Relationship between Crude Oil Prices and the U.S. Dollar Exchange Rates: Constant or Time-varying?

Transcription

1 Journal of Applied Finance & Banking, vol. 7, no. 5, 2017, ISSN: (prin version), (online) Scienpress Ld, 2017 Relaionship beween Crude Oil Prices and he U.S. Dollar Exchange Raes: Consan or Time-varying? Duong Le 1 Absrac This paper aims o analyze he ineremporal ineracion beween crude oil prices and he U.S. dollar rade-weighed exchange raes from January 1997 hrough December To his end, he sudy assumes ha he condiional covariance marix beween crude oil and he dollar exchange rae reurns follows a bivariae GARCH process. Using daily daa, I find srong evidence of a ime-varying condiional covariance and correlaion beween crude oil prices and he U.S. dollar exchange raes. If on one day he change in he dollar price of oil is largely due o a change in he dollar s value, here is a endency for he nex day s change in oil prices o be primarily caused by changes in he dollar s value as well. On he oher hand, if one day he change in he dollar price of oil is caused primarily by facors oher han he dollar s value, here is a endency for hose o be primarily causes of changes in he dollar price of oil on subsequen days. JEL classificaion numbers: E31, F31 Keywords: Garch process, crude oil prices, exchange rae 1 Inroducion This paper examines he ineremporal ineracion beween crude oil prices and he U.S. dollar exchange raes from January 1997 hrough December Crude oil is one of he mos essenial energy sources in he U.S., accouning for abou 40% of he naion s energy consumpion. Since OPEC s 1973 decision o regulae is oil price independenly of large oil companies, crude oil prices have been subjec o dramaic volailiy. Oil prices increased from less han $11 per barrel in he beginning of 1999 o $38 per barrel in Sepember 2000, decreased o $18 per barrel in January 2002 and wen up o $77 per barrel in July The crude oil marke experienced an unprecedened dramaic volailiy in 2008 as crude oil prices reached an all-ime high level of $145 per barrel in July and hen fell sharply o $30 per barrel in December. This large oil price flucuaion endency has coninued in recen 1 Deparmen of Business and Economics, Mariea College, 215 Fifh Sree, Mariea, OH Phone: (740) Fax: (740) Aricle Info: Received : June 1, Revised : July 2, Published online : Sepember 1, 2017

2 104 Duong Le years. From less han $68 per barrel in May 2010, oil prices increased o $112 in April 2011 and hen fell o $77 in Ocober The high volailiy in crude oil prices is likely due o acual and anicipaed flucuaions in supply and he shor-erm inelasiciy of demand. Given ha crude oil is one of he mos essenial energy sources, i is very difficul for mos oil users o reduce heir consumpion wihin a shor period of ime following a price increase. On he oher hand, here is considerable flucuaion in oil supply which depends on a variey of facors, such as changes in supply condiions, responses o geopoliics, insiuional arrangemens, and he dynamics of he financial markes. One of he mos imporan facors impacing crude oil supply and demand is he value of he U.S. dollar whose appreciaion or depreciaion is ofen accompanied by a decrease or increase in oil prices. For example, in June-July 2008, a combinaion of supply uncerainies in oil producing counries and a falling dollar caused an unprecedened oil price spike. On he reverse, an appreciaion of he dollar and signs of worldwide economic slowdown led o a sharp decrease in oil price in he end of 2008 and also in Ocober I is ofen argued ha because oil prices are denominaed in U.S. dollar, oil prices and he value of he dollar should be negaively correlaed. An appreciaion of he U.S. dollar would end o make oil more expensive in non-dollar currencies and would reduce demand for crude oil hereby possibly lowering oil prices in dollars. On he conrary, a depreciaion of he dollar is associaed wih a decline in he purchasing power of oil revenues for oil exporing counries and herefore, hese counries have an incenive o counerbalance he adverse effec of he dollar depreciaion by raising oil prices. Moreover, a depreciaion of he dollar makes oil priced in dollar an aracive financial asse for foreign invesors and herefore, a large amoun of money would end o flow o he oil marke, hus oil price will be driven up. A causal relaionship beween oil price movemens and changes in he U.S. dollar value has been commonly referred o in he financial marke commenary as he following quoes illusrae: Weak dollar cenral o oil price boom 2 or Oil prices fall on dollar srengh 3. 2 hp:// 3 WSJ, Sepember 4, 2014

3 $/barrel Relaionship beween Crude Oil Prices and he U.S. Dollar Exchange Raes U.S. dollar value Crude oil fuures price (lef axis) U.S. dollar index value (righ axis) Figure 1: Crude oil prices and he U.S. dollar exchange raes Figure 1 plos crude oil prices agains he U.S. dollar exchange raes from January 1997 hrough December While apparenly here is no clear relaionship from 1997 o 2001, crude oil prices and he U.S. dollar value appear o be negaively correlaed in recen years. As he dollar los 35.40% of is value agains he Trade Weighed Major Currencies Exchange Index beween January 2002 and July , oil prices soared from $18 o $145 per barrel during he same ime period. On he conrary, during he financial crisis, oil prices collapsed from $145 o $50 per barrel from July 2008 o March 2009 while he dollar appreciaed 23% in ha 9-monh period. 4 Consruced by he auhor using daa from he Federal Reserve Saisical releases, downloaded from hp://

4 106 Duong Le Figure 2: Oil prices and U.S. dollar exchange raes correlaion Figure 2 depics he correlaion beween oil prices and he U.S. dollar exchange raes, compued over 30-day moving windows. While he correlaion flucuaes beween negaive and posiive values during mos of he sample period, i ends o be more persisenly negaive afer While he negaive relaionship beween oil prices and he U.S. dollar value is widely discussed in he popular economic press and among marke praciioners, he academic lieraure documens mixed evidence regarding wheher a change in he dollar exchange rae drives changes in oil prices or vice versa. Prior academic sudies generally find ha oil prices Granger-cause exchange raes, bu no vice versa. For example, Zhou (1995) [1], Chaudhuri and Daniel (1998) [2], Amano and Norden (1998a,b)[3] [4], and Chen and Chen (2007) [5] find ha oil price is he dominan source of real exchange rae movemens. They argue ha if an oil imporing counry is dependen on impored oil, an oil price rise may increase he prices of radable goods in ha counry by a greaer proporion han in oher counries, and hereby cause a real depreciaion of ha currency and an appreciaion of he U.S. dollar. On he conrary, Lizardo and Mollick (2010) [6] argue ha as oil price goes up, he supply of U.S. dollars relaive o he oil exporer s currency goes up which would lead o a depreciaion of he U.S. dollar. However, Zhang, Fan, Tsai and Wei (2008) [7] documens ha a change in he U.S. dollar exchange rae does Granger cause oil price changes, bu a change in oil price does no significanly Granger cause U.S. dollar exchange rae changes. They furher prove ha he U.S. dollar depreciaion is a crucial reason for he recen soaring oil price. On he conrary, Couder, Mignon, and Peno (2008) [8] documen ha an oil price increase is linked o a dollar appreciaion in he long run and herefore, he siuaion of a weakening dollar and an increasing oil price is aypical.

5 Relaionship beween Crude Oil Prices and he U.S. Dollar Exchange Raes 107 However, while here is a considerable amoun of lieraure on he correlaion beween oil prices and he U.S. dollar values, none of he previous research have aemped o examine wheher ha correlaion is consan or varying over ime. An undersanding of he condiional correlaion beween crude oil prices and he U.S. dollar exchange raes is essenial for risk managemen and asse allocaion since oil is one of he dollar-denominaed asses ofen included in he commodiy porfolios of mos serious individual and insiuional invesors. Furhermore, oil prices and exchange raes are among asse prices which are likely o respond insanly o economic news and developmens in financial markes. The purpose of his sudy is o analyze he ineremporal ineracions of crude oil prices and he U.S. dollar rade-weighed exchange raes. To his end I allow he condiional covariance marix of oil and he dollar exchange rae reurns o vary over ime, according o a bivariae GARCH model since he evidence of heeroskedasic covariances among oher financial asses 5 has been well documened in numerous previous sudies. This sudy hypohesizes ha he condiional correlaion beween crude oil prices and he U.S. dollar exchange raes is ime-varying raher han consan over ime. Generally, oil price and he value of he dollar end o have a negaive relaionship. An increase in he value of he dollar causes more expensive oil prices in non-dollar currencies which should resul in a downward pressure on oil demand and hence lower oil prices in dollar and a decrease in he dollar value implies cheaper oil prices which would resul in more money flowing o he oil marke and hence drive up oil prices. However, oil prices are also impaced by inernaional supply-demand shifs, such as changes in he global oil demand and supply condiions, responses o geopoliics, insiuional arrangemens (such as he OPEC), and he dynamics of he financial markes, which are no caused by changes in he value of he U.S. dollar. In hose cases, here should be no correlaion beween oil prices and he U.S. dollar exchange raes. Occasionally, here may be forces, such as ineres rae movemens or he global growh oulook, ha simulaneously increase or decrease oil prices and he value of he dollar, resuling in a posiive correlaion beween he wo. Hence, I es he hypohesis of a ime-varying correlaion beween crude oil prices and he U.S. dollar exchange raes. To he bes of my knowledge, his is he firs sudy o examine wheher he condiional covariance and correlaion beween crude oil prices and he U.S. dollar exchange raes vary over ime. Alhough he relaionship beween oil prices and he dollar value has been invesigaed previously, no sudy has ye focused on he ime-varying correlaion beween he wo and his paper is a firs sep oward filling his gap. The paper is organized as follows. The daa is presened in Secion 2. Secion 3 analyzes he bivariae GARCH model for he condiional covariance beween crude oil prices and he U.S. dollar exchange raes. Secion 4 presens he resuls and Secion 5 concludes he paper. 5 See, for example, Bollerslev e al. (1988) [9], Harvey (1989) [10], Bodurha and Mark (1991) [11], Fleming, Kirby, and Osdiek (1998) [12] and Goeij and Marquering (2004) [13].

6 108 Duong Le 2 Daa The crude oil daa used in his sudy consis of daily closing prices of fuures conracs raded on he New York Mercanile Exchange (NYMEX). Crude oil fuures conracs, which began rading on he NYMEX on March 30, 1983, rade in unis of 1,000 U.S. barrels. The sample period is January 1, 1997 o December 31, 2012 oaling 4,010 daily observaions. This sample period includes boh he fall and rise of oil prices and U.S. dollar value where he years 2002 and 2008 are supposedly he principal urning poins. Crude oil prices are from he Energy Informaion Adminisraion, downloaded from hp:// Fuures prices are used in place of spo prices for he following reasons. Firs, fuures prices are he major prices in he crude oil marke. The NYMEX crude oil fuures conrac is he world's mos liquid forum for crude oil rading and is used as a principal inernaional pricing benchmark. Crude oil fuures prices are also he prices repored in newspapers. Second, he fuures marke for crude oil is liquid and cenralized while spo markes are localized and illiquid. Third, fuures prices are he prices normally used in mos oil risk managemen conracs such as swaps and opions. To examine volailiy in a GARCH ype framework, I uilize daily log reurns 6 defined as r 1, =ln(p /P -1 ) wherein P is he price of he fuures conrac on day and P -1 is he price of he same conrac he previous day. As raders ofen cover heir posiions on he las rading day of a conrac s life, rading volume and open ineres decline and price volailiy increases subsanially. To avoid his hin marke problem, in consrucing he r series I replace he reurn of he neares conrac on is las rading day of each monh wih ha of he second neares conrac. As a measure of he exchange value of he dollar, I use he rade-weighed average of he foreign exchange value of he U.S. dollar agains a subse of he broad index currencies ha circulae widely ouside he counry of issue, including he Euro Area, Canada, Japan, Unied Kingdom, Swizerland, Ausralia, and Sweden. The exchange index daa is from he Federal Reserve Saisical releases, downloaded from he following websie (daily h10 repors): hp:// The index value is se 100 in March 1973 and calculaed using he formula: N() wj, 1 ( j, / j, 1), j 1 EI EI e e where EI is he value of he index a ime, e j, and e j,-1 are he prices of he U.S. dollar in erms of foreign currency j a imes and -1, w j, is he weigh of currency j in he index a ime (based on annual daa on inernaional rade), N() is he number of foreign currencies in he index a ime, and w, 1. I also uilize daily log reurns for he U.S. dollar exchange rae which is defined as r 2, =ln(ei /EI -1 ) wherein EI is he index value on day and EI -1 is he index value he previous day. j j 6 The daily crude oil reurns are used o measure price changes only. These reurns are no invesmen reurns since no money is acually invesed.

7 Relaionship beween Crude Oil Prices and he U.S. Dollar Exchange Raes 109 Table 1: Descripive saisics for daily log changes of crude oil prices and U.S. dollar exchange raes Crude oil U.S. dollar s value Mean (x10 2 ) Minimum Maximum Sandard deviaion Annualized Sandard deviaion Skewness Kurosis This able gives descripive saisics for he daily log changes of crude oil prices and U.S. dollar s exchange index value for he period from January 01, 1997 o December 31, Table 1 provides a summary of he descripive saisics a he daily frequency. Boh log changes in crude oil prices and U.S. dollar exchange raes are characerized by excess kurosis, indicaing ha heir empirical disribuions have faer ails han a normal disribuion. Moreover, as illusraed in Figure 1, crude oil prices and he dollar exchange raes exhibi volailiy clusering in ha large price changes end o be followed by large price changes of eiher sign. GARCH models are aracive and empirically successful in ha hey are, o a large exen, able o explain boh he volailiy clusering behavior and he excess kurosis of he empirical disribuion of reurns. 3 Model Specificaion I uilize a mulivariae generalized auoregressive condiional heeroskedasiciy (GARCH) model o es for a ime-varying covariance beween crude oil prices and he U.S. dollar exchange raes. While he GARCH specificaion does no follow any economic heory, i provides a good approximaion o he heeroskedasiciy ypically found in financial imeseries daa. The developmen of mulivariae GARCH models represens a major sep forward in he modeling of volailiy since hese models allow for ime-varying condiional variances as well as covariances. Among various mulivariae GARCH models in he lieraure 7, he Diagonal VECH model inroduced by Bollerslev, Engle and Wooldridge (1988) [9] is one of he mos popular since i is a naural exension of he univariae GARCH model and is easy o undersand. Moreover, recen sudies by Ferreira and Lopez (2005) [23] and Bauwens, Lauren and Rombous (2006) [24] show ha among he mos popular mulivariae models, he diagonal VECH seems o provide he bes ou-of-sample (co)variance forecass. In he general Diagonal VECH model, he condiional covariance follows a mulivariae GARCH (1,1) process: 7 Some examples include Harvey (1989) [10], Bollerslev (1990) [14], Bodurha and Mark (1991) [11], Ng (1991) [15], Ng, Engle, and Rohschild (1992) [16], Braun, Nelson, and Sunier (1995) [17], Engle and Kroner (1995) [18], Nijman and Senana (1996) [19], Ng and Kroner (1998) [20], Ding and Engle (2001) [21], and Engle (2002) [22].

8 110 Duong Le H A ε ε B H (1) ' (7) where H is he condiional covariance marix a ime, he coefficien marices AB, and are NxN symmeric marices, and he operaor denoes he Hadamard produc (elemen by elemen marix muliplicaion). Since H mus be symmeric, so mus be he parameer marices, and only he lower porions of hese marices need o be parameerized and esimaed. I hypohesize ha he condiional covariance marix of crude oil and exchange rae reurns follows a bivariae GARCH process and esimae he following Diagonal VECH model: r μ ε (8) (2) ε ~ N(0, H ) ' (7) H A ε ε B H (1) where r ( r1,, r2, )' is a (2x1) vecor conaining crude oil and exchange rae reurns and H is a (2x2) condiional covariance marix. Le H follow he mos unresriced process among all Diagonal VECH models where he parameers in he marices, A, and B are allowed o vary wihou any resricion, he model may be wrien in single equaion forma as: ( H ) ( ) ( A ) ( B) ( H ) (9) (3) ij ij ij j, 1 i, 1 i, j 1 ij where, for insance, ( H ) is he i-h row and j-h column of marix H. is a (3x1) ij parameer vecor; A and B are (3x3) diagonal parameer marices. The covariance equaions are esimaed by maximum likelihood. 4 Resuls This secion presens he esimaion resuls of he ineremporal correlaion beween crude oil prices and he U.S. dollar exchange raes.

9 Relaionship beween Crude Oil Prices and he U.S. Dollar Exchange Raes 111 Table 2: The Diagonal VECH model of he crude oil and U.S. dollar exchange rae covariance marix Univariae GARCH (1,1) Diagonal VECH U.S. dollar s Crude oil price value Ω(1,1) ** ** (0.0005) (0.0005) Ω(1,2) * (0.0020) Ω(2,2) *** *** (0.0437) (0.0421) A(1,1) *** *** (0.0053) (0.0050) A(1,2) *** (0.0074) A(2,2) *** *** (0.0067) (0.0064) B(1,1) *** *** (0.0074) (0.0071) B(1,2) *** (0.0275) B(2,2) *** *** (0.0123) (0.0118) This able repors he maximum-likelihood esimaion resuls of Equaions (1-2) using daa from January 1, 1997 o December 31, 2012 (T=4,010). Sandard errors are shown in parenheses. ( *** ), ( ** ) and ( * ) designae esimaes significanly differen from zero a he 0.001, 0.01 and 0.05 levels, respecively. Esimaion resuls from specificaion (1-2) are presened in he fourh column of Table 2. In order o provide some inuiion on he bivariae model parameers, I presen he esimaes of he univariae GARCH(1,1) specificaion for exchange rae and crude oil volailiies in he second and hird columns of Table 2. Resuls from Table 2 indicae ha he bivariae GARCH esimaes of volailiy persisence for exchange rae and crude oil reurns are close o, and no significanly differen from, he univariae GARCH (1,1) esimaes. The esimae of (1,2), he uncondiional mean of he covariance beween crude oil and exchange rae reurns, is negaive and significan a he 0.05 level, which is consisen wih he observaion of a negaive correlaion beween crude oil prices and he value of he dollar.

10 112 Duong Le The esimaes of A(1,2) and B(1,2) (he ARCH and GARCH erms in he covariance equaion) are boh posiive and significan a he 0.01 level, implying ha he covariance beween crude oil prices and he value of he dollar ends o cluser over ime. The posiive esimae for A(1,2), he ARCH erm, means ha shocks o oil prices and he U.S. dollar exchange raes of he same sign affec he condiional covariance posiively, while shocks of opposie signs affec he forecased covariance negaively. Apparenly wo negaive (or posiive) shocks lead o a significan increase in nex period s covariance. Given ha he uncondiional mean of he covariance, Ω(1,2), is significanly negaive, wo shocks of he same sign would decrease and wo shocks of opposie signs would increase he prediced covariance in absolue value erms. A significanly posiive esimae of A(1,2) also indicaes ha causes of he correlaion beween oil prices and he dollar s value end o persis. If on one day he change in he dollar price of oil is largely due o a change in he dollar s value, here is a endency for he nex day s change in oil prices o be primarily caused by changes in he dollar s value as well. On he oher hand, if on one day he change in he dollar price of oil is caused primarily by facors oher han he dollar s value, here is a endency for hose o be he primary causes of changes in he dollar price of oil on subsequen days. To examine wheher he ime variabiliy in he covariance of crude oil and exchange rae reurns is solely due o variaion in he wo variances, I calculae he condiional correlaion coefficien a ime +1, : 12, 1 Cov{ r1, 1, r2, 1) 12, 1 (4) Var ( r ) Var ( r ) 1, 1 2, 1 If ρ 12,+1 is consan over ime, he variabiliy in covariance is solely due o variaion in variances. In ha case, modeling of ime-varying covariances is no very ineresing, as all he dynamics are capured in variances. To es he null hypohesis of a consan correlaion coefficien, I esimae he Consan Condiional Correlaion (CCC) model and es he Diagonal VECH model agains he CCC model. The likelihood raio es saisics is 9.8 wih 2 degrees of freedom and significan a he 0.01 level. Therefore, he Consan Condiional Correlaion hypohesis is rejeced, clearly showing ha he correlaion beween oil prices and he value of he dollar is no consan over ime. Consequenly he variabiliy in covariances is no solely due o ime-varying variances, and modeling ime-varying covariances is imporan. Figures 3 and 4 presen he plos of he condiional covariance forecass and he esimaed correlaion coefficien over ime, based on he esimaion resuls of he diagonal VECH model as presened in Table 2. The figures show ha he condiional covariance and he correlaion coefficien vary considerably over ime.

11 Relaionship beween Crude Oil Prices and he U.S. Dollar Exchange Raes 113 Figure 3: Condiional covariance beween crude oil prices and he value of he dollar Figure 4: Condiional correlaion beween crude oil prices and he value of he dollar 5 Summary and Conclusions Crude oil prices and he U.S. dollar value end o move ogeher, and appear o have been negaively correlaed in recen years. A dollar appreciaion (depreciaion) is ypically associaed wih lower (higher) oil prices. This paper aims o analyze he ineremporal ineracion beween crude oil prices and he U.S. dollar exchange raes from January 1997 hrough December To his end, he sudy assumes ha he condiional covariance marix follows a bivariae GARCH process. The conribuion his paper makes is o provide srong evidence of a ime-varying condiional covariance and correlaion beween oil prices and he U.S. dollar exchange value.

12 114 Duong Le ACKNOWLEDGEMENTS: I am graeful o Louis Ederingon for helpful commens and suggesions. I benefied from he commens of Duane Sock, Chiru Fernando, Sco Linn, Xin Huang and paricipans in he Finance workshop a he Universiy of Oklahoma. All misakes remain my responsibiliy. References [1] S. Zhou, The response of real exchange raes o various economic shocks, Souhern Economic Journal, vol. 61, 1995, pp [2] K. Chaudhuri and B. Daniel, Long-run equilibrium real exchange raes and oil prices, Economic Leers, vol. 58, 1998, pp [3] R.A. Amano and S. Van Norden, Exchange raes and oil prices, Review of Inernaional Economics, vol. 6, 1998, pp [4] R.A. Amano and S. Van Norden, Oil prices and he rise and fall of he US real exchange rae, Journal of Inernaional Money and Finance, vol. 17, 1998, pp [5] SS. Chen and HC. Chen, Oil prices and real exchange raes, Energy Economics, vol. 29, 2007, pp [6] R.A. Lizardo and A.V. Mollick, Oil price flucuaions and U.S. dollar exchange raes, Energy Economics, vol. 32, 2010, pp [7] YJ. Zhang, Y. Fan, HT. Tsai and YM. Wei, Spillover effec of US dollar exchange rae on oil prices, Journal of Policy Modeling, vol. 30, 2008, pp [8] V. Couder, V. Mignon and A. Peno, Oil price and he dollar, Energy Sudies Review, vol. 15, 2008, pp [9] T. Bollerslev, R. Engle and J.M. Wooldridge, A Capial Asse Pricing Model wih ime varying covariances, Journal of Poliical Economy, vol. 96, 1988, pp [10] C.R. Harvey, Time-Varying Condiional Covariances in ess of asse pricing models, Journal of Financial Economics, vol. 24, 1989, pp [11] J.N. Bodurha and N.C. Mark, Tesing he CAPM wih ime-varying risks and reurns, Journal of Finance, vol. 46, 1991, pp [12] J. Fleming, C. Kirby and B. Osdiek, Informaion and volailiy linkages in he sock, bond, and money markes, Journal of Financial Economics, vol. 49, 1998, pp [13] P. Goeij and W. Marquering, Modeling he condiional covariance beween sock and bond reurns: A Mulivariae GARCH approach, Journal of Financial Economerics, vol. 2, 2004, pp [14] T. Bollerslev, Modelling he coherence in shor-run nominal exchange raes: a Mulivariae Generalized Arch Model, Review of Economics and Saisics, vol. 72, 1990, pp [15] L. Ng, Tess of he CAPM wih ime-varying covariances: A Mulivariae GARCH approach, Journal of Finance, vol. 46, 1991, pp [16] V. Ng, R.F. Engle and M. Rohschild, A muli-dynamic-facor model for sock reurns, Journal of Economerics, vol. 52, 1992, pp [17] P.A. Braun, D.B. Nelson and A.M. Sunier, Good news, bad news, volailiy, and beas, Journal of Finance, vol. 50, 1995, pp [18] R.F. Engle and K.F. Kroner, Mulivariae Simulaneous Generalized ARCH, Economeric Theory, vol. 11, 1995, pp

13 Relaionship beween Crude Oil Prices and he U.S. Dollar Exchange Raes 115 [19] T. Nijman and E. Senanab, Marginalizaion and conemporaneous aggregaion in mulivariae GARCH processes, Journal of Economerics, vol. 71, 1996, pp [20] V. Ng and K.E. Kroner, Modeling asymmeric comovemens of asse reurns, Review of Financial Sudies, vol. 11, 1998, pp [21] Z. Ding and R.F. Engle, Large scale condiional covariance marix modeling, esimaion and esing, Working Paper, NYU Sern School of Business (2001). [22] R. Engle, Dynamic condiional correlaion: A simple class of Mulivariae Generalized Auoregressive Condiional Heeroskedasiciy models, Journal of Business and Economics Saisics, vol. 20, 2002, pp [23] M.A. Ferreira and J.A. Lopez, Evaluaing ineres rae covariance models wihin a Value-a-Risk framework, Journal of Financial Economerics, vol. 3, 2005, pp [24] L. Bauwens, S. Lauren and J.V.K. Rombous, Mulivariae GARCH models: A survey, Journal of Applied Economerics, vol. 21, 2006, pp