A CASE OF US AND INDIA ABSTRACT

Transcription

1 A CASE OF US AND INDIA K. Kiran Kumar * and Ciranji Mukopadyay ABSTRACT Tis paper empirically invesigaes e sor run dynamic linkages beween NSE Nify in India and NASDAQ Composie in US during e recen period using inra-daily daa, wic deermine e dayime and overnig reurns. Te sudy carries ou a compreensive analysis from correlaion o Granger causaliy and en o applicaion of GARCH models o examine e co movemen and volailiy ransmission beween US and Indian sock markes. Specifically, e sudy employs a wo sage GARCH model and an ARMA-GARCH model o capure e mecanism by wic NASDAQ Composie dayime reurns and volailiy ave an impac on no only e mean bu also on e condiional volailiy of Nify overnig reurns. I is found a e simple ARMA- GARCH model performs beer an e more complex Two-sage GARCH model, described in e lieraure. Te main findings of is sudy are as follows: Firs, e granger causaliy resuls indicae unidirecional granger causaliy running from e US sock markes (bo NASDAQ Composie and S & P 500 indices) o e Indian sock marke, NSE Nify index. Second, e previous dayime reurns of bo NASDAQ Composie and NSE Nify ave significan impac on e NSE Nify overnig reurns. However, e volailiy spillover effecs are significan only from NASDAQ Composie implying a e condiional volailiy of Nify overnig reurns is impored from US. We found a on an average e effec of NASDAQ dayime reurn volailiy socks on Nify overnig reurn volailiy is 9.5% and a of Nify dayime reurn is a mere 0.5%. In ou of sample forecass, owever, we found a by including e informaion revealed by NASDAQ day rading provides only beer forecass of e level of Nify overnig reurns bu no is volailiy. * Researc Suden, Deparmen of Managemen Sudies, IISc, Bangalore. [email protected] Ass. Prof., Deparmen of Managemen Sudies, IISc, Bangalore. Te auors acknowledge financial suppor from e NSE Researc Iniiaive. Commens and suggesions received from e anonymous referees are graefully acknowledged. Te views expressed and e approac suggesed are of e auors and no necessarily of NSE.

2 . INTRODUCTION I is well known a e movemens in e sock prices are influenced by e flow of marke informaion. One possible source of is informaion is movemens in oer sock markes in e world. Tere are several reasons wy e reurns of wo differen equiy markes mig be relaed. Te wo markes belonging o wo differen economies mig be relaed roug rade and invesmen, so a any news abou economic fundamenals of one counry permeaes o anoer and us affec eac oer s equiy markes. Given e degree of openness o rade and invesmen, i is a well-acceped fac a e naional markes are iner-relaed and increasingly global (vide Jon e. al. (995)). Wen making decisions, raders incorporae informaion peraining o price movemens and volailiy in e asse ey are rading including informaion abou relaed asses. Te movemen of markes in rym and corus could nullify muc of e gain ou of diversificaion across borders, besides being vulnerable o e caprices of global capial. Tus, undersanding ow markes influence one anoer is imporan in pricing, edging and regulaory policy. In recen years, globalizaion of capial flows as led o e growing relevance of emerging capial markes and India is one of e counries wi an expanding sock marke a is increasingly aracing funds from e FIIs. In paricular, deregulaion and marke liberalizaion measures, rapid developmens in communicaion ecnology and compuerized rading sysems, and increasing aciviies of mulinaional corporaions ave acceleraed e grow of Indian capial marke, wic is now slowly moving owards global financial inegraion. From 999 onwards, Indian firms are raising capial from e US marke by lising emselves in US excanges. A presen Indian companies ave issued ADRs and are cross-lised in US excanges and many more companies are planning o cross lis in e near fuure. Moreover as per e Economic Survey , 3% of Indian expors go o US and 0% of oal Indian impors are from US making US e major rading parner of India. Tus i will be ineresing o examine e co-movemen of Indian sock markes wi US markes and e mecanism roug wic e price canges and volailiy are ransmied a e wake of lifing resricions on capial flows and foreign ownersip. Tree feaures of ese markes moivae our ineres in examinaion of e sor run dynamics of sock reurns and volailiy beween NASDAQ Composie and NSE Nify. Firs, e excanges do no ave any overlapping rading ours and ence e case of volailiy ransmission can be clearly examined. Second, e economic dailies as well as official publicaions ave been full of sories of a newfound alliance beween e NSE and e NASDAQ. Te Economic Times of November 4, 000 as a sory wi e eadline Uncerainy in US polls, seep NASDAQ fall riggers cras, and says, sor-covering by operaors and a rebound in e NASDAQ indices reversed e rend on e domesic markes on Tuesday. Similar repor as been ecoed in official documens as well. For example, RBIs Annual Repor, as noed a, Marke senimen According o SEBI, e ne invesmen of FIIs in e calendar year 998 is -Rs.479 crores, in 999 Rs 6696 crores, in 000 i is Rs. 65 crores and in 00 Rs crores.

3 decline in e NASDAQ index during e second alf of e mon (November 000).also affeced e marke senimen adversely (p04). In a similar vein, Te Economic Survey, as noed,. Tis erosion in sare prices refleced e influence of sare price movemens abroad, specially a e ec-eavy NASDAQ (p 9). Troug ese news repors, marke regulaors, raders, and e general invesing public in India ave become sensiized o marke movemens in e NASDAQ Composie and is impac on NSE Nify. Finally, a quick examinaion of sock marke movemens of ese wo markes, during e sudy period under consideraion, suggess a ere exiss a subsanial degree of inerdependence beween NASDAQ Composie & NSE Nify indices. (See figure a & b) Te objecive of is paper is o empirically examine e sor run iner linkages beween e US and Indian sock markes. In invesigaing ese issues, we ake NSE Nify index as e core baromeer of e Indian sock marke as i capures e major cunk of Indian sock marke. On e oer and, NASDAQ Composie Index as been aken as a represenaive of US marke as i is a paceseer of e global sock marke aving a bearing on naional markes worldwide including India, is mecca saus among ecnology socks, volume lead, no. of lised companies and is sar aracion as a unique source of capial even in excange of a small equiy sake. Te exercise as been simulaneously carried ou for e compeing represenaive of US sock marke, namely S & P 500 index. Te sudy carries ou a compreensive analysis from correlaion o Granger causaliy and en o applicaion of GARCH models o examine e co movemen and volailiy ransmission beween US and Indian sock markes. We found unidirecional granger causaliy running from NASDAQ Composie o NSE Nify. Te resuls are broadly e same even if we use S & P 500 insead of NASDAQ Composie o represen e US sock marke. Te res of e repor is organized as follows: Secion presens a snapso of e lieraure on sock marke inegraion, Secion 3 provides a seleced accoun of e srucural developmen in e 990s, aving a bearing on e inegraion process of e Indian sock marke. Secion 4 deals wi Daa and ypoeses, Secion 5 delve ino e meodological issues of modeling e co movemen of markes. Secion 6 does a model selecion and secion 7 does evaluaion of seleced model bo in-sample validiy and ou of sample forecas performance. Finally, Secion 8 summarizes e findings.. LITERATURE REVIEW Te naure of e inernaional ransmission of sock reurns and volailiy as been focus of exensive sudies. Earlier sudies (e.g., Ripley 973, Lessard 976, and Hilliard 979, among many oers) generally find low correlaions beween naional sock markes, supporing e benefis of inernaional diversificaion. Te links beween naional markes ave been of eigened ineres in e wake of e Ocober 987 inernaional marke cras a saw large, correlaed price movemens across mos sock markes: Eun & Sim (989), Von Fursenberg and Jeon (989); King and Wadwani (990); Scwer (990); King e.al. (994); Longin & Solnik (995), o name a few. Tese 3

4 Analysis, Simple Regression, ARCH models ec. and repor several empirical feaures:: (i) e correlaions across e sock markes are ime-varying (ii) wen volailiy is ig, e price canges in major markes end o become igly correlaed (iii) correlaions in volailiy and prices appear o be causal from e US marke wic is e mos influenial marke and none of e oer marke explains US sock marke movemens. Te lieraure concenraed mosly on well-developed equiy markes in e U.S., Japan, and Europe, and do no pay muc aenion o oer sock markes. To capure e dynamic iner-linkages beween e markes, wic ave non-overlapping rading ours, e lieraure largely applied a Two Sage GARCH model wi inra-daily daa a define overnig and dayime reurns. Becker e al (990) employ opening and closing daa for Tokyo Sock Excange (Nikkei) and New York Sock Excange (S&P 500), from 985 o 988, o sudy e syncronizaion of sock price movemens. Teir simple regression analysis indicae a e US dayime performance grealy influences overnig reurns in Japan e following day and e cange in e TSE only as a marginal impac on e NYSE overnig reurns on e same day. Ceung and Ng (99) invesigae e dynamic properies of sock reurns in Tokyo and New York, using daily close-o-close marke indices from January 985 o December 989. GARCH ype models are used o describe e iner-emporal beavior of ese sock indices. Tey included foreign marke index s lagged reurn in e mean equaion and lagged squared reurns in e variance equaion of e ome marke model o capure mean and volailiy spillovers. Tey found a in e pre-cras period Tokyo sock price movemens can be parially explained by ose in New York, bu e former as very lile impac on e laer. In conras, owever, e spillover marke effecs in e mean and variance exis in bo direcions afer e cras. Hamao e al (990), Kee-Hong Bae and Karolyi(994) and Lin e al (994) examined e sor-run inerdependence of prices and price volailiy across ree major inernaional sock markes namely, e Tokyo, London and New York wi dayime and overnig reurns daa. Teir analysis uilizes a Two-sage GARCH model, were in e firs sage ey exrac e unexpeced socks from e dayime reurns of one marke and use i as a proxy for volailiy surprise wile modeling e oer marke s overnig reurns in e second sage GARCH model. Tey found a cross-marke inerdependence in reurns and volailiies is generally bi-direcional beween e New York and Tokyo markes paricularly afer 987 cras. So far very few sudies ave examined e co-movemen of Indian sock marke wi foreign markes. Sarma & Kennedy (977) examined e price beavior of Indian marke wi US and London markes. Te objecive of eir sudy was o es e random-walk ypoesis by runs analysis and specral densiies, for e Bombay Variable Dividend Indusrial Sare Index (BVDISI), e New York Sandard and Poor s 45 Common Sock Index (S &P 45), and e London Financial Times-Acuaries 500 Sock Index (London F.T.-A). Te es period covered 3 monly observaions for e -year period Tey found a e beavior of e BVDISI is saisically indisinguisable from a of London F.T.-A. and S&P 45. In e runs analysis of 4

5 and expeced disribuion of runs leng urns ou o be very similar, wi probabiliy equal o 0.5 for rise or fall. Furer, e specral densiies, esimaed for e firs difference series (raw and log ransformed) of eac index, confirmed e randomness of e series, wi no evidence of sysemaic cyclical componen or periodiciy was presen. Based on ese ess, ey concluded a socks on e Bombay Sock Excange obey a random walk and are equivalen in is sense o e beavior of sock prices in e markes of advanced indusrialized counries, like UK and US. Rao & Naik (990) examined e iner-relaedness of USA, Japanese and Indian sock markes. Teir sudy uses monly sock indices of e Bombay, New York and Tokyo excanges, for e period Jan 97 o December 988. Teir approac is o use Cross-Specral analysis for e ree pair-wise ses of daa and e gains esimaes o deermine wic marke sould be considered as independen in a bivariae relaionsip. For e USA and Indian series se, e gains esimaes sugges a USA series is independen. For e Japan and India series se, e gain esimaes sugges a Japanese marke is independen. For e USA and Japan series se, i appears a Japan sould be considered as independen, wic may seem o go agains e noion a Japan is a follower in inernaional sock markes. On e wole, ey concluded a e relaionsip of Indian marke wi inernaional markes is poor reflecing e insiuional fac a e Indian economy as been caracerized by eavy conrols rougou e enire sevenies wi liberalizaion measures iniiaed only in e lae eigies. To dae, no in-dep analysis of inerdependence srucure of Indian markes wi oer naional markes is available in e lieraure. Te purpose of is sudy is o provide suc an analysis wi a special empasis on e inernaional ransmission mecanism of sock marke movemens beween e US and Indian sock markes. 3. INDIAN STOCK MARKET AND GLOBALIZATION Te Indian sock marke oug one of e oldes in Asia being in operaion since 875, remained largely ouside e global inegraion process unil e lae 980s. A number of developing counries in concer wi e Inernaional Finance Corporaion and e World Bank ook seps in e 980s o esablis and revialize eir sock markes as an effecive way of mobilizing and allocaion of finance. In line wi e global rend, reform of e Indian sock marke began wi e esablismen of Securiies and Excange Board of India in 988. However e reform process gained momenum only in e aferma of e exernal paymens crisis of 99 followed by e securiies scam of 99. Among e significan measures of inegraion, porfolio invesmen by FIIs allowed since Sepember 99, as been e urning poin for e Indian sock marke. As of now FIIs are allowed o inves in all caegories of securiies raded in e primary and secondary segmens and also in e derivaives segmen. Te ceiling on aggregae equiy of FIIS including NRIs (non-residen Indians) and OCBs (overseas corporae bodies) in a company engaged in aciviies oer an agriculure and planaion as been enanced in pases from 4 percen o 49 per cen in February 00. 5

6 sea cange in erms of ecnology and marke pracices. Following e commissioning of e NSE in June 994, Naional Securiies Clearing Corporaion in April 996 and Naional Securiies Deposiory in November 996, a screen-based, anonymous, order-driven online demaerialized rading as been e order of e day coupled wi improved risk managemen pracices for clearing and selemen. Finally, e process of inegraion received a major impeus wen e Indian corporae was allowed o go global wi GDR / ADR issues. Saring wi e maiden issue of Infosys in Marc 999, ADR issues as emerged as e sar aracion due o is iger global visibiliy. Till dae, around Indian companies ave aken advanage of e US marke and 76 companies ave capured e global marke. In Marc 00, wo-way fungibiliy for Indian GDR / ADRs was inroduced wereby convered local sares could be reconvered ino GDR/ADR subjec o secoral caps. Tus, e Indian sock marke, wic was in isolaion unil recenly, urns ou o ave been sensiive o developmens in e res of e world by e end of e 990s. Pursui of a novel se of policy iniiaives wi FII porfolio invesmen and Indian ADR issues a is cener-sage seems o ave conribued significanly o e emerging sock marke inegraion. Besides, India s cauious experimen wi openness appears o ave faciliaed e seady pursui of a policy milieu for sock marke inegraion. In is repor, we make a sympomaic analysis of e relaion beween domesic and foreign equiy indices. In e nex secion, we examine e relaionsip beween e US and Indian sock indices and repor some sylized facs. 3. Price Movemen: Sylized Facs Te media as well as financial press ave been replee wi insances and counerfacuals of a srong (or weak) and posiive (or negaive) correlaion beween e wo crucial baromeers of sock markes in e Indian psyce, namely e S & P CNX Nify and NASDAQ Composie (encefor referred o as Nify and NASDAQ respecively). Do suc claims and couner-claims arise from e causal issues and iner-linkages beween ese markes To is end, as a firs insance e plo of e daily closing quoes of e Nify and NASDAQ (vide Fig A) over a five year-period (996 o 00) reveal a disinc posiive rend. Te picure is comparable if e S & P 500 is subsiued for e NASDAQ Composie (vide Fig B). As is obvious from e plo, e Nify, wic was insensiive o e global sock rend, as sared o mirror and magnify e wiss and urns of e NASDAQ (S&P500) in e recen years. Wile a priori e sape of e grap could be a moivaing reason in pursuing e relaionsip beween Nify and NASDAQ, i is also clear from e grap a on a number of occasions, e associaion is jus e reverse. So, we ave calculaed e year wise correlaion coefficien beween Nify and NASDAQ over a five-year period. I is ineresing o noe a e correlaion coefficien canged from negaive (-0.54) in o posiive (0.008) in and (0.5) in and en i as become significanly posiive (0.789) in and (0.653) in 6

7 indicaes a from e period around mid of 999, NSE Nify is moving in andem wi NASDAQ Composie / S & P 500. Tus e recen period, s July 999 o 30 June 00, is e period a becomes e focus of our invesigaion. 3.: Granger Causaliy:: Te ig correlaion beween e NSE Nify and NASDAQ is in no way indicaive of any causaion. So o examine e causaliy beween NASDAQ Composie and NSE Nify, we use e es suggesed by Granger (969). Te sandard Granger causaliy es examines weer pas canges in one saionary variable X elp o predic curren canges in anoer saionary variable Y, beyond e explanaion provided by pas canges in Y iself. If no, en X does no Granger cause Y. Te es of X no Granger-causing Y is simply a es of a linear ypoesis H 0: = = = q=0 in a linear model Y p q Y j j j X j j j u () were p and q are e opimal lag lengs deermined by AIC model selecion crieria. Te null ypoesis of no- Granger-causaliy can be esed using e sandard linear F-es under model (). To examine e Granger causaliy beween daily reurns of NASDAQ (S&P500) and Nify, a maximum leng of eig lags are seleced and reduced according o e AIC and SBC model selecion crierion. Table sows a only for NIFTY, e F-saisic is significan indicaing a e pas values of NASDAQ / S & P 500 elp o predic curren canges in NIFTY. Tis suggess a unidirecional granger causaliy running from NASDAQ / S & P 500 reurns o NIFTY reurns bu no e oer way round. Te effec of NASDAQ is a lile more pronounced an S&P500 on Nify in erms of e value of e F-saisics and e resuling p-values. Te fac a NSE Nify can influence e NASDAQ Composie is ardly surprising given e relaive sizes of e equiy markes of e wo economies. As is unidirecional granger causaliy from NASDAQ (S &P 500) o Nify is very apparen from is preliminary analysis, now we seek o examine and quanify e impac of NASDAQ (S & P 500) flucuaions on NSE Nify. 4. DATA AND HYPOTHESES 4.. TIME ZONE CONSIDERATIONS:: In order o undersand e inernaional ransmission mecanism beween e wo markes under consideraion, firs i is imporan o recognize a e NSE and NASDAQ markes do no ave any overlapping rading ours.tere is a ime lag of welve-and-alf ours beween US Easern Sandard Time and Indian Sandard Time. Te rading ours of bo e markes are sown in Fig.. As sown in Fig., in Indian Sandard Time (IST), NSE opens a 0.00 AM and closes a 3.30 PM., Nify Daily Reurns (NIFTY) = Log (Nify close on day / Nify close on day -)*00 NASDAQ Daily Reurns (NASDAQ) = Log (NASDAQ close on day / NASDAQ close on day -)*00 S&P 500 Daily Reurns (S&P 500) = = Log (S&P 500 close on day /S&P 500 close on day -)*00 7

8 common ime inerval in wic bo markes remain open. Following Hamao e al (990), Lin e al (994) and Kee-Hong Bae & Karolyi (994) o sudy e syncronizaion of sock price movemens, a daily (close-o-close) reurn is divided ino a dayime (open-o-close) and an overnig (close (-)-o-open) reurn for bo NSE Nify and NASDAQ Composie indices. Since ere is no overlap beween e rading ours of e wo markes, i is possible o sudy e influence of dayime reurn in one marke on e overnig reurn of e oer. Inuiively, raders in India use any relevan informaion revealed overnig in NASDAQ in pricing eir socks as soon as e opening bell rings. So, e decomposiion of daily price canges (reurns) ino dayime [Close () o-open ()] and overnig [Open ()-o-close (-)] reurns is crucial in modeling and undersanding ow informaion is ransmied from one marke o e oer. 4.. DATA SOURCES In mos major sock markes, ere are problems in calculaing opening prices for ese marke indices due o delayed opening of individual socks. Soll& Waley (990) repor a afer e marke opens for e firs ransacion o occur on an average i akes 5 minues for large socks and 67 minues for small socks in NYSE for e firs ransacion o occur afer e marke opens. Wen delays occur, e prior day closing prices are used for e unavailable curren price in calculaing e ig-frequency index of sock marke. Tis creaes arificial serial correlaions in close-o-open and open-o-close reurns, wic biases inra day reurn and volailiy esimaes. In order o minimize e effecs of ese sale prices, e lieraure suggess one o use e index quoes 5 minues afer e firs open quoe, so a e arificial correlaion beween e inra-day reurns are minimized. For NSE Nify, e firs open quoe of e index is available a around 9.55 AM. A is firs open quoe, since all e 50 consiuen scrips of Nify ave no been raded, aking is value as e open quoe would be inappropriae. Bu usually by e official opening ime of 0.00 AM, around 0,000 rades ake place on a ypical day in NSE. So we ake e open quoe of Nify in e analysis as is value a clock. Te clock daa of NSE Nify is provided by Naional Sock Excange Researc Iniiaive. Daily official open(9.30am, EST) and close (4.00PM, EST) quoes of NASDAQ Composie Index ave been downloaded from and a of S & P 500 index are downloaded from For S & P 500 index on mos of e days e open quoe of mos of is exacly same as a of previous day s close quoe aving serious sale quoe problems. For NASDAQ Composie index e close quoe on day - is differen from open quoe on day, e sale price effec will be minimal as compared o S&P 500 index. We unable o ge e inra-day daa of S & P 500, so as o minimize e sale quoe problem. Hence we unable o use S & P 500 index in our furer inra day 8

9 similar o a of NASDAQ. Specifically, in is sudy, we calculae e reurns as follows 3 : Nify Overnig Reurns (NIFON ) = Log (Nify open on day / Nify close on day - )*00 Nify Dayime Reurns (NIFD ) = Log (Nify close on day / Nify open on day )*00 NASDAQ Overnig Reurns (NASON )=Log (NASDAQ open on day / NASDAQ close on day-)*00 NASDAQ Dayime Reurns (NASD )= Log (NASDAQ close on day / NASDAQ open on day )* Hypoeses In our analysis, we gauge e marginal effec of e NASDAQ and Nify dayime reurns and volailiies on e Nify overnig reurns and volailiy. To is end, we formulae e following ypoesis ess as follows. H 0: NASDAQ dayime reurns do no influence Nify overnig reurns H 0: NASDAQ dayime volailiy does no influence Nify overnig volailiy. H 0: Nify dayime reurn does no influence Nify overnig reurn H 0: Nify dayime volailiy does no influence Nify overnig volailiy. Tese ypoeses ess will be examined by looking a e marginal significance of e respecive coefficiens by Wald s es in our empirical model in e nex secion. 5. METHODOLOGY :: GARCH MODELING 5.. Prelim inary Analysis Table presens a wide range of descripive saisics for e sock index reurns of e NASDAQ Composie and NSE Nify. Te sample momens indicae a empirical disribuions of reurns are all skewed and igly lepokuric, wen compared wi e normal disribuions. Tis is reinforced by e Jarque-Bera ess for normaliy, wic are igly significan. From e raw reurn series plos in Fig 3 i appears a e volailiy of reurns varies over ime. All e reurn series display e volailiy-clusering penomenon, large (small) socks of eier sign end o follow large (small) socks. To furer analyze e sock reurns beavior, e Ljung-Box saisic for 0 & 0 lags for reurns and squared reurns are also repored in Table. Te presence of significan auocorrelaions, excep for NASD reurn series, suggess a markes are no efficien as e pas reurns can be used o predic e fuure reurns. Te presence of significan auocorrelaions in e 3 Preliminary analysis as sown a e ypoesis of a uni roo is srongly rejeced for e logarimic firs difference of e price index. Terefore, all sock reurn series follow a saionary process 9

10 auocorrelaion among squared reurns and excess kurosis are compaible wi e volailiy clusering penomenon a as been documened for mos developed sock markes, e.g., Bollerslev, Cou and Kroner (99). Tese feaures of e daa, lead us o consider GARCH ype models a can accommodae e ime varying and persisen beavior of volailiy of reurns. We sar modeling wi a Two-sage GARCH model as suggesed in e lieraure for nonoverlapping markes. Also we approac e problem wi a simple ARMA-GARCH model were e squared reurns will proxy for volailiy. Tis simple model urns ou o be as good as e more complex Two-sage GARCH model. 5.. Spillover - effecs wi Two-Sage GARCH model:: Hamao e al (990), Kee-Hong Bae & Karolyi (994) and Lin, Engle & Io (994) use a Two-sage GARCH model for esimaing e spillover effecs beween New York, London & Tokyo markes. In e firs sage ey esimae an appropriae MA-GARCH model for foreign marke dayime reurns. In e second sage, ey esimae an appropriae MA-GARCH model for domesic overnig reurns, were ey include e residuals or residual squares obained in e firs sage GARCH model as a regressor, wic capures e poenial volailiy spillover effec from e previously open foreign dayime reurns ino e domesic overnig reurns. Teir main finding is a Japanese marke is mos sensiive o volailiy spillover effecs from New York marke, wile e New York marke is a mos moderaely sensiive o volailiy spillovers from Japan marke. We esimae is Two-sage GARCH model (Model ) o see e spillover effecs from NASDAQ dayime reurns o NSE Nify overnig reurns. We begin by specifying an appropriae ARMA-GARCH-in-Mean model, for bo dayime reurns of NSE Nify and NASDAQ Composie, inroduced by Engle, Lilien and Robins (987) as follows:. R D, p q,0 R, i D, i, j j, mdum i j,..() ~ N(0, ), r s j,,0,, i j DUM, i i ; j v R NIFD D, NASD Te dummy variable DUM accouns for muliple-day reurns associaed wi weekends and olidays in eier marke. Te coefficien links e condiional marke volailiy o expeced reurns and is significance can be used o es for ime-varying marke risk premia. We refer o is model as e firs-sage GARCH, as e esimaed residual squares from () will proxy for e news socks a spillover from dayime reurns of NSE Nify and NASDAQ Composie o e volailiy of e nex day NSE Nify Overnig reurns. In e second sage we fi an appropriae ARMA-GARCH-in-Mean model for NSE Nify Overnig reurns. We allow for mean spillover effecs by including previous dayime reurns of NASDAQ and Nify in e mean equaion and include residual squares obained from () for NIFD 0

11 Overnig reurns, our model is given by: NIFON u v NIFON i, j j, mdum NIFD NASD,,0, i i j ~ N(0,, k l,,0,,, i i j j DUM NASDRES v NIFDRES i j (3) were NASDRES - is e mos recen residual esimaed from e firs-sage model for e NASDAQ Composie dayime reurn and NIFDRES - is e same measure obained for e previous NSE Nify dayime reurn. A saisically significan value for indicaes a e condiional mean NSE Nify Overnig reurns is influenced by previous dayime reurns of NSE Nify (own-mean spillovers). On e oer and, a saisically significan value suggess a pas dayime reurns of NASDAQ Composie affec e condiional mean of NSE Nify Overnig reurns (cross-mean spillover). Saisically significan values for and respecively indicae e influence of cross and own volailiy spillovers from previous dayime reurns of NASDAQ Composie and NSE Nify o e NSE Nify Overnig reurns Firs Sage Resuls:: Te ARMA (,)-GARCH (,) wi normal disribuion as condiional error disribuion fis well for bo NSE Nify dayime reurns and NASDAQ Composie dayime reurns on e basis of AIC crieria. All models are esimaed using e numerical maximum likeliood procedures of Bernd e al. (974) in RATS 5.0. Table 3 repors e final esimaion resuls for e firs sage model afer dropping all e insignifican erms in e general model considered in () and en refiing is reduced model. Panel A repors e coefficien esimaes and Panel B presens a number of residual diagnosics. Te consan in e mean equaion of bo dayime reurns is insignifican and ence dropped from e model. Te GARCH-in-Mean erm is insignifican for bo dayime reurns and ence ere is no evidence of ime varying risk premia. Te dummy variable for oliday and weekend reurns is significan for NASDAQ Composie dayime reurns only. Te esimaes of GARCH parameers and are significan and e sum of ese wo coefficiens, measuring e persisence of volailiy, is close o uniy. Te pormaneau (Box-Ljung) saisics evaluae e serial correlaions in e raw and squared sandardized residuals of e model up o lags 0 and 0 and find a mos of e condiional dependence in e reurns is also modeled reasonably well. Te excess kurosis is no a problem and ere is some residual negaive skewness Spillover effecs o NSE Nify overnig reurns:: We nex esimae e second sage GARCH model (3) a allow bo NSE Nify and NASDAQ Composie dayime reurns and socks o influence e condiional mean and volailiy of NSE Nify overnig reurns. Te ARMA (,) GARCH (,) model urns ou o be appropriae in describing )

12 ence we consrained i o be non-negaive, yielding an esimae of zero. 4 Te oliday dummy is insignifican in bo mean and variance equaions and is e GARCH-in-Mean coefficien,. Te final model for e NSE Nify overnig reurns are summarized in Panel A afer dropping e insignifican erms in e general model (3) and en refiing e reduced model. Te objecive diagnosic ess of is final model are presened in Panel B of Table 4. Te resuls for e condiional mean equaions sow saisically significan posiive mean spillover effec from e previous NASDAQ Composie dayime reurns; a ig reurn in e NASDAQ marke is followed by a ig reurn in e NSE Nify Overnig reurns. We find clear evidence a e mos recen dayime reurns of NASDAQ Composie ave posiive influences on e opening price in e NSE Nify. Te parameer esimaes for e condiional variance,, and, are igly significan, indicaing a e condiional variance process of NIFON is indeed ime varying. Te sabiliy condiion for e volailiy process is saisfied because e sum of e esimaed GARCH parameers is less an uniy, suggesing a e condiional variances follow a saionary process. Te cross volailiy spillover effec from NASDAQ Composie dayime reurns is 0.09 and igly significan wereas e own volailiy spillover effec from NSE Nify dayime reurns is 3.848e-04 and insignifican, indicaing a condiional volailiy in NSE Nify overnig reurns is impored from e U. S. Te model diagnosic graps namely e Residual Plo, Correlogram of residuals and residual squares are displayed in Fig 4. o Fig 4.3. Tese diagnosics sow a e model s residuals are reasonably well beaved. Te pormaneau (Box-Ljung) saisics in Panel B of Table 4 evaluae e serial correlaions in e raw and squared sandardized residuals of e model up o lags 0 and 0 and find a mos of e condiional dependence in e reurn as also been modeled reasonably well. Finally, we repor e sign and size bias es saisics indicaing no measurable degree of asymmery in e residuals. On e wole e Two Sage GARCH model seems o capure well e Nify overnig reurn linkages wi NASDAQ dayime reurns fairly well Spillover - effecs wi ARMA GARCH model:: Aloug e Two Sage GARCH approac is very inuiive in capuring e effecs of volailiy spillover, i enails e generaed regressors problem. So one simple alernaive is o go for ARMA- GARCH model were e squared reurns, as a proxy for volailiy, of foreign marke are appended in e condiional variance equaion of domesic marke. In is secion, we model e NIFON reurns by allowing for possible auocorrelaion from e preceding overnig reurns, possible cross auocorrelaion / influence from previous dayime reurns of bo NASDAQ and Nify, and for Monday or pos oliday effecs roug a dummy variable, DUM. In general is model for NIFON can be wrien as 4 If we unresric e consan ou of sample variance series is negaive oug i is posiive for observed daa

13 NIFON NIFON i i u j j DUM NIFD NASD 0 i j u (4) In (4) e NASDAQ informaion is effeced roug e parameer and a of NIFTY roug e parameer. A sock (news) revealed afer e close of NASDAQ bu before e opening of NIFTY marke is denoed by u. As i as been noiced in secion 4.3 a e volailiy in e NIFON series is ime varying, we exend e above specificaion of NIFON in (4) by modeling u as a GARCH process insead of wie noise. To capure e volailiy ransmission effecs from e dayime reurns of bo Nify and NASDAQ, following Ceung and Ng (99), we include eir squared reurns as proxy for volailiy in e GARCH specificaion of condiional variance of u. We also include a dummy variable for Monday or pos oliday effecs, in e GARCH specificaion yielding, u ~ N(0, )..(5) DUM p q iu i j j NIFD NASD ` i j Te Maximum likeliood esimaion resuls of (4) & (5), wi e same se of daa as e Two-sage GARCH model, are repored in Table 5 along wi diagnosic ess. Hencefor is model is referred o as Model. Te appropriae ARMA-GARCH order again urns ou o be ARMA (,) GARCH (,). Since, MLE of e consan in GARCH equaion is negaive and ence we consrained i o be non-negaive, yielding an esimae of zero. 5 Te dummy variable is insignifican in bo mean and variance equaions implying a no sysemaic effec of olidays in eier mean reurns or volailiy. Te resuls for e condiional mean equaions sow saisically significan posiive mean spillover effec from e previous NASDAQ Composie dayime reurns; a ig dayime reurn in e NASDAQ marke is followed by a ig overnig reurn in e NSE Nify, as was also revealed by e Two-sage approac. Te parameer esimaes for e condiional variance, and are igly significan, indicaing a e condiional variance process of NIFON is indeed ime varying. Te sabiliy condiion for e volailiy process is saisfied because e sum of e esimaed GARCH parameers is less an uniy, suggesing a e condiional variances induce a saionary process. Te cross volailiy spillover effec from NASDAQ Composie dayime reurns is 0.03 and igly significan wereas e own volailiy spillover effec from NSE Nify dayime reurns is only e-04, wic is no saisically significan eier, indicaing a condiional volailiy in NSE Nify overnig reurns is impored from e U. S. Tis is again in une wi e findings of e earlier Two-sage approac. Te model diagnosic graps namely e Residual Plo, Correlogram of residuals and residual squares are displayed in Fig 5. o Fig 5.3. Tese diagnosics sow a e model s residuals are reasonably well beaved. Te pormaneau (Box-Ljung) saisics in Panel B of Table 5 evaluae e serial correlaions in e raw and squared sandardized residuals of e model up 5 If we unresric e consan, ou of sample variance series is negaive oug i is posiive for observed daa 3

14 modeled reasonably well. Finally, as before e sign and size bias es saisics also do no indicae any measurable degree of asymmery in e residuals. On e wole e simple ARMA-GARCH model also seems o capure e Nify overnig reurn linkages wi NASDAQ dayime reurns fairly well. 6. MODEL COMPARISON To compare compeing models of inernaional ransmission of sock reurns and volailiy, we employ AIC / SBC model selecion crieria, wic gives a comparaive indicaion of e goodnessof-fi of compeing models. Table 6 compares ree models: Two-sage GARCH, simple ARMA- GARCH model and Domesic model. Te firs wo models ave already been described in secion 5. Ignoring e effec of NASDAQ informaion alogeer bo in mean and variance equaions, e domesic model is specified as follows: NIFON p q d,0 NIFON d, i d, j j DUM NIFD d, m d d d, i j ~ N(0, d, ) r s,,0,,,, d d d i i d j d j d vdum d NIFD i j (6) Te domesic model (Model 3) been fied wi an appropriae ARMA-GARCH model, were e spillover effecs ave been included only from Nify dayime reurns. As e volailiy spillovers from NIFD - o NIFON are insignifican, measured eier NIFD or by NIFDRES, e final esimaed reduced model would be e same for bo Two-sage GARCH model and simple ARMA-GARCH model. Te model comparison wi e domesic model examines weer e inclusion of informaion revealed by NASDAQ dayime reurn provides beer forecas of NIFON reurn an e domesic model. Te comparison is based on e same daa se bu differen model specificaions. Table 6 reveals some ineresing resuls for e models performance. In erms of e AIC / SBC crierion and Log Likeliood value, e simple ARMA- GARCH model (Model ) is beer an e oer wo models for NIFTY overnig reurns. 7. MODEL EVALUATION & FORECASTING In is secion, we evaluae weaer e esimaed ARMA-GARCH model is an adequae descripion of e NIFON volailiy process. Esablising e effeciveness of a volailiy forecas is no sraigforward as volailiy process iself is inerenly unobservable. We circumven is problem by using a proxy, squared reurns for acual realized volailiy. To see e in-sample performance of esimaed ARMA-GARCH model, we simply ceck e abiliy of prediced volailiy from e esimaed model (denoed by ) o forecas e acual volailiy, e proxy of squared reurns, r. Specifically is amouns o regressing volailiy proxy on a consan and prediced volailiy (Engle & Paon 000) 4

15 A good forecas sould ave e properies: a =0, b= and a ig R. Eqn 7 is esimaed using e usual OLS procedure wi Wie s eeroscedasiciy consisen sandard errors and resuls are repored in Table 7. We see a, e prediced volailiy saisfies e wo desirable properies viz. e esimaed values of a and b are insignificanly differen from 0 and respecively. However, e R of e regression is around 0%, seems o be quie low. Te reason for is seemingly poor R is e coice of wa is considered as e rue volailiy, wic can be observed direcly. Finally, in order o examine e relaive imporance of e Nify dayime and NASDAQ dayime reurn volailiies on e Nify overnig reurn volailiy, e following variance raios, as suggesed by Angela Ng (000), are compued from e esimaed ARMA-GARCH model: VR NASD NASD [0,]; VR NIFD NIFD [0,] Te raios NASD VR and NIFD VR measure e proporions of condiional variance of NIFON accouned for by e NASDAQ and Nify dayime reurn volailiies respecively. Fig 6 presens ese variance raios along wi eir mean values. I is very clear a e relaive influence of e NASD and NIFD volailiies sifs over ime. Nify overnig reurn volailiy is more dependen on e NASD volailiy an on e NIFD volailiy over e wole sample period. On an average, e NASD volailiy accoun for 9.5% of e Nify overnig volailiy wile e NIFD volailiy capure only 0.5%. Now we urn o ou of sample forecas evaluaion. Te only real es of e performance of a forecasing model is o see, ow well i performs in realiy, and e way o do i is o use e model o forecas reurns beyond e ime- period during wic i was esimaed and en compare e model forecass wi e real observed reurns. We repor ese ou-of-sample mean forecass of ARMA-GARCH model and compare i wi e acual realized Nify overnig reurns. We calculae muli-sep aead forecass for e nex 45 days, from s July 00 o 3 s Augus 00. To bencmark e forecas performance agains an alernaive, we also calculae e mean forecass based on e domesic model (Model 3), wic does no consider informaion flow from NASDAQ. Fig 7 plos e acual Nify overnig reurn, forecas values, NIFONF and NIFONF_DOM, from model and 3. I is eviden a e model wi NASDAQ informaion (model ) clearly ouperforms model 3 in predicing e acual Nify overnig reurns. Tis is furer reinforced by e leas mean squared error forecas of model. Fig 8 plos e ou of sample volailiy forecas errors, HF_error and HFDOM_error, from model & 3. In predicing e ou of sample volailiy, is no so clear wic model performs beer. However, e MSE of volailiy forecas error of model is marginally smaller an a of model 3.From figs 7 & 8, we conclude a using 5

16 no volailiy. 8. CONCLUSION We invesigae e sor run dynamic iner linkages beween e US and Indian sock markes, using dayime and overnig reurns of NSE Nify and NASDAQ Composie from s July 999 o 30 June 00. Tis approac provides an explici, empirically based, quaniaive descripion of e way informaion propagaes from NASDAQ and is being incorporaed by NSE overnig reurns. Te sudy employs Two- sage GARCH model and a simple univariae ARMA-GARCH model o capure e mecanism by wic NASDAQ Composie dayime reurns and volailiy ave an impac on no only e condiional reurns bu also on e condiional volailiy of Nify overnig reurns. We found a e simple ARMA-GARCH model performs beer an e more complex Two Sage GARCH model suggesed in e lieraure. We also bencmark e simple univariae model wi a model involving informaion peraining o only e domesic marke and discarding e informaion revealed by NASDAQ. Te main findings are as follows: Firs, e granger causaliy resuls indicae unidirecional granger causaliy running from e US sock markes (bo NASDAQ Composie and S & P 500) o Indian sock marke, NSE Nify index. Second, e previous day s dayime reurns of bo NASDAQ Composie and NSE Nify ave significan impac on e NSE Nify overnig reurn of e following day. However, e volailiy spillover effecs are significan only from NASDAQ Composie implying a e condiional volailiy of Nify overnig reurns is impored from US. We found a e effec of NASDAQ dayime reurn volailiy socks, on average, is 9.5% and a of Nify dayime reurn volailiy is a mere 0.5%. Turning o ou of sample forecass owever, we found a by including e informaion revealed by NASDAQ day rading provides beer forecass of mean levels of Nify overnig reurns bu does no significanly improve e predicion of volailiy. A foremos ineres in muc of e empirical inernaional financial lieraure is o sudy e exen o wic markes ave become inernaionally inegraed. Insigs ino informaion flows in markes will increase e undersanding of e relevan mecanisms a work during exreme siuaions suc as marke crases, wic in urn can provide guidelines for inervenion and ax policies. Tis paper conribues in a modes manner wi reference o Indian sock marke inegraion wi e US sock marke. Te resuls repored are in conras wi e previous sudies, wic ave examined e co-movemen of Indian markes wi oer markes and suggesed a very low degree of correlaion. Here ere is srong evidence a NSE Nify is in une wi NASDAQ Composie over e sample period. Various explanaions can be offered for is penomenon and ese range from (i) Deregulaion of Indian financial marke since 99, including increased effors o implemen liberalizaion measures. (ii) Increase in macro economic policy coordinaion, (iii) Expanding influence of mulinaional corporaions, (iv) Increased paricipaion of FIIs in Indian sock marke. (v) Increasing inernaional cross-lising of Indian firms in US markes and (vi) 6

17 ransmied from one marke o e oer. REFERENCES:: Angela Ng (000), Volailiy spillover effecs from Japan and e US o e Pacific-Basin, Journal of Inernaional Money and Finance, 9, pp Becker, K. G., Finnery, J. E. & Manoj Gupa (990), Te Ineremporal Relaion Beween e US & Japanese Sock Markes, Journal of Finance, 45, pp Engle, R.F. and V. Ng. (993), "Measuring and Tesing e Impac of News on Volailiy," Te Journal of Finance, 48, Engle R. F.. and Andrew J. Paon (000), Wa Good is A Volailiy Model, Quaniaive Finance, Volume (00) Eun, C. & Sim, S. (989), Inernaional Transmission of Sock Marke Movemens, JFQA, 4, pp4-56. Ceung & Lilian K. Ng (99), Ineracions Beween e U. S. and Japan Sock Marke Indices, Jl. of Inernaional Financial Markes, Insiuions & Money, Vol (), pp5-70 Granger, Clive W.J. (969), Invesigaing Causal Relaions by Economeric Models and Cross Specral Meods, Economerica,37 pp Hamao, Y., Masulis, R., and Ng, V. (990) Correlaions in Price Canges and Volailiy across Inernaional Sock Markes, Review of Financial Sudies, 3, Hilliard, J. (979), Te Relaionsip beween Equiy Indices on World Excanges Journal of Finance, 34(), pp Jon Wei, K.C., Yu-Jane Liu, Yang & Caung (995), Volailiy and price cange spillover effecs across e developed and emerging markes, Pacific-Basin Finance Journal, Vol 3, pp Kee-Hong Bae, Karolyi (994), Good news, bad news and inernaional spillovers of sock reurn volailiy beween Japan and e US, Pacific-Basin Finance Jl.,, King, M. A. and S. Wadwani (990), Transmission of Volailiy beween Sock Markes, Review of Financial Sudies, 3, pp King, M., Senana, E. & Wadwani, S. (994), Volailiy and Links beween naional markes, Economerica, 6(4), pp Koc, P. & Koc, R.(99), Evoluion in Dynamic Linkages Across Daily Naional Sock Indexes, Journal of Inernaional Money and Finance, 0, pp3-5. Koumos, G. (999), Asymmeric price & volailiy adjusmens in emerging Asian sock markes, Journal of Business Finance & Accouning, 6, ()&(), pp83-0. Lin, Engle & Io (994), Do Bulls or Bears Move Across Borders Inernaional Transmissions of Sock Reurns and Volailiy, Review of Financial Sudies,7,pp

18 Journal of Inernaional Money and Finance, 4, pp -6. Panon, D., Lesseg, V. & Joy, O (976), Co-movemen of Inernaional Equiy Markes: A Taxonomic Approac, JFQA, Rao, B.S.R & Umes Naik (990), Iner-Relaedness of Sock Markes: Specral invesigaion of USA, Japanese and Indian Markes Noe, Ara Vignana, Vol 3(3&4), pp Ripley, D. (973), Sysemaic Elemens in e Linkage of Naional Sock Marke Indices, Te Review of Economics and Saisics, 5, pp Scwer, G. W. (990), Sock Volailiy and e Cras Review of Financial Sudies, 3, Sarma, J.L. & Kennedy, R.E (977) Comparaive analysis of sock price beavior on e Bombay, London & New York Sock Excanges, JFQA, Sep 977, pp Von Fursenberg, G. M. & B. N. Jeon (989), Inernaional Sock Price Movemens: Links and Messages, Brooking Papers on Economic Aciviy,, pp

19 s July 999 o 30 June 00. Cause (X) Effec (Y) F-saisic p-value Causaliy Inference NASDAQ -i Nify NASDAQ Nify Nify NASDAQ Nify NASDAQ S & P 500 -i Nify S & P 500 Nify Nify S & P Nify S & P 500 Nify Daily Reurns (NIFTY ) = Log (Nify close on day / Nify close on day -)*00 NASDAQ Daily Reurns (NASDAQ ) = Log (NASDAQ close on day / NASDAQ close on day -)*00 S&P 500 Daily Reurns (S&P 500 ) = = Log (S&P 500 close on day /S&P 500 close on day -)*00 Table : Descripive Saisics of Reurns NIFON NIFD NASD NASON Mean Sd. Dev Skewness Kurosis Jarque-Bera Probabiliy (0.000) LB(0) (0.008) LB(0) (0.000) LB (0) (0.000) LB (0) (0.000) (0.000) 7.64 (0.06) 9.64 (0.083) (0.000) (0.000) (0.000) 3.4 (0.0) (0.0) (0.000) 06.4 (0.000) (0.000) (0.00) (0.005) 35. (0.000) (0.000) Table 3:: Esimaion resuls and diagnosics for dayime reurns of NASDAQ Composie and NSE Nify indices from s July 999 o 30 June 00. STAGE I : NASD,,,0, ~ N(0,, NASD ),,,,,,, m DUM, NIFD,,,0, ~ N(0,, NIFD ),,,,,,, DUM is a dummy variable for oliday and weekend reurns. Esimaion is performed by e BHHH algorim wi robus errors opion in RATS 5.0 package. 9

20 Panel A Esimae p-value Esimae p-value, , ,m , , , Panel B : Residual Diagnosics Skewness Kurosis J-B es LB(0) LB(0) LB (0) LB (0) LB(k) is e pormaneau saisic esing join significance of reurn auocorrelaions up o lag k; LB (k) is e pormaneau saisic esing join significance of reurn auocorrelaions up o lag k; Table 4:: Nify Overnig Reurns NIFON,, ~ N(0,,0,0, ),,, NIFON,,, dnifd NIFDRES fnasd NASDRES ;,,0 0 Sage II NSE NIFTY Overnig Reurns PANEL - A Coefficiens p-value, , , d f , e , , e Panel B: Residual Diagnosics Skewness Kurosis J-B es LB (0) LB (0) LB (0) LB (0) LM (0) Sign Bias Neg. Bias Pos. Bias Join Bias LB (k) is e pormaneau saisic esing join significance of reurn auocorrelaions up o lag k; LB (k) is e pormaneau saisic esing join significance of reurn auocorrelaions up o lag k; LM (k) is e pormaneau saisic esing e presence of ARCH effecs up o lag k Sign bias, Negaive size, Posiive size, and Join bias ess are asymmeric es saisics developed by Engle and Ng (993) 0

21 NIFON u ~ N(0, ) u 0 NIFON NASD u NIFD NIFD ; NASD 0 Esimaion is performed by e BHHH algorim wi robus errors opion in RATS 5.0 u Panel A::Resuls Parameer Coefficien p-value a b c d f e e Panel B : Residual Diagnosics Skewness Kurosis Jarque-Bera s LB(0) LB(0) LB (0) LB (0) LM(0) Sign Bias Neg. Bias Pos. Bias Join Bias LB (k) is e pormaneau saisic esing join significance of reurn auocorrelaions up o lag k; LB (k) is e pormaneau saisic esing join significance of reurn auocorrelaions up o lag k; LM (k) is e pormaneau saisic esing e presence of ARCH effecs up o lag k Sign bias, Negaive size, Posiive size, and Join bias ess are asymmeric es saisics developed by Engle and Ng (993) Table 6 :: Model Comparison Model AIC / SBC Log Likeliood value Rank Two Sage GARCH / ARMA-GARCH / Domesic Model / Table 7: Forecas Performance of ARMA-GARCH Model is e prediced volailiy as prediced by ARMA-GARCH model in Table 5. r is e acual esimae of volailiy calculaed as e squared daily reurns. Te following wo regressions are esimaed. r a b * u

22 Adjused R is in percen. Coefficien -saisic p-value Adjused R a b saisic of b is for null of b =

23 6000 F i g A : : N S E N I F T Y V s N A S D A Q C o m p o s i e 0/04/996 o 30/06/ Lef Y-axis : NASDAQ, Rig Y-axis : NIFTY 600 Fig B : NSE Nify Vs S & P 500 0/04/996 o 30/06/ Rig Y-axis :NIFTY, Lef Y-axis :SP500 3

24 Fig :: Marke Trading ours:: Indian Sandard Time Midnig 4 am 0 am 3.30 pm 9 pm Midnig 3.30am day - day NSE rading NASDAQ rading 0 5 Fig 3 :: Reurn Series Graps :: 0/07/999 o 30/06/ NASD NASON NIFD NIFON 4

25 F i g 4. :: S d R e s i d u a l P l o : n d S a g e G A R C H m o d e l Fig 4. Sd Residual C orrelogram X -axis :: N o. of Lags Y - a x i s : : A C F & P A C F o f S d R e s i d u a l s A C F P A C F..0 8 F ig 4.3 S d R e s id u a l S q u a re s C o rre lo g ra m X a x i s : : N o o f L a g s Y a x i s : : A C F & P A C F A C F P A C F 5

26 6 F i g 5. S d R e s i d u a l P l o : : A R M A - G A R C H F ig 5. S d R e s id u a ls C o rre lo g ra m X a x is : N o o f L a g s Y a x i s : A C F & P A C F A C F P A C F..08 F ig 5.3 :: S d R esidual Squares C orrelogram X axis : N o of Lags Y a x i s : A C F & P A C F A C F PAC F 6

27 F i g 6 R e l a i v e I m p o r a n c e : : V a r i n a c e R a i o s Mean of VR_NASD:0.095 Mean of VR_NIFD : VR_NASD VR_NIFD.5.0 F i g 7 : M e a n F o r e c a s C o m p a r i s o n MSE :: NIFONF = N I F O N F _ D O M = X - a x i s : D a y s a e a d Y - a x i s : N I F O N, N I F O N F & N I F O N F _ D O M NIFON NIFONF_DOM NIFONF 7

28 3 F i g 8 :: V o l a i l i y F o r e c a s C o m p a r i s o n MSE :: HF_error = H F D O M _ e r r o r = HF_error HFDOM_error X - a x i s : : D a y s a e a d Y - a x i s : : V o l a i l i y f o r e c a s e r r o r 8