resdual n ; (v) compue he es sascs Q ˆ( ) n Eq (7) and Hˆ ( ) n Eq (); (v) compare he value of Q ˆ( ) or H ˆ ( ) wh he upper-aled N (,) crcal value a level C 645 (eg, 5 ) The upper-aled raher han wo sded N (,) crcal values s suable snce negave Q ˆ( ) and Hˆ ( ) occurs only under correc model specfcaon when n s suffcenly large Boh of Q ˆ( ) and H ˆ ( ) { Z, Z } dverge o + when are no ndependen or U[,] under model specfcaon granng he ess asympoc un power Ŝ z C

10 466 CHOOSING THE BEST PERFORMING GARCH MODEL FOR SRI LANKA STOCK MARKET BY NON-PARAMETRIC SPECIFICATION TEST 5 Emprcal Sudy The daa analyzed here s he daly closng prce ndex for CSE n Sr Lanka from January, 7 o March, 3 The parameer esmaon process choce here s MLE The ndces prces are ransformed no her reurns o oban saonary seres The ransformaon s: r * ln( y ) ln( y ), where s he reurn ndex a me Refer able Some of he descrpve sascs for daly reurns are dsplayed n Table Mean reurns of he CSE s 67 Volaly (measured as a sandard devaon) s 6 The reurn of CSE marke s lepokurc n he sense ha kuross exceeds posve hree and he reurn seres also dsplay sgnfcan skewness Accordng o Jarque and Bera (987) sascs normaly s reeced for he reurn seres The resuls from ARCH es can no reec he ARCH effec whch ndcae ha he seres have ARCH effec Overall hese resuls clarfy suppor he reecon of he hypohess ha CSE me seres of daly reurns are me seres wh ndependen daly values Moreover, he sascs usfy use of he GARCH specfcaon n modelng he volaly of Sr Lanka sock marke y Table : Descrpve Sascs of CSE daly reurns Sample Sze Mean Mn Max Sandard Devaon Skewness Kuross Jarque-Bera (JB) Tes (p-value) ARCH Tes () (97) Parameer Esmaon In comparson of he performance of GARCH models he smple mean equaon s used: y for all models Table : MLE of he parameers and her correspondng -sasc N 8 (4568) S 9 (3) G (9) N 59 (438) S 5 (3) G 4 (8) N 6 (4685) 9 (363) 46 (7448) 39 (87) -55 (-4633) -36 (-87) (784) 937 (568) 379 (657) 799 (758) 8 (59) -343 (-6558) 3 (34) -5 (-37) 859 (4575) 83 (556) 3388 (8754) 776 (678) 699 (86) 436 (859) 578 (7359) 385 (678) k (or 558 (63) 7338 (44) 638 (84) 5 (657) ) 3883 (7944) 335 (6365) r 85 (678) 843 (53979)

11 3 S 55 (377) G 59 (43) N 494 (3353) 4 S -9 (-3) G 4 (34) 466 (7556) 34 (477) 6554 (47493) 66 (74) 663 (793) -89 (-9) -74 (-4745) 3697 (98) 46 (9334) 4738 (6645) Aboobacker Jahufer (65) 49 (6) 48 (583) 546 (947) 454 (65) 3397 (88) 5648 (679) 3943 (99) (-475) -46 (-575) 395 (84) 386 (787) [Noe:,, 3 and 4 represen GARCH, EGARCH, TGARCH and APARCH model respecvely and N, S, G ndcae Gaussan, Suden- and Generalzed error dsrbuon respecvely] Table presens he maxmum lkelhood esmae (MLE) of he parameers and her correspondng -sasc The use of GARCH se of models seems o be usfed All coeffcens are sgnfcan a 5% level of sgnfcance excep he coeffcen of n case of Suden- and generalzed error denses Table 3 repors some useful sascs such as Box-Perce sascs for boh resduals and he squared resduals, Akake Informaon Crera (AIC) and Log Lkelhood value 93 (767) 846 (57) 4387 (66) 88 (73469) 877 (65) Table 3: Esmaon Sascs-Model comparson Q () Q () AIC Log-lkelhood Gaussan Suden- GED GARCH EGARCH TGARCH APARCH GARCH EGARCH TGARCH APARCH GARCH EGARCH TGARCH APARCH The Akake Informaon Crera (AIC) and he log-lkelhood values sugges he fac ha TGARCH, EGARCH or APARCH models f he daa well han he radonal GARCH On he bass of AIC and log-lkelhood value he APARCH model ouperforms han TGARCH and EGARCH model EGARCH model gves beer resul han TGARCH model n case of Gaussan and Generalzed error denses Regardng he denses, he Suden- and Generalzed error

12 468 CHOOSING THE BEST PERFORMING GARCH MODEL FOR SRI LANKA STOCK MARKET BY NON-PARAMETRIC SPECIFICATION TEST dsrbuons clearly ouperform he Gaussan In he case of Suden- dsrbuon he AIC value for he model GARCH, EGARCH, TGARCH and APARCH are less han he denses of Gaussan densy The log lkelhood value s srcly ncreasng n case of Suden- denses comparng wh he generalzed error and Gaussan denses All he models seem o do a good ob n descrbng he dynamc of he frs wo momens of he seres as shown by he Box-Perce sascs for he resduals and he squared resduals whch are all non-sgnfcan a 5% level Table 4: Models wh Gaussan dsrbuonal assumpon J GARCH EGARCH TGARCH APARCH Table 5: Models wh suden - dsrbuonal assumpon J GARCH EGARCH TGARCH APARCH Table 6: Models wh generalzed error dsrbuonal assumpon J GARCH EGARCH TGARCH APARCH To denfy he bes performng model n hs secon, o do he specfcaon ess follow he es procedures of Hong and L (5) and compue he relevan Q () sas and pckng up from o 5 In hs paper, has been aken only, 5, and 5 as he value of o calculae he value of Q ˆ( ) from he each class of volaly rae models, ( s menonable ha he resuls of H () ess are que smlar)

13 Table 4 repors he Q ( ) Aboobacker Jahufer 469 es sascs as funcon of lag order =, 5,, 5 for hese Q ( ) models wh Gaussan dsrbuonal assumpons As shown n he able 4 he sascs for he GARCH, EGARCH, TGARCH and APARCH model under Gaussan dsrbuon ranges from 84 o 6645 Compared wh he upper aled N (,) crcal value (eg 33 a he % Q ( ) level and 66 a he 5% level), he large sascs are overwhelmngly sgnfcan, suggesng ha all four models are severely ms-specfed a any reasonable sgnfcance level Q ( ) suden- 6 Conclusons Under Suden- dsrbuonal assumpon he sascs for he followng four models are gven n Table 5 ranges from -5 o 4 whch can pass he orgnal premse on 5% as well as % level I means ha GARCH, EGARCH, TGARCH and APARCH models under he dsrbuonal assumpon are he mos successful models Table 6 repors hese models wh Generalzed Error dsrbuon The Q () sascs for hese models are range from 358 o 9647 Addng Generalzed Error dsrbuon no hese models reduces he Q () sascs bu hese Q () sascs are hgher han suden- wh he upper aled N (,) crcal value he large Q () sascs are overwhelmngly sgnfcan, suggesng ha all four models are no sgnfcance a any reasonable sgnfcance level dsrbuonal assumpon However, compared Ths research paper examned a wde varey of popular GARCH models for CSE ndex reurn, ncludng GARCH, EGARCH, TGARCH and APARCH model wh Gaussan, Suden- and generalzed error dsrbuon The comparson focused on wo dfferen aspecs: he dfference beween symmerc and asymmerc GARCH (e, GARCH versus EGARCH, TGARCH and APARCH) and he dfference among Gaussan, Suden- and Generalzed error denses The resuls show ha noceable mprovemens were made by usng an asymmerc GARCH model n he condonal varance Accordng o dsrbuonal assumpon hese models wh Suden- dsrbuon gve beer resuls The Non Paramerc Specfcaon es also suggess ha he followng model under suden- dsrbuon can pass he orgnal premse on 5% as well as % level I means he GARCH, EGARCH, TGARCH and APARCH models under Suden dsrbuonal assumpon are sgnfcan models for CSE Fnally he sudy suggesed ha hese four models were very suable for he sock marke of Sr Lanka As a resul, hs sudy would be of grea benef o nvesors and polcy makers a home and abroad Acknowledgemens

14 47 CHOOSING THE BEST PERFORMING GARCH MODEL FOR SRI LANKA STOCK MARKET BY NON-PARAMETRIC SPECIFICATION TEST The Auhor would lke o hank an anonymous referees for her valuable commens and suggesons Ths research work was suppored by a research gran No: SEU/EX/RG/8 by Souh Easern Unversy of Sr Lanka References [] A-Sahala, Y (996) Tesng Connuous-Tme Models of he Spo Ineres Rae Revew of Fnancal Sudes 9, [] Balle, R and Bollerslev, T (989) The Message n Daly Exchange Raes: A Condonal- Varance Tale Journal of Busness and Economc Sascs 7, [3] Bara, A (4) Sock Reurn Volaly Paerns n Inda Workng Paper no4, Indan Councl for Research on Inernaonal Economc Relaons, New Delh, Inda [4] Bene, M Lauren, S and Lecour, C () Accounng for Condonal Lepokuross and Closng Days Effecs n FIGARCH Models of Daly Exchange Raes, Appled Fnancal Economcs [5] Black, F (976) Sudes of Sock Marke Volaly Changes Journal of Busness and Economc Sascs 6, 77 8 [6] Bollerslev, T (986) Generalzed auoregressve condonal heeroskedascy Journal of Economercs 3, [7] Bralsford, T and Faff, R (996) An evaluaon of volaly forecasng echnques Journal of Bankng and Fnance, [8] Chapman, D and Pearson, N (), Recen Advances n Esmang Models of he Term- Srucure Fnancal Analyss Journal 57, [9] Debold, F X Gunher, T A and Tay, A S (998) Evaluang Densy Forecass Wh Applcaons o Fnancal Rsk Managemen Inernaonal Economc Revew 39, [] Dng, Z, Granger, CWJ and Engle, RF (993) A Long Memory Propery of Sock Marke Reurns and a New Model Journal of Emprcal Fnance, 83 6 [] Engle, R (98) Auoregressve condonal heeroscedascy wh esmaes of he varance of Uned Kngdom nflaon Economerca 5, [] Fama, E (965) The Behavour of Sock Marke Prces Journal of Busness 38, 34-5 [3] Franses, P Neele, J and Van Dk, D (998) Forecasng volaly wh swchng perssence GARCH models Workng Paper Erasmus Unversy, Roerdam [4] Gallan, AR and Tauchen, G (996) Whch Momens o Mach?, Economerc Theory, [5] Geweke, J (986) Modelng he Perssece of Condonal Varances: A Commen Economerc Revew 5, 57-6 [6] Glosen, L, Jagannahan, R and Runkle, D (993) On he relaon beween expeced reurn on socks Journal of Fnance 48, 779 8

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16 47 CHOOSING THE BEST PERFORMING GARCH MODEL FOR SRI LANKA STOCK MARKET BY NON-PARAMETRIC SPECIFICATION TEST [35] Vlaar, P and Palm, F (993) The message n weekly exchange raes n he European moneary sysem: mean reverson, condonal heeroskedascy and umps Journal of Busness and Economc Sascs, [36] Zakoan, JM (994) Threshold Heeroscedasc Models Journal of Economc Dynamcs and Conrol 8, Receved March 5, 3; acceped November, 3 Aboobacker Jahufer Deparmen of Mahemacal Scences Faculy of Appled Scences Souh Easern Unversy of Sr Lanka Sr Lanka ahufer@yahoocom, ahufer@seuaclk