A New Approach o Combine conomeric Model wih ime-series Analyses-An mpirical Sudy of Inernaional xchange Markes Ming-Yuan Leon Li Assisan Professor Deparmen of Accounancy Graduae Insiue of Finance and Banking Naional Cheng Kung Universiy, aiwan L: 886-6-2757575 ex. 5342, FAX: 886-6-274404 -mail: lmyleon@mail.ncku.edu.w
A New Approach o Combine conomeric Model wih ime-series Analyses-An mpirical Sudy of Inernaional xchange Markes Absrac his paper uses he Markov-swiching (MS) mechanism o creae a composie model wih an endogenous and non-consan loading on boh of economeric model and ime-series approach. he empirical daa include he monhly U.S. dollar exchange raes of he currency of four indusrialized counries including France, Germany, U.K. and Japan as well as wo Asian developing counries including Souh Korea and aiwan from 980 o 2000. Our empirical findings are consisen wih he following noions. Firs, he forecasing performances of he composie model wih non-consan weigh ouperform each echnique and random walk model in all cases. In conras, he performances of he composie model wih consan weigh are unremarkable. Second, he sae of low (high) volailiy corresponds o he sae of he forecasing echnique of ime-series approach (economeric model). hird, we denoe he high volailiy sae of exchange markes of Souh Korea (indusrialized counries) as a crisis (an unusual) condiion. Moreover, he fundamenal variables derived from economic heories would be invalid (valid) during he crisis sae (unusual sae) for Souh Korea (he indusrialized counries). Keywords: exchange rae, ARMA, economeric model, Markov-swiching model, Volailiy JL Code: G5, F3, F37 2
. Inroducion conomeric model for generaing exchange rae forecass are based on fundamenal analysis. hey ry o measure and quanify he relaionships beween exchange raes and a se of economic fundamenals. However, he difficuly in predicing he exchange raes has been a longsanding problem in inernaional economics. In a highly influenial paper, Meese and Rogoff (983) noe ha he forecas performances of exchange raes produced by economeric models based on fundamenals are no beer han hose using random walk models. ven some recen sudies have found some success a forecasing changes in exchange raes a longer horizons or using nonlinear mehods (please refer o MacDonald and aylor (994), Chinn and Meese (995), Mark (995), Groen (2000), Mark and Sul (200), Kilian and aylor (2003)), however, he Meese-Rogoff resuls have no been convincingly overurned. Specifically, here are no srong evidences o prove any given economeric models/specificaions as being very successful. In oher words, one economeric model migh do well for one exchange rae, bu no for anoher. Because of unremarkable predicion performances of economeric models based on fundamenal variables, some economeriss propose ime-series approaches o analyze he exchange raes. he ideas of ime-series approaches are based heir expecaions of fuure changes of exchange raes solely on he pas behaviors of 3
exchange raes, under he assumpion ha he lagged values of he change of he lagged exchange raes could be used o predic heir fuure values. In oher words, he ime-series analyss do no believe in economic heories and assume ha hey are beer off allowing he daa o deermine he models. Among various kinds of ime-series models, ARMA (AuoRegressive Moving Average) model could serve as he represenaive. Review he prior sudies which adoped he framework of ARMA model. Pong, Shackleon, aylor and Xu (2004) used hem o forecas currency volailiies. Aguirre and Saidi (2000) incorporae ARMA models wih hreshold model o es he asymmeries in exchange raes. schernig (995) used hem o examine he long memory behavior in exchange raes. Nijman, Palm and Wolff (993) employed hem o analyze risk premium in forward foreign exchange raes. In his paper, we ake a new line of aack on he quesions of he link beween economeric models and ime-series approaches. In deail, his paper raises an ineresing quesion: could we design a composie model ha incorporaed boh of economeric models and ime series echniques? he underlying idea is ha he informaion from boh of fundamenal variables derived from economic heory and heir own lagged variables should be valuable for marke paricipans. Specifically, we believe ha porfolio managers should weigh he informaion form fundamenal variables from economic heories and he own lagged daa. Moreover, in some periods, 4
we announce ha managers would lisen o he economeric models (ime-series approach) wih more (less) aenion and vice versa. Following he above line of houghs, his paper esablishes and examines a composie model from economeric models and ime-series approaches on he exchange raes. Neverheless, one of he main obsacles is he decision of weigh on each of hese wo differen forecasing echniques. In his paper, we employ he Markov Swiching (MS) mechanism o decide he ime-varying weigh on various alernaives. In brief, we se up a framework wih wo saes o capure wo differen forecasing alernaives. Moreover, one of feaures of MS model is o esimae he probabiliies of specific sae a each ime poin by daa iself. In his paper, we use he esimaed and ime-varying probabiliies o serve as he weigh of each echnique. Furhermore, one quesion we wan o address and examine is: Do he composie models wih ime-varying loading ouperform each of hese wo echniques and he random walk models? Our work is relaed o he model in ngle and Hamilon (990). hey also employed he MS echniques and examine he long swing behaviors of exchange raes. However, here are several remarkable difference poins in his paper. Firs, in conras wih hem defining he seing wih wo saes on he consan erms of regression equaion, we esablish and examine a framework wih wo saes on he slop erms. 5
Second, ngle and Hamilon (990) focus on discussing he nonlineariy of firs momen for he quarerly exchange raes. We highligh he discussions of he second momens for he monhly daa. By examining he realized percenage change in he exchange raes, we can find hey are much more volaile during cerain periods. he derivaive quesion is: wha are he relaionships beween he various volailiy regimes and various forecasing echniques? Specifically, does he siuaion of high volailiy regime correspond o he ime-series approaches or economeric models? Las bu no he leas, because of mos of relaive prior sudies concenraing on analyzing he exchange raes ofindusrialized counries curency, one of he feaures of our paper is ha we are more ineresed in examining he exchange raes of developing counries curencies and compare he diferences beween hem. he nex secion esablishes our empirical models. In Secion 3, we presen our empirical resuls. In secion 4, we provide several discussions and explanaions for our empirical findings. Las, we conclude our paper in Secion 5. 2. Model Specificaions () ime-series Approach We adop he ARMA (, ) o sever as a represenaive ime-series approach. he ARMA (, ) seing is presened as following: 6
y u, u ~ N(0, ) () y 2 u In he above seing, y and y - are he percenage change in he exchange rae in ime and ime -, respecively. u and u - are he residual erm in ime and ime -, respecively and follow he Gaussian disribuion wih sandard error σ. Specifically, we use he β and β 2 o capure he impacs of he one-period-ahead percenage change in he exchange rae (y - ) and is residual erm (u - ) on he curren percenage change in he exchange rae (y ), respecively 2. (2) conomeric Model In his paper, we use wo economic fundamenals, such as he inflaion differenials (derived from Purchasing Power Pariy) and he ineres rae differenials (derived from Ineres Rae Pariy) o esablish he following regression 3 : y u, u ~ N(0, ) (2) * * ( ) 2 ( r r ) In he above seing, π - and π * - (r - and r * -) presen he inflaion raes (ineres We adop he percenage changes in he exchange raes insead of he exchange raes o achieve saionariy. he Dickey-Fuller es (no repored here) shows ha all of he daa series adoped in his paper rejec he null hypohesis of uni roo. 2 Surely for each counry we can find and use he bes ARMA model. However, in his paper, we do no arge on finding he bes ARMA model. In brief, he adopion of simple ARMA (, ) in his paper is accepable for convenience. 3 here are some oher fundamenal variables o explain he exchange raes, such as relaive money supplies and relaive real income as well as relaive accoun balances. However, he arge of his paper is no o find he bes economeric model for he exchange raes. herefore, for he reasons of convenience, we only adop wo fundamenal variables o esablish he economeric model. 7
raes) of home and foreign counries in ime -, respecively. u is he residual erm in ime and follows he Gaussian disribuion wih sandard error σ. Specifically, we use he β and β 2 o capure he impacs of one-period-ahead inflaion differenials (π - -π * -) and ineres differenials (r - -r * -) on he curren percenage change in he exchange rae (y ), respecively. (3) Composie Models For capuring boh he informaion from he fundamenal variables and he lagged percenage changes in he exchange raes, we creae he following wo kinds of composie models. (a) Composie Model wih Consan Weigh y u, (3) * * ( ) 2 ( r r ) y 2 u u ~ N(0, ) Inuiively, he above regression considers boh of he wo fundamenal including (π - -π * -) and (r - -r * -) as well as wo ime-series componens including y - and u - as he explanaion variables for he percenage change in he exchange rae, y. he poenial disadvanage of he seing is o lisen o each echnique wih equal concern. Specifically, we can rewrie he above equaion as following: 8
9 ] [ )] ( ) ( [ 2 * 2 * u y r r y (4) In deail, he above equaion does is o inroduce a mehod which consiss of a specificaion including all he explanaory variables appearing in boh of he separae forecasing equaions. Moreover, he consan, in he quaion 4 represens ha he loading of he informaion from each echnique is equal and fixed a any ime poin. herefore, in he following discussions, we name he above specificaion as he composie model wih consan weigh. (b) Composie Model wih Non-consan Weigh For solving he poenial demeri of he design of consan weigh on each echnique, we use he MS mechanism o design he following model specificaion: u r r y ) ( ) ( * 2 *, ) (0, ~ N u, when s = u u y y 2, ) (0, ~ N u, when s = (5),where s is an unobservable sae variable and follows a Markov chain wih one order:
p( s p( s s s ) p ) p,, p( s p( s s s ) p ) p (6) In he above seing, we denoe s = () o represen he sae of economeric model (ime-series approach). Here we wan o denoe ha. ven he sae variable, s is unobservable, bu we can use he daa o esimae he probabiliy of specific regime a any ime period. When he informaion se for esimaion includes signals daed up o ime, he regime probabiliy is p(s I ) or filering probabiliy. On he oher hand, one could also use he overall sample period informaion se o esimae he sae a ime : p(s I ) or smoohing probabiliy. In conras, a predicing probabiliy denoes he regime probabiliy for an ex ane esimaion, wih he informaion se including signals daed up o he period -: p(s I - ) 4. Inuiively, a he sandpoin of, a he end of he es period, we can predic he smoohing probabiliy measure is wih more informaion. By he same logic, since we use he informaion from he curren period in measuring he filering probabiliy, is accuracy and smoohness rank in beween hose of predicing and smoohing probabiliies. In his paper, we use he smoohing probabiliy (namely, p(s I ), where I means he informaion se from he beginning period o he las period) o serve as he loading of each echnique. Specifically, he predicion measure of he percenage 4 Please refer o Hamilon (989) for he esimaion process of he probabiliy of specific sae. 0
change in he exchange rae a he period (namely, y e ) can be presened as he following: y e p ( s p ( s I I ) [ ( ) [ y * ) ( r 2 u ] 2 r * )] (7) Comparing quaions 4 and 7, one can easily find he main difference beween he wo composie models. Specifically, he seing wih consan weigh uses an exogenous and equal loading o evaluae he impac of each forecasing echnique. In conras, he specificaion in quaion 7 employs an endogenous and non-consan loading. In oher words, he probabiliy of specific sae (namely, p(s I )) is esimaed by daa iself and will change over ime. In he following discussions, we denoe he model specificaion as he composie model wih non-consan weigh. o conclude, even each composie model lisens o he informaion from boh of he fundamenal variables and he own lagged values, neverheless, he seing wih consan weigh ignore he characers ha managers migh more lisen o he macroeconomic variables han lagged reurns in some periods and vice versa. In oher words, he loading on each forecasing echnique migh be changeable a differen ime poin. herefore, we esablish a composie mode wih non-consan weigh in which adops he MS mechanism o idenify wo possible regimes. Specifically, in he
regime of economeric model, he percenage change in he exchange rae depends on he fundamenal variables in conras wih he regime of ime-series approach in which he percenage change in he exchange rae lisens o heir own lagged values. Las, we employ he esimaed probabiliy of specific sae a each ime poin o serve as he ime-varying loading on each forecasing echnique. I is worh noing ha we assume he consan erm, αin quaions 5 and 7 is he same for he wo differen saes. In conras, ngle and Hamilon (990) se up a seing wih wo measures of αo capure he long swing behaviors of he exchange raes. he behind ideas of our model designs are ha we focus on disinguishing wo ses of informaion, namely he fundamenals variables versus he own lagged values. herefore, we define he consan erm, αo be fixed a each sae. In brief, all of he forecasing alernaives in his paper have one measure of consan erm. his design is for excluding he poenial noises from various seings on he consan erm and concenraing on discussing he problems of how o weigh he informaion from he wo differen ses of explanaory variables. Furhermore, in he composie model wih non-consan loading esablished by our paper, we se up wo measures of he sandard error o capure he behaviors ha various echniques migh correspond o various volailiy measures. Specifically, in quaion 5, he echnique of economic model (ime-series approach) is associaed 2
wih he measure of volailiy, σ (σ ). 3. mpirical Resuls he daa used in his paper are he monhly bilaeral exchange raes (in U.S. dollars per uni of foreign currency) for he currency of four indusrialized counries (France, Germany, U.K. and Japan) and wo Asian developing counries (Souh Korea and aiwan). In he following discussions, he U.S. represens he foreign counry and each of oher six counries (including four indusrialized and wo Asian developing counries) represens he home counry. he daa period is from January, 980 o Augus, 2000 for 248 observaions. he proxies of ineres raes and inflaion raes are hree-monh reasury raes and change raes of CPI (consumer price index) index, respecively. Daa source is ARMOS daabase. We use OPIMUM, a package program from GAUSS, and he buil-in BFGS7 algebra o ge he negaive minimum likelihood (ML) funcion value of all specificaions 5. For examining he forecasing performances of various alernaives, we adop wo common crieria such as () MS (Mean Square rror) and (2) MA (Mean Absolue rror). he definiions of hem can be expressed as: MS e 2 ( y y ) (8) 5 We randomly generae 50 ses of iniial values, and hen derive he ML funcion value for each of he 00 ses of iniial value respecively. he mapped converged measure of he greaes ML funcion value hen serves o esimae he parameer. 3
MA e y y (9),where y e and y denoe he predicing and realized values of exchange rae reurns, respecively and is he number of observaion. Moreover, we employ he random walk model as a benchmark o calculae he forecasing error reducions percenage relaive o he random walk model for various alernaives. able presens he percenage of forecas error reducions for various forecasing alernaives. Remarkably, he percenages of forecas error reducion of he composie model wih non-consan weigh are greaer han zero and greaer han he measures of oher alernaives in mos cases 6. In conras, he performances of he composie model wih consan weigh are unremarkable. In brief, he percenages of forecas error reducion of he composie model wih consan weigh are negaive and less han one single forecasing echnique for many cases. Our conclusion is clear. he design of ime-varying loading esablished in his paper can enhance predicion performances on he exchange raes. Panels (a) and (b) of able 2 presens parameer esimaes of he composie model wih consan and non-consan weigh, respecively. Firs, examining he 6 xcep he MA in he case of he U.K., he composie model wih non-consan loading esablished in his paper performs a maximum forecasing error reducion performance for all cases. 4
resuls of he composie model wih non-consan loading, he esimae of σ is greaer han σ for all cases. Consequenly, we denoe he sae of () as he high (low) volailiy sae. hese findings are consisen wih he noion ha he high (low) volailiy marke sae will correspond o he forecasing echnique of economic model (ime-series approach). Second, he wo parameers of ARMA componen (namely, β and β 2 ) in he composie wih non-consan loading are significan for all cases 7. In conras, he wo ARMA parameers in seing wih consan weigh are insignifican for he wo cases of Japan and Souh Korea. hese resuls are consisen wih he noions ha one can find more remarkable impacs of he own lagged daa on he percenage change in he exchange rae afer filering ou he high volailiy periods. hird, examining he significance of he wo parameers of fundamenal variables (namely, β and β 2 ) in he seing wih non-consan loading, he β (β 2 ) is significan for he cases of France and Germany (U.K., Japan and aiwan). However, boh of he β and β 2 are insignifican for he case of Souh Korea. hese findings are consisen wih he following noions ha. During he high volailiy periods, he fundamenals variables are invalid (valid) for he case of Souh Korea (oher five cases). 7 In he case of he U.K., he β 2 (β ) is significan (insignifican). Moreover, boh of β and β 2 are significan for oher five cases. 5
4. conomic and Financial xplanaions for Our mpirical Resuls In his secion, we summarize our main empirical resuls and provide he economic and financial explanaions o hem. Firs, he composie model wih non-consan loading on wo forecasing echniques ouperforms he seing wih consan loading. his resul is consisen wih he noion ha exchange markes would lisen o boh of fundamenal variables and he own lagged values o deermine he value of he exchange rae in he nex period. Moreover, he loading of each se of explanaory variables is non-consan and will change over ime. Second, our empirical findings indicae ha he high (low) volailiy sae corresponds o he forecasing echnique of economic model (ime-series approach). Here we provide an explanaion for his resul. From he perspecive of nonlinear adjusmen, one would srongly expec he speed of convergence oward heoreical values which are derived from economic heories should be greaer as he deviaion from heoreical values rise in absolue value. Moreover, because he heoreical exchange raes are sable, he grea/small deviaion from heoreical values should be well associaed wih he high/low volailiy sae. his is one of reasons of why he sae of economic model wih he fundamenal variables corresponds o he sae of high volailiy. On he oher hand, he sae of ime-series approach wih he own lagged values corresponds o he sae of low volailiy. his finding denoes ha 6
invesors migh well picure he fuure exchange raes via heir own pas values during he sable periods. Las, our empirical resuls indicae ha, afer filering ou he high volailiy periods, he wo lagged values in he ARMA approach are significan for all cases. However, during he volaile period, he fundamenal variables are insignifican (significan) for he case of Souh Korea (oher five cases). In able 3, we use (σ /σ ) o evaluae he measure of volailiy a high volailiy sae relaive o low volailiy sae for various currencies. Quie ineresing, he values of (σ /σ ) for indusrialized counries currencies are absoluely smaller han he developing ones. Specifically,.777,.590,.708 and.69 (3.543 and 4.58) are for France, Germany, U.K. and Japan (Souh Korea and aiwan), respecively. Regarding he above findings, our explanaions are consisen wih he following noions. In his paper, we use Souh Korea and aiwan o serve as wo represenaive developing counries. he policy of he wo developing counries is o peg heir curencies value o he U.S. dollar, however, heir currencies exremely suffered from he Asian crisis in 997. By using France and Souh Korea as wo represenaive examples, Figure presens heir monhly percenage changes in he exchange rae and smoohing probabiliy of high volailiy sae (namely, he sae of ). Apparenly, he sae-varying framework of MS model idenifies he 997 crisis period as a high 7
volailiy regime for he case of Souh Korea. In conras, he high volailiy regime for he case of France is jus an uncommon, no crisis, period. his is why he (σ /σ ) values of developing counries currencies are much greaer han he indusrialized ones. Moreover, during he 997 Asian crisis periods, Souh Korea was faced wih subsanial dollar depreciaions and large scale of capial flighs. hese capial flighs would more accelerae o diminish cenral bank s reserve, and cause cenral bank o lack srengh o inervene he exchange marke again. So he exchange rae volailiy would be a lager amoun han planed. his is why he value of (σ /σ ) for he case of Souh Korea is much graer han oher cases. Besides, he crisis period would be associaed wih invesors irraional overreacion behaviors. Furhermore, hese irraional behaviors could provide a reason why he fundamenal variables derived from he economic heories would be invalid during he exreme high volailiy periods for he case of Souh Korea. Unlike he case of Souh Korea, we denoe he high volailiy sae of indusrialized counies as an unusual condiion, no a crisis siuaion. herefore, we can find fundamenal variables are valid on explaining he exchange rae during he volaile period. In deail, he inflaion differenials (he ineres rae differenials) are significan for he cases of he cases of France and Germany (U.K. and Japan). 8
Las, regarding he case of aiwan, he sae-varying framework of MS model also idenify he 997 Asian financial crisis period as a high volailiy regime for i (no repored here). However, aiwanwas one of Asia s few sar performers compared wih is recession-hi neighbors during he Asian financial crisis in 997 8. Moreover, our empirical findings show ha he value of (σ /σ ) for he case of aiwan is 4.53 and i is much smaller han he value of 3.543 for he case of Souh Korea. herefore, we recognize he high volailiy sae of aiwan as an unusual condiion, no a crisis regime. Moreover, his can explain why he ineres rae differenials are significan during he high volailiy regime for he case of aiwan. 5. Conclusion In his paper, we adop he MS mechanic o esablish a composie model wih an endogenous and non-consan loading on each of ime-series approach and economeric model. he U.S. dollar exchange raes of he currencies of four indusrialized counries including France, Germany, U.K. and Japan and wo Asian developing counries including Souh Korea and aiwan serve as he represenaive examples in his paper. Our empirical resuls are consisen wih he following noions. Firs, he forecasing performances of he composie model wih non-consan weigh ouperform oher alernaives and random walk models in all cases. In conras, he 8 One can also refers o aiwan Is Ye o Find Profi in Asia s Woes, A5, he Wal Sree Journal, Augus 9, 998. 9
performances of he composie model wih consan weigh are rivial. Second, he sae of low (high) volailiy regime corresponds o he sae of he forecasing echnique of ime-series approach (economeric model). hird, afer filering ou he high volailiy periods, he AR and MA commens are remarkable. Las, we denoe he high volailiy sae of he exchange marke of Souh Korea as a crisis regime in conras wih an unusual condiion for oher cases. Moreover, he fundamenal variables would be invalid during he crisis sae for he case of Souh Korea; however, hey are valid during he unusual condiion for oher cases. 20
References Aguirre, M. S. and Saidi, R. (2000), Asymmeries in he Condiional Mean and Condiional Variance in he xchange Rae: vidence from wihin and across conomic Blocks, Applied Financial conomics, 0, 40-43. Chinn, M. D. and Meese, R. A. (995), Banking on Currency Forecass: How Predicable Is Change in Money? Journal of Inernaional conomics, 38, 6-68. ngel, C. and Hamilon, J. D. (990), Long Swings in Dollar: Are hey in he Daa and Do Markes Know I? American conomic Review, 80, 689-73. Groen, J. J. (2000), he Moneary xchange Model as a Long-Run Phenomenon, Journal of Inernaional conomics, 52, 299-39. Hamilon, J. D. (989), A New Approach o he conomic Analysis of Nonsaionary ime Series and he Business Cycle, conomerica, 57, 357-384. Kilian, L. and aylor, M. P. (2003), Why is I so Difficul o Bea he Random Walk Forecass of xchange Raes? Journal of Inernaional conomics, 60, 85-07. Mark, N. C. (995), xchange Raes and Fundamenals: vidence on Long-Horizon Predicabiliy, American conomic Review, Vol. 85, 20-28. Mark, N. C. and Sul, D. (200), Nominal xchange Raes and Moneary Fundamenals: vidence from a Small Pos-Breon Woods Sample, Journal of Inernaional conomics, 53, 29-52. MacDonald, R. and aylor, M. P. (2003), he Moneary Approach o he xchange Rae: Raional xpecaions, Long-Run quilibrium, and Forecasing, IMF saff Papers, 40, 89-07. Meese, R. and Rogoff, K. (983), mpirical xchange Rae Models of Sevenies: Do hey Fi Ou of Sample? Journal of Inernaional conomics, Vol. 4, 3-24. Nijman,.., Palm, F. C. and Wolff, C. P. (993), Premia in Forward Foreign xchange as Unobserved Componens: A Noe, Journal of Business and conomic Saisics,, 36-365. Pong, S., Shackleon, M. B., aylor, S. J. and Xu, X. (2004), Forecasing Currency Volailiy: A Comparison of Implied Volailiies and AR(FI)MA Models, Journal of Banking and Finance, 28, 254-2564. schernig, R. (995), Long Memory in Foreign xchange Raes Revisied, Journal of Inernaional Financial Markes, Insiuions and Money, 5, 54-78. 2
able Percenage of Forecas rror Reducions Relaive o he Random Walk Model for Various Forecasing Alernaives (a) Mean Square rror (MS) ime Series Model conomeric Model Consan Weigh Composie Model Non-consan Weigh Indusrial counries France 2.623%.843% -.69% 5.356%* Germany 0.896% 0.467%.830% 5.633%* UK 3.208% 2.795% 2.008% 4.207%* Japan 0.47% 3.044% -2.03% 3.449%* Developing Counries Souh Korea 0.78% -0.567% -0.957% 2.597%* aiwan 4.067% -0.446% -0.595% 7.866%* (b) Mean Absolue rror (MA) Composie Model ime Series Model conomic Model Consan Weigh Non-consan Weigh Indusrial counries France.982% 0.73% -.229% 5.4%* Germany 0.357% -0.59% -0.38% 3.905%* UK 0.206%.932% 2.795%* 2.020% Japan -.444%.074% -.259% 2.896%* Developing counries Souh Korea 0.639% -2.958% -5.6% 6.73%* aiwan.390% -.854% -2.202% 4.4%* Noe:. he wo loss funcions are defined as he follows: MS e 2 e ( y y ), MA y y,where y e and y denoe he predicing and realized values of exchange rae reurns, respecively. is he number of observaion. 2. In his able, we adop he random walk model as a benchmark o calculae he percenage of forecasing error reducion for each alernaive. 3. * presens he maximum values in he row. 22
able 2 Parameer simaes of he Composie Models: Consan Weigh versus Non-consan Weigh (a) Composie Model wih Consan Weigh α β Indusrial Counries France 0.45 0.630*** (0.3) (0.98) Germany 0.085-0.400* (0.447) (0.243) UK -.263*** -0.56** (0.445) (0.242) Japan -0.866** 0. (0.377) (0.255) Developing Counries Souh Korea 0.87 0.42 (0.232) (0.342) aiwan -0.038 0.885*** (0.77) (0.086) (b) Composie Model wih Non-consan weigh α β Indusrial Counries France -0.03 0.994*** (0.029) (0.043) Germany 0.33-0.606*** (0.292) (0.089) UK -0.60 0.079 Japan Developing Counries (0.68) -0.975*** (0.389) (0.246) -0.673*** (0.92) β 2 -.868*** (0.648).5* (0.799).653** (0.86) -0.30 (0.864) -0.993 (0.834) -0.776*** (0.7) β 2-0.894*** (0.088) 0.900*** (0.033) -0.370* (0.230) 0.844*** (0.24) β 0.843* (0.492).082* (0.593) 0.445 (0.34) -0.39 (0.355) -0.35 (0.32) 0.039 (0.09) β 0.604* (0.363).056* (0.63) 0.7 (0.520) -0.232 (0.424) 0.07 0.877*** -0.564*** -.93 Souh Korea (0.025) (0.00) (0.250) (2.026) -0.03 0.793*** -0.70*** 0.256 aiwan (0.07) (0.096) (0.0) (0.470) Noe:. he ***, ** and * denoe he significance in %, 2.5% and 5 %, respecively. 2. he value in he parenhesis denoes he sand error of he parameer esimae. β 2-0.532 (0.500) -2.038 (.507) 5.227*** (.554) -2.354** (.82) 0.098 (0.628).033 (0.826) β 2 0.48 (.779) -.65 (.58).895*** (0.897) -2.706** (.364).469 (2.938) 4.640* (2.698) σ 3.87*** (0.43) 3.252*** (0.46) 3.008*** (0.35) 3.482*** (0.57) 3.338*** (0.5).403*** (0.90) Log-Lik. -636.798-64.727-622.55-658.666-648.24-429.745 σ σ P P Log-Lik. 2.307*** (0.357) 2.424*** (0.98) 2.026*** (0.72) 2.335*** (0.308) 0.635*** (0.068) 0.652*** (0.063) 4.00*** (0.555) 3.854*** (0.290) 3.460*** (0.97) 3.83 (0.238) 8.600 (.270) 2.7*** (0.365) 0.57** (0.293) 0.973*** (0.020) 0.994*** (0.97) 0.95 (0.036) 0.98 (0.03) 0.88*** (0.045) 0.359* (0.22) 0.97*** (0.023) 0.996*** (0.006) 0.984 (0.04) 0.884 (0.070) 0.553*** (0.40) -633.096-634.58-65.80-656.062-355.370-367.34 23
able 3 Measure of Volailiy a High Volailiy Sae Relaive o Low Volailiy Sae Parameer Indusrialized Counries Developing Counries France Germany UK Japan Souh Korea aiwan (σ /σ ).777.590.708.69 3.543 4.58 Noe: We use (σ /σ ) o evaluae he measure of volailiy a high volailiy sae relaive o low volailiy sae for various currencies. Quie ineresing, he values of (σ /σ ) for indusrialized counries currencies are absoluely smaller han he developing ones 24
5 (a) France Unusual Regime 50 Crisis Regime (b) Souh Korea 0 40 30 5 20 0 980/ 982/ 984/ 986/ 988/ 990/ 992/ 994/ 996/ 998/ 2000/ 0-5 -0 0-0 980/ 982/ 984/ 986/ 988/ 990/ 992/ 994/ 996/ 998/ 2000/ -5-20 0.75 0.75 0.5 0.5 0.25 0.25 0 980/ 982/ 984/ 986/ 988/ 990/ 992/ 994/ 996/ 998/ 2000/ 0 980/ 982/ 984/ 986/ 988/ 990/ 992/ 994/ 996/ 998/ 2000/ Figure Monhly Percenage Change in he xchange Rae and Smoohing Probabiliy of High Volailiy Sae for xchange Markes of France and Souh Korea 25