1 Forecasing Exchange Raes Ou-of-Sample wih anel Mehods and Real-ime Daa Onur Ince * Universiy of Houson Absrac his paper evaluaes ou-of-sample exchange rae forecasing wih urchasing ower ariy () and aylor rule fundamenals for 9 OECD counries vis-à-vis he U.S. dollar over he period from 973:Q o 009:Q a shor and long horizons. In conras wih previous work, which repors forecass using revised daa, I consruc a quarerly real-ime daase ha incorporaes only he informaion available o marke paricipans when he forecass are made. Using boosrapped ouof-sample es saisics, he exchange rae model wih aylor rule fundamenals performs beer a he one-quarer horizon and panel specificaions are no able o improve is performance. he model, however, forecass beer a he 6-quarer horizon and is performance increases wih he panel framework. he resuls are in accord wih previous research on long-run and esimaion of aylor rule models. Keywords: Exchange Rae Forecasing, aylor Rules, Real-ime Daa, Ou-of-Sample es Saisics JEL Classificaion: C3, C53, E3, E5, E58, F3, F47 I hank David apell for encouragemen and guidance, and Chris Murray, Sebnem Kalemli-Ozcan, Nelson Mark, Luz Kilian, anya Molodsova, James Morley, Claude Lopez, and Vania Savrakeva for helpful commens and discussions. * Deparmen of Economics, Universiy of Houson, Houson, X el: + (73)
2 . Inroducion Following he collapse of he Breon-Woods sysem, he inroducion of flexible exchange rae regimes araced much aenion o he area of inernaional macroeconomics in an aemp o explain exchange rae behavior. heoreical papers such as Dornbusch (976), which exended he Mundell-Fleming model o incorporae raional expecaions and sicky prices and inroduced overshooing as an explanaion for high exchange rae variabiliy, and empirical work such as Frankel (979), which found success in esimaing empirical exchange rae models, inspired research in his field by poining ou he abiliy of macroeconomic models o explain exchange rae variabiliy. he seminal papers by Meese and Rogoff (983a, 983b) pu an end o he amosphere of opimism in exchange rae economics by concluding ha empirical exchange rae models do no perform beer han a random walk model ou-of-sample. heir finding is sill hard o overurn more han wo decades laer. Cheung, Chinn and ascual (005), for example, examine ou-of-sample performance of he ineres rae pariy, moneary, produciviy-based and behavioral exchange rae models, and sugges ha none of he models consisenly ouperforms he random walk a any horizon. Are empirical exchange rae models really as bad as we hink? Recen sudies have found evidence of exchange rae predicabiliy using eiher panels or innovaive modeling approaches. Engel, Mark, and Wes (007) use panel specificaions of he moneary, urchasing ower ariy () and aylor (993) rule models, Rossi (006) uses he moneary model in he presence of a srucural break, Gourinchas and Rey (007) use an exernal balance model, Molodsova and apell (009) use a heerogeneous symmeric aylor rule wih smoohing, and Cerra and Saxena (008) use a broad panel specificaion of he moneary model. A common problem wih he papers discussed above is heir reliance on ex-pos revised daa for he forecasing analysis. Alhough i seems obvious ha ou-of-sample exchange rae forecasing should be evaluaed using real-ime daa, which reflecs informaion available o marke paricipans, i is sill very rare in he exchange rae lieraure. Almos all exising sudies on exchange rae forecasing exploi revised daa which conains fuure informaion, due o revisions and addiions of new daa, ha is no available o eiher policymakers or marke paricipans. Ou-of-sample forecasing evaluaions based on ex-pos revised daa yield misleading inferences abou he exchange rae models and informaion problems of marke agens are no accouned in he analysis.
3 he firs paper o use real-ime daa o evaluae nominal exchange rae predicabiliy is Faus, Rogers and Wrigh (003). Examining he predicive abiliy of Mark s (995) moneary model using real-ime daa for Japan, Germany, Swizerland and Canada vis-à-vis he U.S, hey repor ha he models consisenly perform beer using real-ime daa han fully revised daa. However, none of he models perform beer han he random walk model. More recenly, Molodsova, Nikolsko- Rzhevskyy, and apell (008, 009) find evidence of predicabiliy wih aylor rule fundamenals using real-ime daa for he Deuschmark/dollar and Euro/dollar exchange raes. here are no sudies on exchange rae forecasing wih real-ime daa for a reasonably large number of counries over he pos Breon Woods period because of he limied availabiliy of realime daa for counries oher han he U.S. In his paper, I consruc a quarerly real-ime daase ha conains 9 OECD counries (Ausralia, Canada, France, Germany, Ialy, Japan, Neherlands, Sweden, he Unied Kingdom) vis-à-vis he U.S. dollar over he period from 973:Q o 009:Q o evaluae boh shor and long-horizon ou-of-sample forecasing performance of he linear exchange models using and aylor rule fundamenals. I consruc real-ime prices and inflaion from he Inernaional Financial Saisics (IFS) counry pages using he consumer price index (CI), and esimae real-ime oupu gaps wih he indusrial producion index. A problem associaed wih recen papers presening evidence of exchange rae predicabiliy is ha hese sudies employ a es developed by Clark and Wes (006) (henceforh, CW es). hey propose an adjusmen o he Diebold and Mariano (995) and Wes (996) (henceforh, DMW es) saisic ha correcs for size disorions. If wo models are non-nesed, he DMW es is appropriae o compare he mean square forecas errors (MSFE s). Applying DMW ess o compare he MSFE s of wo nesed models, however, leads o non-normal es saisics, and using sandard normal criical values usually resuls in very poorly sized ess wih far oo few rejecions of he null. his is a problem for ou-of-sample exchange rae forecasing because, since he null is a random walk, all ess wih srucural models are nesed. While he CW adjusmen produces a es wih correc size, Rogoff and Savrakeva (008) argue ha i canno evaluae forecasing performance because i does no es he null hypohesis of equal MSFE s of he random walk and he srucural model. In order o saisfy he condiions for a good exchange rae forecasing model, empirical sudies need o presen evidence ha he exchange rae model has MSFE ha is significanly smaller han ha of he random walk model, which canno be done solely wih CW es in he case of
4 forecasing bias. hey advocae he use of DMW ess wih boosrapped criical values o produce correcly sized ess. Engel, Mark and Wes (007) find ha panel error-correcion exchange rae models wih fundamenals are able o produce large improvemens in ou-of-sample forecasing a longer horizons. Because hey use ex-pos revised daa, he exchange rae models in heir sudy conain fuure informaion ha was no available o marke paricipans. Forecasing exercises involving fuure news in he informaion se of he linear model canno be evaluaed as an ou-of-sample forecasing exercise. Forecass wih real-ime daa, however, do no conain any unrealized fuure informaion in he informaion se of he linear model, and hus are a rue ou-of-sample forecas. Molodsova and apell (009) find evidence of ou-of-sample predicabiliy wih he aylor model a shor horizon using single-equaion esimaion. Alhough hey use ex-pos revised daa o calculae inflaion, hey esimae oupu gaps wih quasi-real-ime daa in order o capure he informaion available o cenral banks as closely as possible. Quasi-real-ime daa is consruced wih ex-pos revised daa, bu he rends do no conain fuure observaions and he daa poins are used wih a lag for esimaion. While quasi-real-ime daa does no conain fuure observaions, i capures revisions which are no available o marke paricipans. herefore, forecasing exercises wih quasireal ime daa are also no rue ou-of-sample forecass. his paper evaluaes ou-of-sample forecasing wih and aylor Rule fundamenals using my newly consruced real-ime daase for 9 OECD counries vis-à-vis he U.S. dollar wih single-equaion and panel error-correcion frameworks based on boosrapped DMW and CW es saisics. 3 he ou-of-sample forecas resuls wih fundamenals confirm he findings in Engel, Mark and Wes (007) ha he predicabiliy of he model increases wih he panel specificaion and he model has higher predicive power a long horizons. Evidence of long-erm predicabiliy wih he model is found for 6 ou of 9 counries agains he drifless random walk and for all he counries agains he random walk wih drif wih panel framework. he exchange rae model wih fundamenals using panel daa ouperforms he drifless random walk for 5 ou Rogoff and Savrakeva (008) consider he scale bias where he observed value is over- or under prediced by a cerain percen. Engel, Mark and Wes (007) use moneary and aylor Rule models as well. However, he ou-of-sample predicabiliy of he model dominaes he oher wo models a longer horizons. 3 I would like o evaluae he ou-of-sample forecasing abiliy of he moneary model. However, i is no possible o find coheren series of real-ime money supply for all he counries. 3
5 of 9 counries and he random walk wih drif for all he counries in he sample a he 6-quarer horizon. he predicabiliy of aylor fundamenals, in conras, is greaes wih he single-equaion specificaion, and he aylor rule model has higher forecasing power a a shor horizon as indicaed in Molodsova and apell (009). Evidence of shor-erm predicabiliy wih aylor rule model is found for ou of 9 counries agains he drifless random walk and for 4 ou of 9 counries agains he random walk wih drif wih single-equaion esimaion. he exchange rae model wih aylor rule fundamenals using a single-equaion framework ouperforms he drifless random walk for ou of 9 counries and he random walk wih drif for 5 ou of 9 counries a he one-quarer horizon. he resuls are in accord wih previous research on and esimaion of aylor rule models. he model works bes wih he panel specificaion a he 6-quarer horizon. Research on shows no evidence a shor-run, and apell (997) finds considerably more suppor for long-run wih panel mehods han wih univariae ess. anel models exploi he informaion conained in he high correlaion beween nominal and real exchange raes for he counries in our sample. he aylor rule model performs beer wih single-equaion esimaion a he one-quarer horizon. Moneary policy rules implemened by cenral banks since he early-o-mid 980s se ineres raes for relaively shor periods and are differen from each oher. Clarida, Gali and Gerler (998) provide empirical evidence of how ineres rae reacion funcions differ among OECD counries. Gerdesmeier, Mongelli and Roffia (007) compare he moneary policies implemened by he Eurosysem, he Fed and he Bank of Japan, and also find differences. Imposing idenical moneary rules across all counries in a panel srucure does no produce successful ou-of-sample exchange rae forecass, hus esimaing he aylor rule model wih a single-equaion framework performs beer.. Daa he real-ime quarerly daa used in his sudy covers he pos-breon Woods period from 973:Q o 009:Q for 0 OECD counries: Ausralia, Canada, France, Germany, Ialy, Japan, Neherlands, Sweden, he Unied Kingdom, and he Unied Saes. he daase is consruced from he counry ables of IMF's Inernaional Financial Saisics (IFS) books, regularly published on a monhly basis since 948. Seasonally adjused indusrial producion index (IFS line 66c) is used as a 4
6 measure of counries income, since quarerly GD daa are no consisenly published and no available for some counries for much of he ime span. he price level in he economy is measured by he consumer price index (CI) (IFS line 64) and seasonally adjused by applying a one-sided moving average of he curren observaion and 3-lagged values. he inflaion rae is he annual inflaion rae calculaed using he CI over he previous 4 quarers. Nominal exchange raes are aken from he IFS CD-ROM (IFS line ae) defined as he end-of-period U.S. dollar price of a uni of foreign currency. Exchange raes for he Euro area afer 998 are normalized by fixing foreign currency per dollar o he Euro/Dollar rae as in Engel, Mark and Wes (007). he real-ime daa has he usual riangular forma wih vinage daes on he horizonal axis and calendar daes for each observaion on he verical axis. he series of real-ime inflaion and oupu gaps are consruced from he diagonal elemens of he real-ime daa marix and conain only he laes available observaions a each period. For each counry, his daa represens a vecor of quarerly observaions from 973:Q o 009:Q, hus resuling in 45 observaions. he oupu gap is calculaed as he percenage deviaion of acual oupu from a Hodrick- resco (997) (H) rend. 4 he indusrial producion index series in each daa vinage ha is used o esimae he oupu gap goes back o 958:Q for all counries. For he firs daa poin, he rend is calculaed using he daa for 958:Q-973:Q, for he second daa poin, i is calculaed using he daa for 958:Q-973:Q, and so on. As wih any mehod ha uses a one-sided filer, he esimaions migh be subjec o end-of-sample uncerainy which is exacerbaed wih real-ime daa, consising of he las observaions in each daa vinage. o ake ino accoun he end-of-sample uncerainy in oupu gap esimaion using real-ime daa, I use Wason s (007) correcion and forecas he indusrial producion series quarers ahead before calculaing he rend Mehodology he economeric analysis in his sudy is based on panel esimaion of he predicive regression, s i+k s i = β k z i + ε i+k () 4 he smoohness parameer for H filer is 600 for quarerly daa. 5 While Wason (007) also suggess o backcas he series, he series in each daa vinage exends hrough 958:Q, which is long enough o remove he disorions in he beginning of he sample creaed by a onesided filer. 5
7 where z i = f i s i and ε i = ζ i + θ + u i. 6 In he predicive regression, s i denoes he naural log of he nominal exchange rae, measured as he domesic price of U.S. dollar (which serves as base currency) for counry i a ime. he deviaion of he exchange rae from is equilibrium value is denoed by z and f sands for he fundamenal in he exchange rae model ha is deermined eiher by or aylor rule. he forecas horizon k, akes he value of for shor-horizon and 6 for long-horizon regressions. he regression error,ε i, has unobserved componens, where ζ i is he individual specific effec, θ is he ime-specific effec, and u i is he residual idiosyncraic error. 3. Fundamenals Numerous sudies ha es for uni roos in real exchange raes using panels of indusrialized counries have found srong rejecions in he pos-973 period. he srong rejecions of uni roos encourage esing he forecasing power of exchange rae models wih fundamenals. Recenly, Engel, Mark and Wes (007) have shown ha fundamenals forecas well a long horizons. Rogoff and Savrakeva (008) also conclude ha specificaion performs he bes ou of all he specificaions hey ry. 7 Under fundamenals, f i = p 0 p i () where p 0 is he log of price level of U.S. which serves as base counry and p i is he log of price level of counry i. I use he real-ime CI as a measure of he naional price level. Subsiuing fundamenals () ino (), I use he resulan equaion for forecasing. 3. aylor Rule Fundamenals When cenral banks se he ineres rae according o he aylor rule, he linkage beween he exchange rae and a se of fundamenals can be examined. According o aylor (993), cenral banks se he moneary policy as: i = π + ф(π π ) + γy g + r (3) where i is he arge for he shor-erm nominal ineres rae, π is he inflaion rae, π is he arge level of inflaion, y g is he oupu gap, or percen deviaion of acual oupu from an esimae of is poenial level, and r is he equilibrium level of he real ineres rae. I is assumed ha he arge for 6 For single-equaion framework, ime-specific effec is zero. 7 Rogoff and Savrakeva (008) compare he forecasing power of he moneary model, he aylor rule model and a srucural model based on he Backus-Smih opimal risk sharing condiion. 6
8 he shor-erm nominal ineres rae is achieved wihin he period, so ha here is no disincion beween he acual and arge nominal ineres rae. he parameers π and r in equaion (3) can be combined ino one consan erm μ = r фπ and we have: i = μ + λπ + γy g where λ = + ф. If he cenral bank ses he arge he level of exchange rae o make hold, equaion (4) becomes: i = μ + λπ + γy g + δq (5) where q is he real exchange rae. he cenral bank increases (decreases) he nominal ineres raes if he exchange rae depreciaes (appreciaes) from is equilibrium value under assumpion in he aylor rule. Allowing ineres raes o achieve is arge level wihin he period: i = μ + λπ + γy g + δq (6) and i is he nominal ineres rae. Subracing he aylor rule equaion for he foreign counry from ha for he base counry, he U.S. (denoed by 0 ), equaion (6) becomes: i 0 i i = λ π 0 π i + γ y g 0 y g i + δ s i + p i p 0 (7) Imposing he uncovered ineres rae pariy condiion E s i+ = i i i 0 + s i, he expeced change in nominal exchange raes is equal o he ineres differenial: E s i+ = λ π 0 π i + γ y g 0 y g i + δ s i + p i p 0 + s i (8) Molodsova and apell (009) refer o specificaion (8) as homogenous asymmeric aylor rule wih no smoohing. hey esimae he parameers λ, γ, and δ in equaion (8) in a rolling regression framework. However, I follow he approach developed by Engel, Mark and Wes (007). Raher han esimaing he coefficiens, hey posi a aylor rule such ha λ=.5, γ=0. and δ=0.. he aylor rule fundamenals o be used in forecasing equaion () become: f i =.5 π 0 π i + 0. y g 0 y g i + 0. s i + p i p 0 + s i (9) I is well known in he lieraure ha he uncovered ineres rae pariy condiion does no hold in he shor run. Wih an error correcion specificaion, he exchange rae forecasing model, E s i+k s i = β k f i s i, is used o generae ou-of-sample forecass boh a he shorhorizon (where k=) and he long-horizon (where k=6). (4) 7
9 4. Ou-of-Sample Forecasing 4. Esimaion o produce ou-of-sample forecass, he sample has o be spli ino wo componens, insample and ou-of-sample. he in-sample componen is used o esimae he parameers in equaion () wihin boh he single-equaion and he panel frameworks. he remaining ou-of-sample componen is used for ou-of-sample forecasing. Following Mark and Sul (00) and Engel, Mark and Wes (007), I esimae he predicive regression by leas squares dummy variable (LSDV) using observaions hrough he end of he insample componen, 98:Q4. For k=(k=6), he predicive regression is used o forecas -sepahead (6-sep-ahead) exchange rae reurns in 983:Q (986:Q4). hen, he in-sample componen is updaed recursively by exending he sample up o 983:Q and equaion () is re-esimaed again. For k= (k=6), he predicive regression is used o forecas -sep-ahead (6-sep-ahead) exchange rae reurns in 983:Q (987:Q), and he loop coninues unil he las observaion. A he end, 05 forecass for k= and 90 overlapping forecass for k=6 are derived wih boh and aylor rule fundamenals. One crucial poin for muli-period ahead forecass in he panel framework is ha he ime effec needs o be forecased. For k-period ahead forecass, he ime effec in period +k is calculaed by aking he recursive mean of he ime effec unil period, such as θ +k = 4. Comparisons of Forecass Based on MSFE j = θ j. o compare he ou-of-sample forecasing abiliy of he wo nesed models, his sudy focuses on he minimum mean-squared forecas error (MSFE) approach, which became dominan in he lieraure afer Meese and Rogoff (983a, 983b). Forecass of linear and random walk models are calculaed as: Linear Model: Δs i+k = ζ i + θ j j = + βz i Drifless Random Walk: Δs i+k = 0 (0) Random Walk wih Drif: Δs i+k = α i 8
10 where α is he esimaed drif erm. 8 aking he difference beween acual and prediced values of exchange raes gives he forecas error. he MSFE approach selecs a model which has significanly smaller MSFE han he random walk wih or wihou he drif. 4.3 Ou-of-Sample es Saisics o measure he relaive forecas accuracy of he linear model agains he drifless random walk and he random walk wih drif, I use wo alernaive es saisics: he Diebold-Mariano and Wes (DMW) and he Clark-Wes (CW) saisics he Diebold-Mariano and Wes (DMW) es Model : Model : Suppose ha a maringale difference process and a linear model are given as: y e y X ' e where E ( e ) 0 where he dependen variable is he change in he exchange rae. Under he null hypohesis, populaion parameer 0 and exchange rae follows a random walk. For simpliciy le us concenrae on one-sep-ahead forecasing. Assume ha sample size is +; he firs R observaions are used for esimaion and is equal o he number of forecass. So we have, +=R+, where +=45, R=40 and =05 for one-sep-ahead forecasing. Informaion prior o is used o forecas for period =R, R+, R+,,. he firs forecas is for he period R+ and he final forecas is for he period +. he esimaed forecass for he random walk and he srucural model are 0 and X ' and is he regression esimae of. Afer esimaing he forecass, he respecive forecas errors for he models are e, y and e, y X. hus, he sample MSFE s of he wo models become: y and ( y X ) () 8 he recursive mean of he ime effec in parenhesis for he linear model is removed in he single-equaion case. 9
11 0 Diebold and Mariano (995) and Wes (996) consruc a -ype saisics which is assumed o be asympoically normal and he populaion MSFE s are equal under he null. Defining he following equaions,,, e e f f f () f f V ) ( he DMW es saisic is V f DMW (3) he asympoic DMW es works fine wih non-nesed models. However, he size properies of he asympoic DMW es have been widely criicized for nesed models. Clark and McCracken (00, 005) and McCracken (007) show ha he limiing disribuion of he DMW es for nesed models under he rue null is no sandard normal. Undersized DMW ess cause oo few rejecions of he null and may miss he saisical significance of he linear exchange rae model agains he random walk he Clark- Wes (CW) es Clark and Wes (006, 007) show ha he sample difference beween he MSFE s of wo nesed models in DMW es is biased downward from zero in favor of he random walk. X X y X y y f ) ( ) ( (4) Under he null hypohesis, he exchange rae follows a random walk, such ha,, y e e. Since he independen variables are no correlaed wih he disurbance erm, he firs erm in
12 equaion (4) is equal o zero. 9 Clark and Wes (006, 007) show ha ( X ) 0 because esimaing he parameers of he alernaive model under he rue null (which are zero) brings noise ino he forecasing process. Clark and Wes (006) recommend an adjused DMW saisic ha adjuss for he negaive bias in he difference beween he wo MSFE. Defining he adjusmens as follows, ADJ f e, e ( ), X f ADJ X ) (5) ADJ f ( V ( f f ADJ ADJ ) he CW es saisic is CW ADJ f (6) ADJ V he CW es has become one he mos popular ou-of-sample es saisic in he exchange rae lieraure. However, Rogoff and Savrakeva (008) show ha he CW es canno always be inerpreed as a minimum MSFE es as he DMW es. heir sudy presens a proof ha in he presence of forecas bias, he null hypohesis of he CW and he DMW ess are no necessarily he same. 0 If one can rejec he null of CW es, he rue naure of exchange rae does no follow a random walk. Neverheless, even if he rue model follows some oher model raher han a random walk, one can sill apply he DMW saisics o es wheher he random walk and he srucural model have equal MSFEs. 9 y X E ( y ) ( X ) E( e, X E e, X ) is zero, because he equaliy of e, e, under null hypohesis suggess ha. Since E ( e, X ) 0 by assumpion, we have E ( e, X ) E( ) E( e, X ) 0. 0 In he presence of scale bias, he null hypohesis of he CW and he DMW ess are differen.
13 4.4 Boosrapping Ou-of-Sample es Saisics Size disorions of he DMW es in small samples can be reduced by boosrapping he finie sample disribuion of he es saisics. Kilian (999) sae ha unlike asympoic criical values, correcly specified (mainaining he coinegraion beween he exchange rae and fundamenals under he null hypohesis) boosrap criical values adap for he increase in he dispersion of he finie-sample disribuion by iself. Kilian (999) also sugges ha he boosrap is appropriae for muli-period ahead forecass. Based on simulaion evidence, Li and Maddala (997) and Li (000) also indicae boosrapped ess have smaller size disorions and higher es power han asympoic ess in coinegraing sysems. Howbei, Berkowiz and Kilian (000) emphasize he imporance of boosrapping ype implemened o preserve coinegraing relaionships in he daa. hey argue ha coinegraion appears o be a parameric noion and parameric boosraps are more accurae han non-parameric ones. Mark and Sul (00) and Rogoff and Savrakeva (008) apply boosrapped ou-of-sample ess o deec forecasing abiliy of linear exchange rae models agains random walk in a panel framework. he boosrap mehods are similar in boh sudies. Mark and Sul (00) implemen parameric boosrap and esimae error correcion equaions wih seemingly unrelaed regressions (SURs); however, Rogoff and Savrakeva (008) use semi-parameric boosrap and esimae error correcion equaions wih counry specific OLS regressions. Having insignifican boosrapped DMW es saisics in cerain cases, as opposed o highly significan asympoic CW es, Rogoff and Savrakeva (008) criicize he asympoic CW es o be oversized and has less power han he boosrapped DMW es in he presence of forecas bias. Oversized asympoic CW es would cause oo many rejecions of he null hypohesis ha exchange rae does no follow a random walk. I may deec spurious saisical significance and favor he alernaive, srucural exchange rae model. In his paper, I evaluae he ou-of-sample forecasing abiliy of exchange rae fundamenals based on he boosrapped DMW es, and he ou-of-sample predicabiliy of exchange rae fundamenals based on he boosrapped CW es. Rogoff and Savrakeva s (008) mehod of boosrap (which imposes coinegraion resricion beween he exchange rae and he fundamenals) for each counry is used in his sudy as follows: In he echnical appendix of Clark and Wes (007), he unadjused power of he boosrapped DMW es is higher han ha of he asympoic CW es for recursive regressions wih one-sep-ahead forecass.
14 s (8) z d l z js j jz j j j u where s is he nominal exchange rae and defined in equaion (). z is he deviaion of exchange rae from fundamenal as s s s k and z z z k where k is he forecas horizon, is a consan and is a rend. o conrol for auocorrelaion in he error correcion equaion (ECE) lags of s and z are included. Akaike s informaion crierion is used for each counry o deermine he opimum number of d and l and o figure ou wheher o include a consan or a rend or boh in he ECE. he sum of coefficiens on lags of z is resriced o. s and z simulaed recursively afer re-sampling he esimaed residuals ( and u ). o reduce he bias caused by he iniial values of he recursion, he firs 00 observaions are hrown away and a new sample is creaed. Applying he esimaion procedure again, es saisics are calculaed wih he pseudo-daa. his process is repeaed 000 imes and semi-parameric boosrap disribuion is derived. Since he ess considered are one-sided ess, he p-values of DMW and CW ess are he percenage of he boosrapped disribuion above he esimaed es saisic using he realized daa. are 5. Empirical Resuls his secion summarizes one- and 6-quarer-ahead ou-of-sample predicive and forecasing performance of he linear exchange rae model wih and aylor Rule fundamenals o ha of he random walk model wih and wihou drif using a newly consruced real-ime daase. he ables repor he MSFE raio, he raio of MSFE of he srucural model o ha of he random walk, and he DMW and CW es saisics wih heir respecive boosrapped p-values. I is imporan o inerpre he resuls of he DMW and CW ess correcly. he DMW es is a minimum MSFE es ha compares he MSFE of he linear exchange rae model o ha of he random walk. A significan DMW es saisic implies ha he linear exchange rae model produces a lower MSFE han he random walk. he forecasing abiliy of he srucural model is higher and he srucural model ouperforms he random walk ou-of-sample. On he oher hand, he CW es is a es of predicabiliy where a significan CW es saisic indicaes ha he coefficiens in he linear exchange rae model are joinly differen from zero, and he random walk null can be rejeced in 3
15 favor of he linear model alernaive. We call rejecions of he equal MSFE null hypohesis wih he DMW es evidence of forecasing abiliy, and rejecions of he random walk null hypohesis wih he CW es evidence of predicabiliy. 5. Fundamenals One-quarer-ahead single-equaion forecas resuls wih he model are presened in able. No evidence of eiher ou-of-sample predicabiliy or forecasing abiliy is found for he model agains he drifless random walk for any exchange rae. he ou-of-sample forecasing performance of he model improves agains he random walk wih drif. Shor-erm predicabiliy is found for Canada and Sweden, and he model ouperforms he random walk wih drif for 4 counries (Canada, Germany, Japan, and Neherlands) a he one-quarer horizon. anel one-quarer-ahead forecass using fundamenals in able are only slighly beer han single-equaion forecass in able. he exchange rae model wih fundamenals using panel daa significanly ouperforms he drifless random walk only for Japan. he evidence of predicabiliy and forecasing abiliy of he model wih panel esimaion, jus like in he singleequaion case, increases agains he random walk wih drif a one-quarer horizon. Shor-erm predicabiliy is found for 5 ou of 9 counries (Ausralia, Canada, Germany, Japan, and Sweden) and he model forecass beer han he random walk wih drif for Ausralia and Sweden. he low predicive and forecasing power a he one-quarer horizon of he model using panel and single-equaion esimaions is no surprising. Exising sudies concerning he halflife of, he expeced number of years for a deviaion o decay by 50%, find half-lives of around.5 years. Accouning for he slow adjusmen of real exchange raes in advanced economies, one would expec he predicabiliy and forecasing abiliy of model o be low a shor horizons. 3 Sixeen-quarer-ahead ou-of-sample forecass of he model wih single-equaion esimaion are presened in able 3. he evidence of long-erm predicabiliy is sronger compared o one-quarer-ahead forecass using he single-equaion framework wih rejecions of he random walk null found for 4 counries (France, Germany, Neherlands, and Sweden). he model, See Wu (996), apell (997, 00), Murray and apell (00), Choi, Mark and Sul (006) for deails concerning he half-lives of deviaions. 3 he correlaions beween real and nominal exchange raes are very high for almos all he counries in our sample. 4
16 however, does no significanly forecas beer han he drifless random walk for any exchange rae. More evidence of long-erm predicabiliy is found agains he random walk wih drif. Ou-ofsample exchange rae predicabiliy is found for 7 ou of 9 counries (Ausralia, Canada, France, Germany, Japan, Neherlands, and Sweden) and he model forecass beer han he random walk wih drif for Ausralia, Canada and Neherlands. he ou-of-sample predicabiliy and forecasing abiliy of he model wih a single-equaion framework is clearly improved a he l6- quarer horizon compared o one-quarer horizon. he model performs bes wih he panel specificaion a he 6-quarer horizon. As repored in able 4, he evidence of predicabiliy is found for 6 ou of 9 counries (Canada, France, Germany, Japan, Neherlands, and Sweden), and he model forecass beer han he drifless random walk for 5 counries (Canada, Germany, Japan, Neherlands and Sweden). anel forecass a long horizon are even more sriking agains he random walk wih drif. Ou-of-sample predicabiliy and forecasing abiliy is found for all he counries in he sample, as he exchange rae model wih fundamenals significanly ouperforms he random walk wih drif for each counry using panel daa. Because he commonaliy of high correlaion beween real and nominal exchange raes for he counries in he sample can be capured wih he panel specificaion, panel esimaion becomes more efficien and he predicabiliy and forecasing abiliy of he panel exchange rae model wih fundamenals is much higher han he single-equaion framework. 5. aylor Rule Fundamenals Following Engel, Mark, and Wes (007), predicive regressions using aylor rule model are esimaed where he coefficiens on inflaion, oupu gap, and real exchange rae are fixed a cerain values. One-quarer-ahead single-equaion forecass wih aylor rule are repored in able 5. Evidence of shor-erm predicabiliy and forecasing abiliy is found only for Japan. he exchange rae model wih aylor fundamenals works much beer agains he random walk wih drif. Evidence of ou-of-sample predicabiliy and forecasing abiliy is found for 4 ou of 9 counries (Ausralia, Canada, Japan, and Sweden), and evidence of forecasing abiliy is found for Neherlands. Comparing ables 5 and 6, evaluaing he performance of aylor rules in a panel framework does no improve he resuls, as incorporaing differen moneary policies operaed by cenral banks 5
17 in a panel framework does no help o forecas exchange raes ou-of-sample. 4 One-quarer ahead forecasing resuls for he aylor rule model wih a panel framework are repored in able 6. No evidence of ou-of-sample predicabiliy or forecasing abiliy agains he drifless random walk, as neiher he equal MSFE nor he random walk null hypoheses can be rejeced for any exchange rae. he resuls are sronger agains he random walk wih drif. Evidence of predicabiliy is found for 4 ou of 9 counries (Ausralia, Canada, Japan, and Sweden), and he aylor rule model using panel esimaion forecass beer han he random walk wih drif for 5 ou of 9 counries (Ausralia, Canada, Germany, Japan, and Sweden). able 7 presens 6-quarer-ahead single-equaion forecass using he aylor rule model. here is no evidence of forecasing abiliy, and evidence of long-erm predicabiliy is found only for Germany agains he drifless random walk. he single equaion forecass wih he aylor rule model perform beer agains he random walk wih drif. Evidence of long-erm predicabiliy is found for Neherlands and Sweden, and evidence of forecasing abiliy for 5 ou 9 counries (Ausralia, Canada, Japan, Neherlands, and Sweden). anel forecass wih he aylor rule model a he 6-quarer horizon perform poorly. As repored in able 8, no evidence of eiher long-erm predicabiliy or forecasing abiliy is found agains he random walk, wih or wihou drif, for any of he counries in he sample. hese resuls are in accord wih previous work using revised or quasi-real-ime daa. Molodsova and apell (009) repor ha he evidence of shor erm predicabiliy disappears a longer horizons wih a single equaion aylor rule model, and Engel, Mark and Wes (007) do no find more evidence of predicabiliy wih panel models. 6. Conclusions he vas majoriy of empirical sudies on exchange rae forecasing over he pos-breon Woods period use ex-pos revised daa. Since his daa conains fuure informaion ha is no available o policymakers and marke paricipans a he ime forecass are made, i canno be used o evaluae predicabiliy and forecasing abiliy of exchange rae models ou-of-sample. he use of 4 See Clarida, Gali and Gerler (998) and Gerdesmeier, Mongelli and Roffia (007) for comparisons of ineres rae reacion funcions among counries. 6
18 real-ime daa overcomes his problem and mimics he informaion se of marke agens as closely as possible. he purpose of his paper is o invesigae how real-ime daa affecs ou-of-sample exchange rae forecass of and he aylor rule models a shor and long horizons wih singleequaion and panel frameworks. Our resuls show ha panel esimaion increases he predicabiliy and he forecasing abiliy of he model relaive o single-equaion esimaion. he high correlaion beween real and nominal exchange raes of he counries in our sample is beer capured by he panel specificaion and esimaing he predicive regression wih panel daa increases he predicive and forecasing power of he model. A he 6-quarer horizon, evidence of predicabiliy is found wih panel esimaion for 6 ou of 9 counries agains he drifless random walk and for all of he counries agains he random walk wih drif based on he boosrapped CW es. he model using panel daa ouperforms he drifless random walk for 5 ou of 9 counries and ouperforms he random walk wih drif for all he counries in he sample based on he boosrapped DMW es. One-quarer-ahead forecass of he exchange rae model wih fundamenals are weaker han long-horizon forecass. he good predicabiliy and forecasing abiliy of he model a longer-horizons is in accord wih esimaed half-lives of deviaions of around.5 years. he predicabiliy and he forecasing abiliy of he model a longer horizons wih panel esimaion confirms he findings in Engel, Mark and Wes (007). In conras, ou-of-sample forecasing wih panel models are unable o improve forecass compared wih single-equaion esimaion for he exchange rae model wih aylor rule fundamenals. As shown in Clarida, Gali and Gerler (998), ineres rae funcions are differen among he OECD counries, and so he assumpion of idenical moneary policy rules for all he cenral banks in panels is no very realisic. Wih boh single-equaion and panel error correcion models, he predicabiliy and he forecasing abiliy of he aylor rule model is higher a he shorhorizon, as in Molodsova and apell (009). Evidence of shor-erm predicabiliy wih he aylor rule model is found for ou of 9 counries agains he drifless random walk and for 4 ou of 9 counries agains he random walk wih drif. he exchange rae model wih aylor rule fundamenals using a single-equaion framework ouperforms he drifless random walk for ou of 9 counries and he random walk wih drif for 5 ou of 9 counries a one-quarer horizon. 7
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