African Journal of Business Managemen Vol. 6(8), pp. 2830-2838, 29 February, 2012 Available online a hp://www.academicjournals.org/ajbm DOI: 10.5897/AJBM10.1657 ISSN 1993-8233 2012 Academic Journals Full Lengh Research Paper Modeling he exchange rae volailiy, using generalized auoregressive condiionally heeroscedasic (GARCH) ype models: Evidence from Pakisan Yasir Kamal 1 *, Hammad-Ul-Haq, Usman Ghani 1 and Muhammad Muhsin Khan 1 1 Insiue of Managemen Sciences, IMS, Peshawar, Pakisan. 2 Shaheed Zulfikar Ali Bhuo Insiue of Science and Technology, SZABIST, Islamabad, Pakisan. Acceped 28 January, 2011 Increasing role of foreign exchange (FOREX) rae in corporae decision making is becoming famous in he developing economies, where FOREX rae volailiy occupied a cenral posiion all over he world in invesmen decision. In a scenario, where FOREX rae volailiy is equally helpful in many micro as well as macro economic decision-making (remembering hisorical roos of some of he financial crises were raced in he FOREX rae volailiy). In his sudy, an aemp is made o examine he performance of GARCH family models (including symmeric GARCH-M, asymmeric EGARCH and TARCH models) in forecasing he volailiy behavior of Pakisani FOREX marke. Daily FOREX raes daa, ranging from January, 2001 o December, 2009 was pu o saisical manipulaion o examine he FOREX volailiy behavior in Pakisan. Theoreically, he firs order auoregressive behavior of he FOREX rae was evidenced in GARCH-M and E-GARCH models while he GARCH-M model suppors ha previous day FOREX rae affeced he curren day exchange rae. The EGARCH-based evaluaion of FOREX raes showed asymmeric behavior of volailiy, where TARCH model showed insignificance bu deailed exploraory analysis of he FOREX rae behavior requires prolonged sudy by applying advance models. Key words: Exchange rae, GARCH-M, TARCH, EGARCH, volailiy, Pakisan. INTRODUCTION Tradiionally, corporae decision makers use volailiy models as a ool in porfolio allocaion, risk managemen and as an inpu in derivaive asse pricing while he policymakers use he same o keep an eye on he economic facors, heir impac on exchange rae, and o develop moneary and fiscal policies as well. Expor oriened counries wih subsanial impac of expors on economic growh emphasize more on he exchange rae volailiy in heir economic policies. Many financial crises semming from sudden and unexpeced *Corresponding auhor. Email: yasirkamal79@gmail.com. Tel: +92 333 5550855. Abbreviaions: ARCH, Auoregressive condiionally heeroscedasic; GARCH, generalized auoregressive condiionally heeroscedasic. oscillaion in he financial crises of Lain American, Souheas Asian and Russian economies highlighed he imporance of measuremen of FOREX rae volailiy, is forecasing and is behavior. FOREX rae sysem can eiher be fixed or floaing, ha is, fixed exchange raes is reaed as a permanen one and he floaing exchange rae may drif, up and down, according o cerain marke rends. Floaing FOREX raes are expeced o be more volaile as hey are free o flucuae. The volailiy in FOREX raes resul in increase of exchange rae risk and adversely affecs he inernaional rade and invesmen decisions. According o he findings of Taylor (2005), FOREX volailiy inpus are supporive in cerain financial decisions relaed o porfolio opimizaion, hedging, risk managemen, pricing of opions and oher ypes of derivaives. FOREX rae is one of he key macroeconomic variables, wih direc effec on inernaional rade balance. Kemal (2005) observes ha, FOREX rae volailiy,
Kamal e al. 2831 adversely, affecs he long-erm decisions by sirring he volume of global markeing and decisions o allocae resources for invesmen, sales and procuremen policies of governmens. In he medium erm, FOREX rae can influence he balance of paymens and level of he overall economic aciviy while affecing he local consumers and raders in he shor run. Sengupa (2002) find resemblance in he FOREX marke and he world s larges financial marke by miles. The FOREX marke is an uninerruped one wih no opening or closing hours, and funcioning 24 hours a day and 7 days a week. An invesor s confidence o inves in a paricular counry is inversely relaed o high volailiies in he exchange rae. This is he basic reason ha volailiy models are used o explain he enduring and significan insances in he FOREX rae movemens. Poon and Granger (2003) assered ha financial volailiy has significan influence on he economy while he policy and decision makers depends heavily upon he volailiy modeling o anicipae on he vulnerabiliies of financial markes and economy. Mos of he research on exchange rae volailiy and is forecasing is focused on he developed markes while he curren sudy aims o adjunc he exising lieraure by examining he exchange rae volailiy of Pakisani rupee agains he US dollar. The prime concern of he researchers revolves around he applicaion of appropriae model o be applied o analyze he FOREX volailiy and he abiliy of a model o forecas movemens in exchange raes based on informaion, conained in hisorical rading aciviies. In he available lieraure of modeling ime series volailiy, he auheniciy and he populariy of ARCH family (GARCH, EGARCH and sochasic volailiy models) is recognized universally. According o Engle (1982) and Bollerslev (1986), ime series' models are more reliable for capuring he volailiy in financial ime series as hese models are specifically designed for volailiy modeling. According o Dimson and Marsh (1990) and Bollerslev (1986), ARCH and GARCH models are very useful o capure he lepokuric and volailiy clusering and help o model he changing condiional variances in ime series. Brooks and Burke (2003) are of he view ha he lag order (1,1) model is effecive enough o capure all he volailiy clusering available in daa. To accoun for asymmerical and leverage effecs, he exension of ARCH models, EGARCH, was inroduced by Nelson (1991). Similarly, Akgiray (1989) was also in suppor of ARCH and GARCH model and praised he model capabiliy while forecasing volailiy in New York Sock Exchange. The purpose of he curren sudy is o model and quanify he volailiy of exchange rae of Pakisani Rupee agains he US Dollar hrough differen available ypes of GARCH family models. The symmeric GARCH-M (1,1), asymmeric EGARCH (1,1) and TARCH (1,1) models will be applied o capure he main characerisics of exchange rae, such as, volailiy clusering and he leverage effec. According o Engle (1993), all of hese hree models are capable of predicing reurns volailiy in he financial marke and may creae an impac on invesors porfolio decision. This forecas of he volailiy of financial variables is a relevan piece of informaion and of paricular significance for making economic decisions. Problem saemen FOREX rae volailiy is an imporan facor involved in he decision making of invesors and policy makers. The lieraure provides a number of volailiy measures o develop model of volailiy behavior of ime series. The curren sudy is he firs such aemp in Pakisan o capure he Pak Rupee volailiy agains US Dollar. The capuring of asymmeric and leverage behavior of Pakisan s exchange rae was really vial and significan from policy makers, individual as well as he group invesors poin of view. Objecive of he sudy The objecive of he paper is o esimae he ime varying variances in Pak-US FOREX rae, from year 2001o 2008, hrough GARCH (1, 1), EGARCH and TARCH models, resuling in a larger esimaed condiional variance indicaing poenial bu subsanial risk. LITERATURE REVIEW Modeling and forecasing FOREX rae has many pracical applicaions in economics and finance wih wide discussion in he lieraure. The basic ARCH/GARCH models are frequenly applied and quoed o describe he volailiy in financial markes, such as, sock exchanges and FOREX markes. Hsieh (1989) used 10 years (1974 1983) of daily closing-bid prices, consising of 2,510 observaions, for five counries in comparison of US dollar o esimae he auoregressive condiionally heeroscedasic (ARCH) and generalized auoregressive condiionally heeroscedasic (GARCH) models along wih he oher modified/alered ypes of ARCH and GARCH. The findings of Hsieh (1989) proved ha he wo undersudy models were capable of removing all heeroscedasiciy in price changes. I was also concluded ha he sandardized residuals from all he ARCH and GARCH models using he sandard normal densiy were highly lepokuric, and he sandard GARCH (1,1) and EGACH (1,1) were found o be more efficien for removing condiional heeroscedasiciy from daily exchange rae movemens. The EGARCH proved o fi he daa, beer han GARCH
2832 Afr. J. Bus. Manage. model, using a variey of diagnosic checks. Mundaca (1991) modeled he NOK/US Dollar exchange rae hrough ARCH and GARCH models, he resuls of which suppored ha hree ou of four analyzed series fied beer hrough GARCH han he ARCH model. Johnson and Sco (2000) examined he Briish Pound, Canadian Dollar, German Mark and Japanese Yen agains he US Dollar, for he years 1978 o 1992, by applying he GARCH models. Though, he findings of Johnson and Sco (2000) idenified ha FOREX rae ime variaion were no he only reason of overall volailiy bu he fac ha afer removing he GARCH effec, he frequency disribuions sill showed he exisence of independence. This puzzled he auhors and forced hem o GARCH family models wih normaliy assumpion ha were unable o provide good descripion of exchange rae dynamics. Kazanzis (2001), who sudied he informaion conens and predicive power of implied volailiy models agains he volailiy esimaes, based on six-year prices daa from he currency opions marke for six differen currencies. The auhor deduced ha, implied volailiy conained more informaion conens han measures based, where informaion embedded in pas price hisory. Applicaion of GARCH model by Chong e al. (2002), o capure FOREX rae volailiy in he daa of Malaysian Ringgi/Pound Serling, for he period 1990-1997, resuled in heir suggesion o possibly rejec he hypohesis of consan variance model, arguing ha he GARCH models were beer ones han naive random walk models. The use of Peso-dollar exchange rae daa, wih 1730 observaions from January 2, 1997 o December 5, 2003, by Mapa (2004) compared, he ou of sample forecasing performance of 68 ARCH-ype models. In he esimaion by Mapa (2004), he model specificaions were observed hrough applicaion of Maximum Likelihood mehod wih Gaussian, suden s - es, Generalized Error disribuions and hrough Quasi- Maximum likelihood. The findings helped he auhor o argue ha focusing on he specificaion of he models is no sufficien bu daa disribuion should also be considered in FOREX rae modeling and heir findings demonsraed ha accommodaing he leveraged effec models, such as, TARCH, PARCH and EGARCH were able o show superior forecasing performance han he models which did no. Longmore and Robinson (2004) applied linear GARCH and asymmerical volailiy models on Jamaican Dollar for he period 1998 o 2003 and found long memory process for he exchange rae wih effecs of shocks being asymmeric, while in erms of explanaory power, he non-linear GARCH model performed well. A weekly Bah/US Dollar exchange rae, for he period 1999-2005, was analyzed by Jihiikulchai (2005) o sudy he applicaion of parameric and non-parameric volailiy models in which ARCH and ARCH-M were found more realisic, boh heoreical and empirically, because of heir low volailiy around zero mean whereas, he asymmeric coefficiens of EGARCH and TGARCH showed insignifican resuls. The TGARCH model was declared he bes model of modeling he exchange rae volailiy in ou-of-sample case by he researcher who suggesed ha non-parameric models could be he bes for he condiional volailiy predicion, while in he case of high frequency daa; i is more preferable han any oher volailiy model. Alberg e al. (2006) invesigaed he forecasing performance of GARCH, EGARCH, GJR and APARCH models and found ha he EGARCH model, which used a skewed Suden- disribuion, produced significan resuls han any oher model. Sandoval (2006) examined he daily exchange rae daa, from year 2000 o 2004, of seven Asian and emerging Lain American counries, by applying he ARMA, GARCH, EGARCH and GJR- GARCH models for modeling he exchange raes and capuring he imporan characerisics of daa. Sandoval (2006) poined ou ha, in he developing counries he absence of saisical significance beween asymmeric and symmeric models was condiional o he applicaion of in-sample and ou-of-sample ess joinly. Hussein and Jalil (2007) applied he parameric and non-parameric echniques on daily exchange rae of Pak Rupee / US Dollar exchange rae and ried o measure he success of inervenion in foreign exchange marke in Pakisan, which was done eiher in shape of aleraion in he exchange rae level or smoohing he exchange rae flucuaions. The GARCH resuls, as repored by Hussein and Jalil (2007) proved ha inervenion was successfully alered, in boh direcion of exchange rae and smoohed he flucuaions in exchange rae while he even sudy confirmed ha he inervenion was successful for level and volailiy of he exchange rae. Olowe and Ayodeji (2009) used a number of GARCH models o invesigae he volailiy of Naira/US Dollar exchange rae in which he hypohesis of leverage effec was rejeced by all asymmery models, hough all he coefficiens of he variance equaions were significan, he TS-GARCH and APARCH models proved o be he bes models. On he oher hand, EGARCH model showed ha in Nigerian foreign exchange marke, wih all variances being non-saionary, he volailiy is highly persisence. Khalid (2008) analyzed he capabiliy of exising exchange rae models by using he monhly daa of 20 years of Pakisan, India and China and repored ha for he developing economies, he model based on macroeconomic fundamenals perform beer han he random walk model in boh in and ou sample. METHODOLOGY Sample of he sudy FOREX rae daa used in his paper has been expressed in erms of US dollar for which daa was obained from he Inernaional Financial Saisics online daabase, available a www.imfsaisics.org. The daa was in he form of daily observaions for he period, from January, 2001 o December, 2009 wih 2005 observaions and monhly daa for he same period wih
Kamal e al. 2833 Figure 1. he ime series plo of he daily and monhly exchange rae daa. 108 observaions (Figure 1). GARCH-M (1,1) Process Daa The presence of uni roo indicaes ha price movemens are nonsaionary, while he absence of uni roo will show he saionary of he daa, since he non-saionary is undesirable; he ime series' daa of his sudy was ransformed ino daily reurns o achieve saionary before he applicaion of he models. The sudy is focused o model and quanify volailiy of exchange rae of Pakisani rupee agains he US dollar wih differen ypes of GARCH family models. The symmeric GARCH-M (1,1) model along wih he oher wo asymmeric EGARCH (1,1) and TARCH (1,1) have been used o capure he main characerisics of exchange rae ime series, such as, volailiy clusering and he leverage effec. According o Engle (1993), all of hese hree models are capable of predicing reurn volailiy in he financial marke and may creae an impac on invesors porfolios' decisions. Measuring he daily reurns The daily represenaive raes daa of Pak Rs. / U.S. Dollar was ransformed ino he nominal reurns by adoping he mehod of coninuously compounded annual rae of reurn. Daily reurns are measured wih he help of following mehod in his sudy: s r log s 1 The dependen variable is he daily nominal reurn, where r is he reurn on he day, S is he exchange rae a ime and S -1 represen he exchange rae a ime -1. Naural log is used o calculae he reurns of he daa. (1) Augmened Dickey Fuller (ADF) uni roo es The equaion used for conducing Augmened Dickey Fuller es has he following srucure: To check he ADF uni roo, he following hypoheses were developed: 2 Y X u h p h ~ iidn(0, h ) 0 h Bollerslev (1986) modified he classical Engle (1982) ARCH model wih his Generalized ARCH or GARCH process, resuling also o he GARCH (p,q) process. According o Bollerslev (1986), he condiional variance is a linear funcion of q lags of he squares of 2 u i i i1 j1 he error erms (u ) or he ARCH erms (also referred o as he news from he pas) and p lags of he pas values of he 2 2 j condiional variances (σ ) or he GARCH erms, and a consan ω. However, in he equaion he inequaliy resricions were imposed o guaranee a posiive condiional variance. Hansen and Lunde (2001) demonsraed ha, he GARCH (1,1) process is sufficien enough o explain he characerisics of he ime series. GARCH-in- Mean (GARCH-M) model was inroduced by Engle e al. (1987). The GARCH-in-mean (GARCH-M) model adds a heeroscedasiciy erm ino he mean equaion. This model allows he condiional mean o depend on is own condiional variance. I has he specificaion: Exponenial GARCH (EGARCH) process q u j The GARCH model is no he bes model o explain he leverage effecs, which are ofen observed in financial ime series. Concep of leverage effecs, which were firs observed by Black (1976), is relaed o he flucuaion in he sock prices which seemed o be inversely relaed o he flucuaion in he sock volailiy. One can deduce ha he effecs of a shock on he volailiy are asymmeric or in oher words, one can say ha he effec of good news, a posiive lagged residual, may be differen from he effecs of he bad ones, a negaive lagged residual. Developmen and he presenaion of EGARCH model by Nelson (1991) which accouns for an asymmeric response o a shock. A commonly used model is he EGARCH (1, 1) given by: H 0: (p -1) = 0 or p = 1 H a: (p -1) < 0 or p < 1
2834 Afr. J. Bus. Manage. Figure 2. The ime series plo of daily and monhly reurns. Table 1. ADF uni roo es on daily exchange rae reurns. Variable Coefficien PKR (-1) -0.961834 0.0000 D(PKR (-1)) 0.037747 0.0910 C 0.000170 0.0064 Durbin-Wason sa 2.001067 0.0000 ADF es saisic -31.62495 5% Criical Value -2.8635 *MacKinnon criical values for rejecion of hypohesis of a uni roo. The erm γ, accouns for he presence of he leverage effecs, which makes he model asymmeric. When he asymmeric model for volailiy is applied, i allows he volailiy o respond, more readily, when he prices are falling due o he bad news han wih corresponding increases due o he good news. Threshold ARCH (TARCH) process Zakoïan (1994) and Glosen e al. (1993) applied he TARCH model wih a purpose of independence han for he asymmeric effec of he news. The TARCH (p,q) specificaion is given by: of daily represenaive exchange raes of he Pakisani currency agains U.S. Dollar. The ime horizon of daa comprises from January, 2001 o December, 2009, wih 2005 observaions. The ime series plo of he daily and monhly exchange rae daa is shown in Figure 1. The ime series plo of daily and monhly reurns is given in Figure 2. The reurn series clearly shows volailiy clusering in he daa, especially in he sar and a he end of sample. Saionary of daa In he TARCH model, good news, u > 0 and bad news, u < 0 -i -i have differen effecs on he condiional variance. When γ k 0, i can be concluded ha he news impac is asymmeric and ha here is presence of leverage effecs. The difference beween he TARCH and EGARCH is ha TARCH assumes leverage effec as quadraic and he EGARCH assumes leverage effec as exponenial. ANALYSIS AND DISCUSSION Display of daa Exchange rae, expressed in erms of US Dollar, consis Prior o GARCH model applicaion, he univariae analysis was necessary o be performed due o ime varying variances of ime series. In he saionary ime series, he shocking effecs will be noed emporarily which will be eliminaed when he series will come back o he long-run mean values. On he oher hand, nonsaionary ime series will necessarily conain permanen componens. Saionary of daa is imporan because if he series is non-saionary hen all he CLRM assumpions were violaed and one can no apply linear regression (Aseriou and Hall, 2007). To check he saionary of ime series he Augmened Dickey-Fuller uni roo es was used, Table 1 and 2 which regress each series on is lagged value in differen ime poins. Following he lieraure, all daa series has been ransformed ino naural logarihms. Boh of above ables show ha he values of ADF saisic remained a -31.625 and -3.841, respecively, and are lesser han all he criical values. So, he null
Kamal e al. 2835 Table 2. ADF uni roo es on monhly exchange rae reurns. Variable Coefficien PKRM (-1) -0.372823 0.0002 D(PKRM (-1)) -0.310990 0.0013 C 0.001086 0.3232 Durbin-Wason sa 1.952935 0.0000 ADF Tes Saisic -3.840652 5% Criical Value -2.8889 Table 3. Resuls of GARCH-M model on daily exchange rae reurns. Coefficien SQR (GARCH) 0.058461 0.3681 C 2.38E-05 0.8389 PKR (-1) 0.035226 0.0968 Variance equaion C 4.44E-08 0.0000 ARCH (1) 0.017690 0.0000 GARCH (1) 0.966839 0.0000 Durbin-Wason sa 1.929059 0.016005 Dependen variable: PKRN1; Mehod: ML ARCH. Table 4. Resuls of GARCH-M model on monhly exchange rae reurns. Coefficien SQR (GARCH) -0.041995 0.9001 C 0.000806 0.6598 PKRM (-1) 0.357223 0.0340 Variance equaion C 4.12E-06 0.0017 ARCH (1) 0.245713 0.0017 GARCH (1) 0.720128 0.0000 Durbin-Wason sa 1.938097 Dependen variable: PKRMN1; Mehod, ML ARCH hypohesis was rejeced as he series conained he uni roo and he alernaive hypohesis was acceped ha boh he ime series are saionary and conclude ha P<1. The resuls show ha daily and monhly reurns of represenaive exchange raes of Pakisani rupee agains US dollar are independen of serial correlaion. Resuls of GARCH-M (1,1) The ARCH model specificaions are similar o moving average specificaion han an auoregressive one; a fac from where Bollerslev (1986) inroduced he lagged condiional variance erms, o be included ino ARCH model as auo regressive erms, hus saring he GARCH model family. The risk behavior of exchange rae is esimaed by GARCH-M model ha allows he condiional mean o depend on is own condiional variance. In his model wih wo equaions, he mean exchange rae equaion explains auoregressive process, ha is, he previous exchange raes affec curren rae and GARCH-M erm, which shows he impac of risk of exchange rae upon he mean exchange rae. The resuls displayed in Tables 3 and 4 describes ha he Pak exchange rae has an order-one auoregressive
2836 Afr. J. Bus. Manage. Table 5. Resuls of EGARCH model on daily exchange rae reurns. Coefficien C 6.47E-05 0.0080 PKR (-1) 0.076445 0.0005 Variance equaion C -0.129287 0.0000 RES /SQR[GARCH] (1) 0.019188 0.0000 RES/SQR[GARCH] (1) 0.065703 0.0000 EGARCH (1) 0.990439 0.0000 Durbin-Wason sa 1.998262 Dependen variable, PKR; Mehod, ML ARCH Table 6. Resuls of EGARCH model on monhly exchange rae reurns. Coefficien C 0.000949 0.0678 PKRM (-1) 0.329340 0.0075 Variance equaion C -1.180407 0.0000 RES /SQR[GARCH] (1) 0.324494 0.0350 RES/SQR[GARCH] (1) 0.349751 0.0000 EGARCH (1) 0.903236 0.0000 Durbin-Wason sa 1.897213 Dependen variable, PKRMN1; Mehod, ML ARCH process in boh he daily and monhly exchange rae reurns, which implies ha he pas day exchange rae affecs he curren day exchange rae. The variance equaion shows ha ARCH (1) erm is significan a 1% showing ha he volailiy of risk is affeced, significanly, by pas square residual erms. The GARCH (1) is also significan a 1% level, which shows ha pas volailiy of exchange rae is significanly, influencing curren volailiy. The GARCH-M erm is no significan a boh he daily and monhly exchange rae reurns, showing he exchange rae risk (variance) which is no significanly compensaed in he exchange rae marke. The condiional sandard deviaion (SQR (GARCH)) coefficien is insignifican, suggesing ha if here is an effec of he risk on he mean reurn, hen ha could no be beer capured by his sandard deviaion mehod. There is posiive insignifican radeoff beween foreign risk and reurn. Resuls of EGARCH (1, 1) EGARCH parameers, displayed in Table 5 and 6 show he calculaed coefficiens and he p' values of he EGARCH model on daily and monhly exchange rae reurns. The resuls shows ha, here is a firs order auoregressive behavior in he exchange rae as in he mean equaion, he erm PKRN (-1) is significan a 1% in daily and monhly reurns. The consan C is also significan a 1% in daily reurns and is significan a 10% in monhly reurns. In he variance equaion, all he erms are significance a 1% level for he daily exchange rae reurns while all he erms of he variance equaion, for he monhly exchange rae reurns, also remain significan. The EGARCH variance equaion indicaes ha here exiss he asymmeric behavior in volailiy which means ha posiive shocks are effecing, differenly, han he negaive on volailiy. The EGARCH model proves o be he bes model o explain he behavior of exchange rae on daily and monhly daa; mos of he coefficiens of mean and variance equaion are significan. Resuls of TARCH (1, 1) TARCH parameers on he daily and monhly reurns are displayed in Tables 7 and 8, where oupu shows calculaed coefficiens and he p' values of he TARCH coefficiens. For he daily exchange rae reurns, he resuls show no auo regressive behavior. In he mean equaion, he erms C remains significan and PKR (-1) shows insignifican resuls. For he monhly exchange rae reurns, he resuls shows he firs order auoregressive behavior in he exchange rae as in he mean
Kamal e al. 2837 Table 7. Resuls of TARCH model on daily exchange rae reurns. Coefficien C 0.000245 0.0000 PKR (-1) 0.033206 0.1514 Variance equaion C 6.28E-08 0.0000 ARCH (1) 0.030487 0.0000 (RESID<0)*ARCH (1) -0.027467 0.0000 GARCH (1) 0.961703 0.0000 Durbin-Wason sa 1.916090 Dependen variable: PKRN1; Mehod, ML - ARCH Table 8. Resuls of TARCH model on monhly exchange rae reurns. Coefficien C 0.000658 0.2552 PKRM (-1) 0.356485 0.0001 Variance equaion C 4.10E-06 0.0051 ARCH (1) 0.411069 0.0432 (RESID<0)*ARCH (1) -0.482825 0.0139 GARCH (1) 0.755390 0.0000 Durbin-Wason sa 1.965453 Dependen variable: PKRM; Mehod: ML ARCH. equaion, he erm PKR (-1) is significan a 1%, while he consan C remains insignifican. In he variance equaion, he ARCH (1) and GARCH (1) erms remained significan for boh he daily and monhly exchange rae reurns. This implies ha he previous square error erms significanly effecs volailiy and ha he pas volailiy of exchange rae is also, significanly, influencing curren volailiy. The leverage effec erm (y) is represened by he (RESID<0)*ARCH (1). This erm is significan for boh he daily and monhly exchange rae reurns, represening ha here are asymmeric behavior and presence of leverage effec. Conclusion A symmeric GARCH-M (1, 1) wih oher wo asymmeric models EGARCH (1, 1) and TARCH (1, 1) were used o analyze he daily and monhly exchange raes of Pakisan. The daa consised of exchange raes of Pakisani Rupee agains he U.S. Dollar for he period January, 2001 o December, 2009. The GARCH-M (1, 1) model has shown ha, he firs order auoregressive process, supporing he previous day exchange rae affecs he curren day exchange rae. In he variance equaion, ARCH (1) and GARCH (1) boh remained significan a 1% for he daily and monhly exchange rae reurns. The EGARCH resuls have shown firs order auoregressive behavior in he exchange rae, while he variance equaion indicaed ha he asymmeric behavior was shown by he ime series, ha is, posiive and negaive news has differen impac on volailiy progression. The TARCH resul did no show any auoregressive behavior in he daily exchange rae reurns bu he monhly exchange rae reurns showed he auoregressive behavior. Whereas, he resuls of TARCH model suppored he asymmeric behavior in boh he daily and monhly exchange rae reurns. The resuls of GARCH-Type models, applied on he exchange rae of Pak Rupee agains he US Dollar can be very much helpful for he invesor s decision and policy making. The resuls can also be helpful o undersand he hisorical paerns of exchange rae behaviors, and hus being helpful o predic he fuure movemens of exchange rae markes. The overall resuls proved ha he EGARCH model remains he bes in explaining he volailiy behavior of he daa, making all he coefficiens of mean and variance equaions significan. The TARCH model suppors he ime series exchange rae, following he asymmeric behavior and depics he presence of leverage effec in boh he daily and monhly reurns. The resuls of his research work also suppor he fac ha
2838 Afr. J. Bus. Manage. EGARCH is he bes model o explain he volailiy behavior of exchange rae daa, similar o he one analyzed in he works of Hsieh (1989), Longmore and Robinson (2004), Mapa (2004) and Alberg e al. (2006). The research can ac as firs sep o observe he volailiy behavior of he Pakisani exchange marke. Specified period's daa can be esed by he fuure researchers using new and more enhanced models o capure he effecs and predicions of he volailiy behavior. REFERENCES Akgiray AK (1989). Condiional heeroscedasiciy in ime series of sock reurns: Evidence and forecass. J. Bus., 62: 55 79. Alberg D, Haim S, Rami Y (2006). Esimaing sock marke volailiy using asymmeric GARCH models. Mon. Cen. Econ. Res., Discussion Paper No. 06-10. Aseriou D, Hall SG (2007). Applied Economerics:. Revised ediion. New York: Palgrave Macmillan. Black F (1976). Sudies of Sock Price Volailiy Changes. Proceedings from he American Saisical Associaion, Bus. And. Econ. Secion, 177-181. Bollerslev TP (1986). Generalized Auoregressive Condiional Heeroscedasiciy. J. Econ., 31, 307-327. Brooks C, Burke, SP (2003). Informaion Crieria for GARCH Model Selecion: An Applicaion o High Frequency Daa. Eur. J. Finan., 9(6): 557-580. Chong CW, Chun LS, Ahmad MI (2002). Modeling he volailiy of currency exchange rae using GARCH model. Peranika J. Soc. Sci. Hum., 10 (2): 85-95. Dimson E, Marsh P (1990). Volailiy Forecasing wihou Daa- Snooping. J. Bank. Financ., 14: 399 421. Engle R (1993). Saisical Models for Financial Volailiy. Financ. Analys. J. 49: 72 78. Engle R, Lilien DM, Robbins RP (1987). Esimaing ime varying risk premia in he erm srucure: The ARCH-M model. J. Finan. Econ., 55: 391-407. Engle RF (1982). Auoregressive Condiional Heeroscedasiciy wih Esimaes of he Variance of U.K. Inflaion. Econ., 50: 987-1008. Glosen LR, Jagannahan R, Runkle DE (1993). On he relaion beween he Expeced Value and he Volailiy of he Nominal Excess Reurn on Socks. J. Financ., 48: 1779-1801. Hansen P, Lunde A (2001). A Forecas Comparison of Volailiy Models: Does anyhing Bea a GARCH (1,1)?. Working paper, Deparmen of Economics, Brown Universiy. Hsieh DA (1989). Modeling Heeroscedasiciy in Daily Foreign- Exchange Raes. J. Bus. Econ. Sa., 7(3). Hussain F, Jalil A (2007). Effeciveness of Foreign Exchange Inervenion: Evidence from Pakisan. SBP Res. Bull., 3(2). Jihiikulchai T (2005). A sudy on Thai exchange rae volailiy model comparison: nonparameric approach. Faculy of Economics. Thammasa Universiy. Johnson K, Sco E (2000). GARCH models and he sochasic process underlying exchange rae price changes. J. Finan. Sraeg. Decis., 13(2), Summer 2000. Kazanzis CI (2001). Volailiy in currency markes. Manag. Financ., 27(6): 1-22 (22). Kemal MA (2005). Exchange Rae Insabiliy and Trade: The Case of Pakisan. PIDE publicaions. Khalid SMA (2008). Empirical exchange rae models for developing economies: A sudy on Pakisan, China and India. Soc. Sci. Res. Ne.. Longmore R, Robinson W. (2004). Modeling and Forecasing Exchange Rae Dynamics: An Applicaion of Asymmeric Volailiy Models. Bank. Jamaica, Res. Serv. Dep., WP 2004/03. Mappa DS (2004). A Forecas Comparison of Financial Volailiy Models: GARCH (1,1) is no Enough. Philippine Sa., 53(1-4): 1-10. Mundaca BG (1991). The volailiy of he Norwegian currency baske. Scand. J. Econ., 93(1): 53-73. Nelson D (1991). Condiional heeroscedasiciy in asse reurns: A new approach. Econ., 59: (2) 347-370. Olowe, Ayodwji R (2009). Modeling Naira/Dollar Exchange Rae Volailiy: Applicaion of Garch and Assymeric Models. In. Rev. Bus. Res. Papers, 5(3): 377-398. Poon SH, Granger CWJ (2003). Forecasing Volailiy in Financial Markes: A Review. J. Econ. Li., 41: 478-539. Sandoval J (2006). Do Asymmeric GARCH models fi beer exchange rae volailiies on emerging markes?. Colombia, Odeon Magazine Cen. Econ.Opera., 1(3): 99-117. Sengupa KJ (2002). Modeling Exchange Rae Volailiy. Deparmen of Economics. UCSB. Deparmenal Working Papers, Paper 12-96. Taylor SJ (2005). Asse Price Dynamics, Volailiy and Predicion. Prin. Uni. Press. Zakoïan JM (1994). Threshold heeroskedasic models. J. Econ. Dynam. Con. Elsevier, 18(5): 931-955.