Forecasting Accuracy of Error Correction Models: International Evidence for Monetary Aggregate M2

Transcription

1 Iqbal & uddin, Journal of Inernaional and global Economic Sudies, 6(1), June 213, Forecasing Accuracy of Error Correcion Models: Inernaional Evidence for Moneary Aggregae M2 Javed Iqbal* and Muhammad Najam uddin Universiy of Karachi and Federal Gov. Urdu Universiy of Ars, Sciences and Technology Absrac: I has been argued ha Error Correcion Models (ECM) performs beer han a simple firs difference or level regression for long run forecas. This paper conribues o he lieraure in wo imporan ways. Firsly empirical evidence does no exis on he relaive meris of ECM arrived a using alernaive co-inegraion echniques paricularly wih Auoregressive Disribued Lag (ARDL) approach of co-inegraion. The hree popular coinegraion procedures considered are he Engle-Granger (1987) wo sep procedure, he Johansen (1988) mulivariae sysem based echnique and he recenly developed ARDL based echnique of Pesaran e al. (1996, 21). Secondly, earlier sudies on he forecasing performance of he ECM employed macroeconomic daa on developed economies i.e. he US, he UK and he G-7 counries. By employing daa from a broader se of counries including boh developed and developing counries and using demand for real money balances his paper compares he accuracy of he hree alernaive error correcion models in forecasing he moneary aggregae (M2) for shor, medium and long run forecasing horizons. We also compare he forecasing performance of ECM wih oher well-known univariae and mulivariae forecasing echniques which do no impose co-inegraion resricions such as he ARIMA and he VAR echniques. The resuls indicae ha, in general, for shor run forecasing non co-inegraion based echniques (i.e. unresriced VAR and ARIMA) resul in superior forecasing performance whereas for long run forecasing ECM based echniques perform beer. Among he co-inegraion based echniques, our analysis provides evidence of comparaively superior forecasing performance of he ARDL based error correcion model. Keywords: Co-inegraion, Error correcion models, ARIMA, VAR. JEL Classificaion: C1, C22, C32, C53, E47 1. Inroducion Having reliable forecass of macroeconomic variables is key informaion for forming sound macroeconomic growh oriened policies useful for governmens. These are equally useful for planning and developmen agencies, cenral banks, long erm direc and porfolio invesors and oher relevan sakeholders. As poined ou by Amao and Swanson (1999) boh he cenral banks and researchers have ineres in he money aggregae M2 which have a poenial role in he conduc of moneary policy eiher as an inermediae arge or simply as an informaion variable. Much applied research in money demand is devoed o is specificaion. Money demand funcions have long been known o be unsable (Judd and Scadding, 1982). The exisence of a sable money demand funcion for any counry is imporan, so i has always been a classic case for applicaion of economeric mehodologies. In recen years, he error-correcion approach o modeling on macroeconomic daa has no been an excepion,

2 Iqbal & uddin, Journal of Inernaional and global Economic Sudies, 6(1), June 213, and applicaions o money demand specificaion and esimaion exis for mos counries. This popular specificaion has he advanage of conaining boh long-run levels and shor-run firs differences of non saionary variables. The Co-inegraion in a vecor ime series (Engle and Granger, 1987) has a number of implicaions for work in empirical macroeconomics. Co-inegraion ransforms he linear combinaion of wo non-saionary ime series ino a saionary one. In economics coinegraion is referred o as a long-run equilibrium relaionship. The inuiion is ha nonsaionary ime series wih a long-run equilibrium relaionship canno drif oo far apar from he equilibrium because economic forces will ac o resore he equilibrium relaionship. Therefore one of he purpored advanages of co-inegraion in an inegraed vecor process is ha i will resul in improved forecasing performance in long horizon. In an exremely influenial and imporan paper, Engle and Granger (1987), (henceforh referred o as EG) showed ha co-inegraion implies he exisence of an error correcion model (ECM) ha describes he dynamic behavior of wo non-saionary series. The ECM links he long-run equilibrium relaionship implied by co-inegraion wih he shor run dynamic adjusmen mechanism ha describes how he variables reac when hey move ou of long-run equilibrium. This ECM makes he concep of co-inegraion useful for modeling and inference for macroeconomic ime series. This paper demonsraes which error correcion echniques yield beer forecas of he macro variables. Forecass are based on informaion conained in he hisorical daa. If forecass are oo far away from he hisorical rends, hey are indicaive of imporan informaion regarding some evens which have alered he hisorical pah of he economy. As co-inegraion and ECM provides a unified framework of modeling boh long and shor run an ineresing quesion for researcher was wheher incorporaing he long-run resricion hrough an error correcion model yields superior forecas in comparison wih pure firs difference model which do no impose co-inegraion resricion. On a heoreical ground coinegraion is expeced o yield beer forecas as poined by Sock (1995, p-1) who assers ha If variables are co-inegraed, heir values are linked over he long run, and imposing his informaion can produce subsanial improvemen in forecas over long horizons. This asserion is based on heoreical resuls by Engle and Yoo (1986) ha long horizon forecass from he co-inegraed sysems saisfy he co-inegraion relaionship exacly and ha he coinegraion combinaion of variables can be forecas wih finie long-horizon forecas error variance. A simulaion sudy by Engle and Yoo (1987) shows ha he wo sep EG ECM provide beer forecas compared o unresriced VAR paricularly a longer horizons while a similar simulaion sudy by Chambers (1993) furher corroboraed his resul using a non-linear onesep ECM. Using he same experimenal se up as in Engle and Yoo, Clemens and Hendry (1995) find ha over-differencing he sysem resuls in inferior forecasing performance. In a simulaion sudy using a four-dimensional VAR(2) Reinsel and Ahn (1992) show ha forecas gains from co-inegraed sysem depends on proper specificaion of he number of uni roos and under specifying he number of uni roos resuls in poor performance for en o weny five seps ahead forecass whereas over-specificaion resuls in inferior shor-erm forecass. In he lieraure some sudies have compared forecas abiliy of he error correcion models resuling from he Engle-Granger and he Johansen VECM echnique. However he lieraure does no provide empirical evidence regarding he forecas accuracy of he ARDL based error

3 Iqbal & uddin, Journal of Inernaional and global Economic Sudies, 6(1), June 213, correcion model and is comparison wih EG and Johansen echniques. In addiion, mos of he empirical evidence employing real daa in forecas comparison using error correcion models comes from he developed economies. This paper provides empirical evidence of forecasing performance of he alernaive error correcion models resuling from he hree echniques as well as from non co-inegraion based echniques using he daa from a broader se of counries including boh developed and developing counries (excep European counries for which daa series on moneary aggregaes disconinue afer formaion of European Moneary Union in 1999). 2. The Lieraure Hoffman and Rasche (1996) compared he forecasing performance of a co-inegraed sysem relaive o he forecasing performance of a comparable VAR ha fails o recognize ha he sysem is characerized by co-inegraion. They considered co-inegraed sysem composing hree vecors, a money demand represenaion, a Fisher equaion, and a risk premium capured by an ineres rae differenial. The daa were from he US economy. They found ha he advanage of imposing co-inegraion appears only a longer forecas horizon and his is also sensiive o he appropriae daa ransformaion. They considered eigh years ousample forecas horizon. Jansen and Wang (26) invesigaed he forecasing performance of he error correcion model arising from he co-inegraion relaionship beween he equiy yield on he S&P 5 index and he bond yield relaive o ha of univariae models. They found ha he Fed Model improves on he univariae model for longer-horizon forecass, and he nonlinear vecor error correcion model performs even beer han is linear version. They considered en years forecas horizon. Wang and Bessler (24) employed five agriculure ime series from he US. They used annual daa from 1867 o 1966 for model specificaion and he daa for 1966 o 2 were used for ou-of sample forecas evaluaion. Their resuls favored ECM for hree o four year ahead forecas. However he differences in forecas obained from various models were no saisically significan. Lin and Tsay (1996) considered boh simulaed daa and financial and macroeconomic real daa from he UK, Canada, Germany, France and Japan and ineres rae daa from he US and Taiwan. Their resuls are conradicory as he simulaed daa yield beer forecas from he ECM whereas he performance of ECM for real daa is mixed. They aribue his conradicion o deficiency in forecas error measure which does no recognize ha forecas are ied ogeher in he long-run. This brief lieraure review indicaes ha a bes he resuls on relaive meri of imposing coinegraion consrain are mixed. If here is some advanage of using he ECM i occurs a longer horizon only. This review also indicaes ha very few sudies employ daa from he less developed economies such as he Asian, African and Lain American counries. Also no sudy has ye considered forecasing performance of he newly developed ARDL based coinegraion. I has been argued (e.g. Narayan and Narayan, 25) ha ARDL has imporan advanages over he Engle-Granger and Johansen approaches. Firsly, i can be applied regardless of wheher underlying variables are I() or I(1). Secondly, ARDL based coinegraion ess have beer small sample properies han he EG and Johansen co-inegraion ess. Thirdly appropriae modificaion of he orders of he ARDL model is sufficien o

4 Iqbal & uddin, Journal of Inernaional and global Economic Sudies, 6(1), June 213, simulaneously correc for residual serial correlaion and he problem of endogenous variables. 3. Forecasing Techniques 3.1. Co-inegraion Based Techniques and ECM ( 1 The Granger Represenaion Theorem (Engle and Granger, 1987) enables simulaneous modeling of firs difference and he level of he variables using an error correcion mechanism which provides he framework for esimaion, forecasing and esing of coinegraed sysems. If X and Y are co-inegraed and individually I(1) variables wih coinegraion vecor 1,, ) he general form of he ECM can be expressed as A ( L) Y B( L) X ( Y 1 1X 1) u (1) wih he lag polynomials A ( L) 1 a L a L 2... a L p 1 2 p ; B( L) b b L b L 2... b L q q 1 2 i where he lag operaor is defined as LY Y i. In his model he coefficiens in he A(L) and B(L) represen he impac of shor run changes while he long run effecs are given by he co-inegraion vecor ( 1,, 1) and he conrols he speed of adjusmen of shor run changes owards long run pah. Afer he pioneering wo-sep esimaor of he ECM parameers proposed by EG several ECM echniques have been developed. The EG echnique can idenify only a single equilibrium relaionship among he variables under sudy. Johansen (1988) proposed a framework of esimaion and esing of vecor error correcion model (VECM) based on vecor auo regression (VAR) equaions. The VECM can be expressed as: Y Y p 1 j Y j u (2) j 1 The is a g g marix conaining he long-run parameers. If here are r co-inegraion vecors hen can be expressed as a produc of wo marices as ' where boh and are g r marices. The marix conains he coefficiens of long-run relaionship and conains he speed of adjusmen parameers which are also inerpreed as he weigh wih which each co-inegraion vecor appears in a given equaion. This approach can accommodae muliple equilibrium relaionships in he VECM. Boh of hese esimaion echniques assume ha he variables o be modeled are I(1). Recenly Pesaran, Shin and Smih (1996) and Pesaran (21) proposed a echnique based on Auoregressive Disribued Lag (ARDL) model which allows boh I() and I(1) variables hus poenially avoids pre-es bias. To explain he hree main echniques of error correcion model we consider he real money balance relaionship. The long run relaionship is expressed as:

5 Iqbal & uddin, Journal of Inernaional and global Economic Sudies, 6(1), June 213, MP 1y 2i u (3) where MP = log(m2/cpi), y = log(oupu), i =nominal ineres rae The Engle Granger echnique uses residuals EC uˆ MP ˆ ˆ 1y ˆ 2i from he long run equaion (3) and es for saionariy of he residuals. Co-inegraion exiss if EC is saionary. The error correcion model will hen be formulaed as: MP m1 m2 m3 MP y i EC 1i i 2i i 3i i 1 (4) The Johansen s (1988) echnique employs he Vecor Error Correcion Model (VECM) Y Y k 1 i Y 1 (5) Where and i are square marices whose elemens depend on he coefficiens of long run model and Y conains he endogenous variables of he model. In presen case of money balance equaion, Y [ MP y i ]'. A es of rank of hen esablishes he number of coinegraion relaionships o ener in he VECM equaion. If here are r co-inegraion relaionships, he marix is expressed as produc of wo marices each of which is of order g r i.e. '. For example if r = 1, he VECM will be wrien as (for g = 3 variable sysem) Y 11 k 12 ( 11y1 y y i y ) 1 1 (6) 1 13 where y 1 = MP and y 2 = y and y 3 = i For esing co-inegraion he ARDL echnique specifies he dynamic equaion as MP m1 m2 m3 MP y r MP y i 1i i 2i i 31 i (7) If here is no co-inegraion,. The corresponding F-es has non-sandard asympoic disribuion. Pesaran e al. (1996) provide wo ses of asympoic criical values for he es. One se assumes ha all variables are I() and he oher assumes hey are all I(1) variables. If he compued F-saisic falls above he upper bound criical value, hen he null of no co-inegraion is rejeced. If i falls below he lower bound, hen he null canno be rejeced. Finally, if i falls inside he criical value band, he resul would be inconclusive. These wo ses of criical values refer o wo polar cases bu acually provide a band covering all possible classificaions of he variables ino I(), I(1) or even fracionally inegraed variables. Once co-inegraion is esablished he error correcion model is formulaed as: MP m1 m2 m3 MP y r EC 1i i 2i i 3i i 1 (8)

6 Iqbal & uddin, Journal of Inernaional and global Economic Sudies, 6(1), June 213, where error correcion erm EC is formulaed by normalizing he long run coefficiens of lagged variables in (7). In all hese cases he opimal lags m 1, m 2 and m 3 may be seleced by employing informaion crieria Non Co-inegraion Based Techniques ARIMA Among saisical ime-series echniques, he ARIMA models achieve exensive use and accepance. The ARIMA models are widely used in forecasing economic and financial ime series such as exchange raes (e.g. Meese and Rogoff, 1983). The ARIMA models aemp o predic a variable using only informaion conained in is pas values. The ARIMA models as concepualized by Box e al. (1994) associae auoregressive wih moving average erms afer differencing d imes o ransform he series o saionariy denoed by ARIMA (p, d, q), ha is, i is an auoregressive inegraed moving average ime series, where p denoes he number of auoregressive erms, d is he number of imes he series has o be differenced before i becomes saionary, and q is he number of moving average erms. To represen he model we consider he real money aggregae MP. d ( L )(1 L) MP ( L) u (9) where μ is he inercep erm ( L) 1 L L 2 L ( L) 1 L L 2 L L p p L q q The ARIMA modeling process includes evaluaion he saionariy of he ime series, idenificaion of he order of auoregression and moving average componens by observing he auocorrelaions, parial auocorrelaions, Akaike Informaion Crieria (AIC) and Bayesian Informaion Crieria (BIC) and hen esimaion of he auoregression and moving average parameers is carried ou as described by Box e al. (1994) VAR Vecor auoregression (VAR) is a widely used economeric echnique for mulivariae ime series modeling. Vecor auoregression provide a convenien represenaion for boh esimaion and forecasing of sysems of economic ime series. Vecor auoregressive (VAR) models are, as suggesed by heir name, models of vecors of variables as auoregressive processes, where each variable depends linearly on is own lagged values and he lagged values of he oher variables in he vecor. This means ha he fuure values of he process are a weighed sum of pas and presen values plus some noise. The wo simple VAR models used in his paper are VAR a level of he daa and VAR a firs difference respecively. A vecor auoregressive model a level of order p is VAR(p) has he following general form: X or A p Aj X j u (1) j 1 X A A X 1 1 A2 X 2 A3 X 3... A p X p u

7 Iqbal & uddin, Journal of Inernaional and global Economic Sudies, 6(1), June 213, where X is a vecor of p variables, A is he ( p 1) consan erm vecor, A, A1, A2,..., Ak are ( p p) marices of coefficiens o be esimaed, and u is a vecor of innovaions wih mean zero and covariance marix. A vecor auoregressive model a firs difference of order p has he following general form: X or A p Aj X j u (11) j 1 X A A X 1 1 A2 X 2 A3 X 3... A X p p u where X is a vecor of p variables afer aking firs difference, A is he ( p 1) consan erm vecor, A, A1, A2,..., Ak are ( p p) marices of coefficiens o be esimaed, and u is a vecor of innovaions wih mean zero and covariance marix. 4. The Daa and he Economic Models 4.1. The Model The economic model we considered is he demand for real money balances funcion. According o economic heory demand of real money balances M/CPI depends posiively on ransacion volume i.e. oupu level Y and negaively on cos of holding cash i.e. nominal ineres rae i i.e. log( M / CPI ) 1 log Y 2i u (12) Thus he ask is o forecas money sock (M2) from he alernaive ECM resuling from he hree co-inegraion echniques as well as from non co-inegraion based echniques The Daa and Their Sources We considered quarerly daa from 197Q1 o 21Q4. For model specificaion and esimaion we employ daa from 197Q1 o 29Q4 for one year (4 quarers) ahead forecas (shor run forecasing) and he forecas evaluaion is conduced for he period 21Q1 and 21Q4. For medium run forecasing i.e. hree years ahead forecas he daa of 197Q1 o 27Q4 are employed and he forecas evaluaion is conduced for he period 28Q1 and 21Q4. For he long run forecasing five years (2 quarers) he daa for 197Q1 o 25Q4 are used in esimaion of he models and he forecas evaluaion is conduced for he period 26Q1 and 21Q4. The quarerly daa (197Q1-21Q4) from a broader se of counries including boh developed and developing counries are employed including he following counries. 1. Ausralia 2. Barbados 3. Canada 4. Colombia 5. Denmark 6. Iceland 7. India 8. Indonesia 9. Israel 1. Japan 11. Jordan 12. Korea 13. Kuwai 14. Malaysia 15. Mexico 16. Morocco 17. New Zealand 18. Nigeria 19. Norway 2. Pakisan 21. Philippines 22. Senegal 23. Singapore 24. Souh Africa 25. Sweden 26. Swizerland 27. Thailand 28. Trinidad and Tobago 29. Turkey 3. UK 31. Uruguay 32. US.

8 Iqbal & uddin, Journal of Inernaional and global Economic Sudies, 6(1), June 213, Ineres rae is measured by discoun rae, lending rae or money marke rae (whichever is available for full sample period). Oupu is measured by manufacuring producion index or GDP which indicae significan seasonaliy in some counries so quarerly dummies are added in esimaion. The daa comes mosly from Inernaional Financial Saisics (IFS). We employ Mean Absolue Percenage Error (MAPE) o evaluae he forecas accuracy. This measure eliminaes he effec of scaling of variables so ha forecas error from counries is comparable. The MAPE is given by: H 1 Y Yˆ MAPE 1 (13) H Y 1 where Y and Ŷ represen acual and forecas respecively and H represen forecas horizon. 5. Resuls and Discussion 5.1 Uni Roo and Co-inegraion Tess The empirical analysis involves cerain challenges e.g. EG and he Johansen echniques require he pre-esing for uni roo in he variables and, sricly speaking, are valid if variables are I(1). However ARDL does no need such pre-esing. Uni roo ess on all he series were conduced. Uni roo ess are applied o check wheher he ime series is saionary. Many uni roo ess are proposed in he lieraure. In his paper we used hree ess namely ADF (Augmened Dickey Fuller) es, Phillips-Peron es and KPSS (Kwiakowski, Phillips, Schmid and Shin, 1992) es. The Dickey-Fuller es is based on esing he hypohesis ha series conains uni roo agains he series is saionary under he assumpion ha errors are whie noise. The es may be carried ou using a convenional saisic. However, he ess do no follow he sandard suden disribuion so he criical values for he es are obained by simulaion. An exension which will accommodae some forms of serial correlaion is he augmened Dickey Fuller es. Phillips and Perron (1988) and Perron (1988) suggesed non-parameric es saisics for he null hypohesis of a uni roo ha explicily allows for weak dependence and heerogeneiy of he error process. The advanage is ha hese modified ess eliminae he nuisance parameers ha are presen in he DF saisic if he error process does no saisfy he i.i.d. assumpion. KPSS proposed an LM es for esing rend and/or level saionariy. Tha is, now under he null hypohesis he series is assumed saionary, whereas in he former ess i was a uni roo process. Taking he null hypohesis as a saionary process and he uni roo as an alernaive is in accordance wih a conservaive esing sraegy. One should always seek ess ha place he hypohesis we are ineresed in as he alernaive one. Hence, if we hen rejec he null hypohesis, we can be confiden ha he series indeed has a uni roo. Therefore, if he resuls of he ess above indicae a uni roo bu he resul of he KPSS es indicaes a saionary process, one should be cauious and he saionariy should be invesigaed furher aking ino accoun he auocorrelaion srucure of he series.

9 Iqbal & uddin, Journal of Inernaional and global Economic Sudies, 6(1), June 213, In some counries he EG and he Johansen s co-inegraion is no sricly applicable since he order of inegraion was no he same for he variables under sudy in he money demand. Also in some cases EG, Johansen and ARDL co-inegraion ess could no uncover any coinegraion. Such counries are excluded from he analysis. The counries for money demand forecasing which saisfied all prerequisie assumpions (i.e. all he variables in he model appear o be I(1) as eviden by a leas one uni roo es and also indicae significan coinegraion from EG, Johansen and ARDL co-inegraion ess) are 1. Ausralia 2. Barbados 3. Colombia 4. Denmark 5. India 6. Indonesia 7. Japan 8. Korea 9. Kuwai 1. Malaysia 11. Mexico 12. Morocco 13. Souh Africa 14. Swizerland 15. Thailand 16. UK (see Table 1). 5.2 Evaluaion of Forecas The following ables (Table 2 hrough 4) presen he comparison of forecas accuracy based on MAPE for shor, medium and long run forecasing horizons for money demand model. The bes ECM model in each case is highlighed. Generally, for shor run forecasing horizon non co-inegraion based echniques (i.e. unresriced VAR or ARIMA) yield he lowes forecas errors. For long run forecasing horizon ECM based echniques (i.e. EG, Johansen and ARDL) yield he lowes forecas errors. Overall, in shor run forecasing ARIMA resuls in he lowes forecas error for Morocco and Thailand (Table 2). In medium run forecasing, he VAR appears o yield he lowes forecas error in boh models (Table 3) for Kuwai a firs difference. In long run forecasing for Japan he ARDL echnique and for Malaysia he Engle Granger wo sep procedure resuls in he lowes forecas error (Table 4). For shor, medium and long run forecasing for UK ECM based echnique resuls in he lowes forecas error. For Barbados, Malaysia, Souh Africa and UK he ECM based echniques resul in he lowes forecas error for all forecas horizons (Table 2 hrough 4). As a summary measure of forecas evaluaion we compued mean and median MAPE across he counries which are repored in he boom par of he ables 2 hrough 4. The mean and median MAPE are smalles for ARDL based ECM and ARIMA respecively in shor run forecasing (see Figure 1 in Appendix). In medium run forecasing, mean and median MAPE are smalles for ARIMA (see Figure 2 in Appendix). In long run forecasing, mean and median MAPE is smalles for EG1 sep based ECM (see Figure 3 in Appendix). Wihin he ECM based echniques, he bes forecass for Japan are obained using he Johansen mehod whereas EG1 sep is superior for Swizerland; he EG2 sep echnique is preferred for Malaysia and he ARDL resuls in lowes forecas error for Thailand for long run forecasing horizon. Evidence from Kuwai and Barbados shows ha he ARDL and he Johansen echniques resul in he lowes forecas error respecively (Table 2 hrough 4). The resuls for oher counries are mixed. From Table 2 hrough 4, i appears ha he generally he ECM based echniques resul in lowes forecas error in long run forecasing. The excepions are for Ausralia, Korea, Kuwai, Swizerland and Thailand. The non co-inegraion based echniques (i.e. unresriced VAR and ARIMA) resul in lowes forecas error in shor run forecasing for Colombia, Indonesia, Korea, Kuwai, Mexico, Morocco and Thailand. I can be concluded ha ECM based echniques resul in lowes forecas error in long run forecasing horizon and he non coinegraion based echniques (i.e. unresriced VAR and ARIMA) resul in lowes forecas error in shor run forecasing.

10 Iqbal & uddin, Journal of Inernaional and global Economic Sudies, 6(1), June 213, Conclusion I is well known ha regression analysis on non-saionary ime series daa may be spurious (non-sense) if he underlying variables are no co-inegraed. Error correcion models provide a convenien framework for esimaion, esing and forecasing. However several coinegraion esimaion and esing echniques have been developed in he lieraure. In his paper we have compared he forecasing accuracy of ECM based echniques (i.e. Engle- Granger, Johansen and he ARDL) wih non co-inegraion based echniques i.e. unresriced VAR and ARIMA. Also hree popular error correcion models ha are derived from he Engle-Granger, Johansen and he ARDL echniques are compared. Overall resuls indicae ha in general for shor run forecasing horizon non co-inegraion based echniques (i.e. unresriced VAR and ARIMA) whereas for long run forecasing horizon ECM based echniques generae beer forecass. In shor run forecasing, he VAR a firs difference and ARDL based ECM resuls in he bes performance in abou 31% and 25% of he cases respecively. In medium run forecasing, VAR a firs difference resuls in he bes performance in abou 44% of he cases, while ARIMA resuls bes performance in 19% of cases. In long run forecasing, he Johansen based ECM resuls in he bes performance in abou 25% of he cases. The ARDL and EG1 sep based ECM resuls bes performance in 19% of he cases. Among he co-inegraion based echniques he resuls are mixed. In shor run forecasing, ARDL based ECM resuls in he lowes forecas error. The mean and median MAPE is smalles for Johansen and ARDL. In medium run forecasing, ARDL resuls in he lowes forecas error. The mean and median MAPE are smalles for Johansen and ARDL respecively. In long run forecasing, EG1 sep resuls in he lowes forecas errors. In summary, for shor run forecasing, he ARDL resuls in bes performance in abou 44% of he cases, for medium run forecasing Johansen and EG1 sep resuls in bes performance in abou 31% of he cases. ARDL resuls in he bes performance in abou 25% of he cases. In long run forecasing, EG1 sep resuls in bes performance in abou 38% of he cases whereas he Johansen and he ARDL yield superior performance in abou 31% and 25% of he cases respecively. Thus among he co-inegraion based echniques, our analysis provides comparaively beer forecasing evidence in favor of he ARDL based ECM. Overall he resuls indicae he superioriy of non co-inegraion based echniques and co-inegraion based echniques for shor run and long run forecasing horizons respecively. Acknowledgemen *Research gran from he Dean Faculy of Science Karachi Universiy via leer daed May 3, 211 is hankfully acknowledged. I also hank he paricipans of 3 rd SAICON conference Lahore, Graduae Seminar a Insiue of Business Adminisraion Karachi and 5 h Mahemaics Colloquium, IoBM Karachi for commens suggesions. Javed Iqbal*, Deparmen of Saisics, Universiy of Karachi, Karachi, Pakisan. Javed_uniku@yahoo.com; jiqbal@uok.edu.pk,

11 Iqbal & uddin, Journal of Inernaional and global Economic Sudies, 6(1), June 213, Muhammad Najam uddin, Deparmen of Saisics, Federal Gov. Urdu Universiy of Ars, Sciences and Technology, Karachi, Pakisan. References Amao, J. and N. R. Swanson The Real Time (in)significance of M2, Working Paper Texas A&M Universiy. Box, G.E.P., G.M. Jenkins and G.C. Reinsel Time Series Analysis, Forecasing, and Conrol, 3rd ed. Englewood Cliffs, NJ: Prenice Hall. Chambers, M.J A noe on Forecasing in Co-inegraed Sysems, Compuers Mehods and Applicaions, 25, Clemens, M. P. and D. F. Hendry Forecasing in Co-inegraed Sysems, Journal of Applied Economerics, 1, Engle, R.F. and C.W.J. Granger Co-inegraion and Error Correcion: Represenaion, Esimaion and Tesing, Economerica, 55, Engle, R.F. and Yoo, B.S Forecasing and Tesing in Co-inegraed Sysems, Journal of Economerics, 35, Haigh, M.S. 2. Co-inegraion, unbiased Expecaions and Forecasing in he BIFFEX Freigh Fuures Marke, Journal of Fuures Marke, 2, Hoffman, D.L and R. H. Rasche Assessing Forecas Performance in a Coinegraed Sysem, Journal of Applied Economerics, 11, Jansen, D.W and Z. Wang. 26. Evaluaing he Fed Model of Sock Price Valuaion: An Ou-of-Sample Forecasing Perspecive, Economeric Analysis of Financial and Economic Time Series/Par B Advances in Economerics, 2, Judd, J. P. and J. L. Scadding The Search for a Sable Money Demand Funcion: A Survey of he Pos-1973 Lieraure, Journal of Economic Lieraure, 2, Johansen, S Saisical Analysis of Coinegraing Vecors, Journal of Economics of Economics Dynamics and Conrol, 12, Lin, J.L. and R.S. Tsay. (1996), Co-inegraion Consrain and Forecasing: An Empirical Examinaion, Journal of Applied Economerics, 11, MacDonald, R., and M.P. Taylor The Moneary Approach o he Exchange Rae, Economic Leers, 37, McCrae M., Y. Lin, D. Pavlik, and C.M. Gulai. 22. Can Co-inegraion-based Forecasing Ouperform Univariae Models? An Applicaion o Asian Exchange Raes, Journal of Forecasing, 21,

12 Iqbal & uddin, Journal of Inernaional and global Economic Sudies, 6(1), June 213, Narayan, P.K. and S. Narayan. 25. Esimaing Income and Price Elasiciies of Impors for Fiji in a Co-inegraion Framework, Economic Modelling, 22, Pesaran, M. H., Y. Shin, and R. J. Smih Bounds Tesing Approaches o he Analysis of Level Relaionships, DEA working paper 9622, Deparmen of Applied Economics, Universiy of Cambridge. Pesaran, M. H., Y. Shin, and R. J. Smih. 21. Bounds Tesing Approaches o he Analysis of Level Relaionships, Journal of Applied Economerics, 16, Sock, J.H Poin Forecass and Predicion Inervals for Long-Horizon Forecas, Manuscrip, J.F.K. School of Governmen, Harvard Universiy. Wang, Z and D.A. Bessler. 24. Forecasing Performance of Mulivariae Time Series Models wih Full and Reduced Rank: An Empirical Examinaion, Inernaional Journal of Forecasing, 2,

13 Iqbal & uddin, Journal of Inernaional and global Economic Sudies, 6(1), June 213, S.No. Table 1: COUNTRIES ECM coefficien of co-inegraion echniques and uni roo evidence for money demand model UNIT ROOT EG1 EG2 Trace Saisic Johansen Max Saisic ARDL 1. Ausralia I(1) * * * 2. Barbados I(1) -.21* -.687*** * * 3. Canada I(1) *** * * * 4. Colombia I(1) * ** * * * 5. Denmark I(1) * * * * * 6. Iceland I(1) ** * * 7. India I(1) * -.359** * * * 8. Indonesia I(1) * -.723* * * * 9. Israel I() ** -.686** * * ** 1. Japan I(1) -.179* ** * * * 11. Jordan I(1) 3.3E * * * * 12. Korea Republic of I(1) -.232* * * ** * 13. Kuwai I(1) -.837*** -.877*** * * -.845* 14. Malaysia I(1) -.338** -.312*** * * ** 15. Mexico I(1) * * * * * 16. Morocco I(1) -.517** ** * * *** 17. New Zealand I(1) * -.14* 18. Nigeria I(1) ** 19. Norway I(1) -3.45E ** 2. Pakisan I() * * Philippines I(1) * * *** 22. Senegal I(1) * * -.222*** 23. Singapore I(1) * * * 24. Souh Africa I(1) * -.338** * * * 25. Sweden I(1) * *.4587* 26. Swizerland I(1) *** -.537** * * * 27. Thailand I(1) -.68** -.494*** * 3.72* * 28. Trinidad and Tobago I(1) ** 29. Turkey I(1) 1.85E * * UK I(1) *** ** * * ** 31. Uruguay I(1) *.7684*** 32. US I(1) *** * * * Significan a 1% ** Significan a 5% *** Significan a 1%

14 Iqbal & uddin, Journal of Inernaional and global Economic Sudies, 6(1), June 213, Noe: In Table 1 he noaions EG1 and EG2 refer o he Engle Granger one sep and wo sep procedure respecively. The coefficien of error correcion erm is repored for he co-inegraion based echniques for EG1, EG2 and he ARDL echniques. If co-inegraion is presen hese coefficiens should be negaive and saisically significan. For he Johansen approach Trace and Max saisics are repored. For he evidence of co-inegraion we consider a leas one of Trace or Max saisic o be significan. All he counries have significan co-inegraion from ARDL echnique excep for Pakisan, Turkey and US. The excepions for he Johansen echnique are from Nigeria, Norway and Trinidad and Tobago. Only for he case of Pakisan and Israel, he variables included in he money demand model do no show ha hey have uni roo from any of he ADF, Phillips-Perron and KPSS ess. This is indicaed by he hird column using noaion I(1) or I().

15 Iqbal & uddin, Journal of Inernaional and global Economic Sudies, 6(1), June 213, Table 2: MAPE for one year ahead forecas of Money Aggregae (M2) EG 1 EG 2 VAR COUNTRIES sep sep Johansen ARDL level 1 s diff ARIMA Ausralia Barbados Colombia Denmark India Indonesia Japan Korea Republic of Kuwai Malaysia Mexico Morocco Souh Africa Swizerland Thailand UK Mean MAPE Median MAPE Mean of Ranks of MAPE Noes: The blue highligher shows he comparison wihin he co-inegraion based echniques i.e. EG1, EG2, Johansen and ARDL. The green shade represens he overall bes model. For comparison purpose we used mean and median as he average, aken for each echnique from he MAPE s of all he counries. The mean of ranks of MAPE is aken by firs ranking he MAPE for each counry from all echnique hen aking mean of ranks.

16 Iqbal & uddin, Journal of Inernaional and global Economic Sudies, 6(1), June 213, Table 3: MAPE for hree year ahead forecas of Money Aggregae (M2) COUNTRIES EG 1 sep EG 2 sep Johansen ARDL VAR Level 1s diff ARIMA Ausralia Barbados Colombia Denmark India Indonesia Japan Korea Republic of Kuwai Malaysia Mexico Morocco Souh Africa Swizerland Thailand UK Mean MAPE Median MAPE Mean of Ranks of MAPE Noes: The blue highligher shows he comparison wihin he co-inegraion based echniques i.e. EG1, EG2, Johansen and ARDL. The green shade represens he overall bes model. For comparison purpose we used mean and median as he average, aken for each echnique from he MAPE s of all he counries. The mean of ranks of MAPE is aken by firs ranking he MAPE for each counry from all echnique hen aking mean of ranks.

17 Iqbal & uddin, Journal of Inernaional and global Economic Sudies, 6(1), June 213, Table 4: MAPE for Five year ahead forecas of Money Aggregae (M2) COUNTRIES EG 1 sep EG 2 sep Johansen ARDL Level VAR 1 s diff ARIMA Ausralia Barbados Colombia Denmark India Indonesia Japan Korea Republic of Kuwai Malaysia Mexico Morocco Souh Africa Swizerland Thailand UK Mean MAPE Median MAPE Mean of Ranks of MAPE Noes: The blue highligher shows he comparison wihin he co-inegraion based echniques i.e. EG1, EG2, Johansen and ARDL. The green shade represens he overall bes model. For comparison purpose we used mean and median as he average, aken for each echnique from he MAPE s of all he counries. The mean of ranks of MAPE is aken by firs ranking he MAPE for each counry from all echnique hen aking mean of ranks.

18 median MAPE median MAPE Iqbal & uddin, Journal of Inernaional and global Economic Sudies, 6(1), June 213, APPENDIX Figure 1: Bar Graph of Median MAPE for one year ahead forecas of Money demand (M2) MEDIAN MAPE EG1 EG2 Johansen ARDL Techniques VAR() VAR(1) ARIMA Figure 2: Bar Graph of Median MAPE for hree year ahead forecas of Money demand (M2) 7 MEDIAN MAPE EG1 EG2 Johansen ARDL Techniques VAR() VAR(1) ARIMA

19 median MAPE Iqbal & uddin, Journal of Inernaional and global Economic Sudies, 6(1), June 213, Figure 3: Bar Graph of Median MAPE for five years ahead forecas of Money demand (M2) 14 MEDIAN MAPE EG1 EG2 Johansen ARDL Techniques VAR() VAR(1) ARIMA