A COMPARISON OF FORECASTING MODELS FOR ASEAN EQUITY MARKETS

Transcription

1 Sunway Academic Journal, 1 1 (005) A COMPARISON OF FORECASTING MODELS FOR ASEAN EQUITY MARKETS WONG YOKE CHEN a Sunway Universiy College KOK KIM LIAN b Universiy of Malaya ABSTRACT This paper compares six models for forecasing he performance of he ASEAN equiy markes of Malaysia, Singapore, Thailand, Indonesia and he Philippines before, during and afer he Asian financial crisis. In he precrisis period, he OLS, ARCH-M and TARCH models have beer forecasing performance han he oher models. In he crisis period, he ARCH-M model has he bes forecas performance for hree markes, while he remaining wo markes are bes forecas wih he random walk model. However, in he pos-crisis period, he TARCH and EGARCH models are found o be he mos suiable models. The differen varians of he GARCH model adequaely capured he ime-varying reurns volailiy. Bu he asymmery of he marke reurns is no significan in all he markes modelled by he TARCH and EGARCH models. Key words: ARCH-M, GARCH, TARCH, EGARCH, random walk, Asian financial crisis. INTRODUCTION A sock marke provides an added dimension of invesmen opporuniy for boh individual and insiuional invesors and, hus, he naure and behaviour of sock marke reurns are of ineres o academic researchers and marke praciioners. One area of paricular ineres is forecasing whereby he ineresed paries aim o exploi informaion conained in he pas realisaions of a vecor of ime series for he purpose of predicing fuure price movemens. Such an endeavour, however, challenges he efficien marke hypohesis, which in urn is closely ied o he random walk concep. Random walk heory assers ha sock price movemens are unpredicable and do no follow any paerns or rends over ime. Emphaically, in a perfecly efficien marke, hisorical reurns would no offer any useful insigh for speculaing on fuure price movemens. Indeed, many of he earlier sudies on he sock markes of developed counries (see Kendall (1953), Fama (1965a, b), Granger and Morgensern (1963), Godfrey e al. (1964), Sharma and Kennedy (1977) and Cooper (198)) indicaed ha heir sock reurns are random in naure and hence hese findings lend suppor o he efficien marke hypohesis. Using new saisical mehods, however, he more recen sudies provide evidence agains he random walk behaviour of sock prices. For example, Lo and Mackinlay (1987), a wyc@academic.sunway.edu.my, b kokkl@um.edu.my. An earlier draf of his paper was presened a he 6 h Annual Malaysian Finance Associaion Symposium, Langkawi, 5 6 May, 004.

2 Wong Y. C. and Kok K. L. Poerba and Summers (1988) and Frennberg and Hansson (1993) found ha sock reurns are mean-revering in he long run and are herefore, o a cerain exen, predicable. Even for shor horizon reurns, here is some evidence conrary o he efficien marke hypohesis. Empirical sudies have concluded ha large changes in prices end o be followed by larger changes in eiher direcion. This implies ha volailiy mus be predicably high afer large changes. The inroducion of ime-varying volailiy in financial ime series daa by Engle (198), and subsequen developmen by Bollerslev (1986), had led o he formulaion of he auoregressive condiional heeroscedasiciy (ARCH) model and is many varians (see Engle e al. (1987), Glosen e al. (1993) and Nelson (1991)). Using hese models, Bollerslev (1987), Akgiray (1989), Tse and Tung (199), Franses and van Dijk (1996), Walsh and Tsou (1998) and McMillan e al. (000) obained findings ha pose ye anoher challenge o he validiy of random walk in sock reurns. Mixed findings are obained on sock price behaviour for he ASEAN sock markes. Laurence (1986), Saw and Tan (1989), Mansor (1989) and Kok and Goh (1994a) found ha sock reurns in Malaysia basically followed a random walk. Moreover, in a separae sudy Kok and Goh (1994b) deeced he presence of mean-revering behaviour in he Malaysian sock reurns while Mansor (1999) and Pan e al. (1999) showed ha he reurns displayed ARCH effecs. However, a sudy on he sock reurns in Singapore by Saw and Tan (1986) concluded ha hese reurns did no exhibi any significan random walk behaviour. A similar finding was obained by Sareewiwahana and Isbell (1985) on he Thailand marke. When a random walk model is used for forecas, i would yield a naïve forecas of no change. Alhough various models have been developed o accoun for he ime-varying volailiy in financial ime series daa, i remains o be seen wheher hese models would provide a beer forecas han ha of he random walk. This paper, herefore, compares he forecas performance of he random walk model and he oher models ha capure he imevarying volailiy in sock reurns for each of he five ASEAN sock markes of Malaysia, Singapore, Thailand, Indonesia and he Philippines. In paricular, he comparison is made for each of he hree periods as divided by he Asian financial crisis ha firs occurred in 1997, namely, he pre-crisis period, he crisis period and he pos-crisis period. The resuls of his sudy have implicaions for weak form marke efficiency, paricularly for asse pricing and hedging since, for example, he Kuala Lumpur Sock Exchange (KLSE) Composie Index is used as he underlying index for sock index fuures rading. The remainder of his paper is srucured in he following forma. Secion explains he daa and he mehodology used in he sudy. In Secion 3 we discuss he findings and in he concluding chaper we draw appropriae conclusions and implicaions of he sudy. DATA AND METHODOLOGY The daa used in he sudy are he daily closing values of he Kuala Lumpur Sock Exchange Composie Index, Singapore Sock Exchange All-Share Index, Sock Exchange of Thailand Index, Jakara Composie Index and he Philippines Composie Index over he period exending from January 199 o 1 Augus 00. The daa are obained from he financial daa provider Bloomberg. The daily marke reurns are compued as log index relaives. Three periods are idenified in his sudy: January 199 o 31 January 1997, 1 February 1997 o 30 Sepember 1998 and 1 Ocober 1998 o 1 Augus 00. In relaion o

3 Sunway Academic Journal, 1 1 (005) 3 he Asian financial crisis, hese 3 periods correspond approximaely o he pre-crisis period, he crisis period and he pos-crisis period, respecively. Excep for he holdou sample reserved for he purpose of examining he ou-ofsample forecasing performance, he six forecasing models are esimaed for each period by using he daily closing values in ha period. The holdou sample comprises he daily closing values of he las 0 rading days in each period. In oher words, he esimaed models are used o generae ex-pos forecass of he daily closing values for hese las 0 rading days, wih he acual values known. By comparing hese ex-pos forecass wih he acual values, he model s forecasing abiliy is evaluaed. If P represens he sock index of a marke a ime, he reurn of he index a ime is compued as follows: r = ln (P / P 1 ) Advocaes of he efficien marke hypohesis asser ha sock prices are essenially random and herefore here is no scope for profiable speculaion in he sock marke. Thus, in mos sudies, a random walk model wihou drif, which is simply an AR (1) process wih a uni coefficien, is ofen used as he fundamenal forecasing model. However, he daily raes of reurns on common sock generally have a slighly upward bias or drif, given he long-erm posiive expecaion for raes of reurns. So in his sudy, we shall allow for his possibiliy of a sochasic rend by incorporaing a drif erm. Therefore, a random walk wih drif is used insead. This random walk (RW) model is given as follows: r = µ + (1) where µ is he mean value of he reurns, which is expeced o be zero; is he error erm wih zero mean and is no auocorrelaed over ime. The second forecasing model is he ordinary leas squares (OLS) model which allows for a lag dependence srucure by including he lagged erm of he index reurns. Is equaion is given by r = µ + α r 1 + () Through his OLS model, he condiional mean of he sock index reurns is modelled. In addiion o esimaing he mean equaion (), i is also perinen o model he condiional variance of he reurns. The nex four models ake ino accoun his ime-varying volailiy. The generalized ARCH, or GARCH, process, as proposed by Bollerslev (1986), is exensively applied in financial ime series analysis. In his sudy, GARCH (1, 1), which is he mos popular specificaion, is used. This model is given by he following se of equaions: r = µ + α r 1 + (3) = z = a + b 1 + c 1 + w

4 4 Wong Y. C. and Kok K. L. where z is a sochasic variable no auocorrelaed in ime, and has a sandardized normal disribuion; is he condiional variance of he reurns and w is a random componen wih he properies of whie noise. The remaining hree models are variaions of model (3). The ARCH-in-Mean (ARCH-M) model, proposed by Engle e al. (1987), is obained by inroducing he condiional sandard deviaion ino he mean equaion of model (3). This model is commonly used in siuaions where he expeced reurns on an asse is relaed o he expeced asse risk. The condiional sandard deviaion acs as a proxy for he risk and he esimaed coefficien on he expeced risk is aken as a measure of he risk-reurns radeoff. This ARCH-M (1, 1) model is given as follows: r = µ + α r 1 + β + (4) = z = a + b 1 + c 1 + w I is ofen observed ha downward movemens in he equiy markes are followed by higher volailiies han upward movemens of he same magniude. This asymmeric effec is commonly referred o as he leverage effec. In he presence of such an effec, he GARCH model would be deemed inadequae o model he volailiy. The Threshold ARCH (TARCH) and Exponenial ARCH (EGARCH) models, proposed by Glosen e al. (1993) and Nelson (1991), respecively, which allow for such asymmeric shocks o volailiy, would hen be more suiable. The TARCH (1, 1) model is given as follows: r = µ + α r 1 + (5) = z = a + b 1 + c 1 ξ 1 + d 1 + w where ξ 1 = 1 if 1 < 0 and ξ 1 = 0 if 1 > 0. The TARCH model is formulaed on he assumpion ha unexpeced changes in he marke reurns, which are expressed in erms of, have a differen impac on he condiional variance of he reurns. Good news is associaed wih an unforeseen increase and hence will conribue o he variance hrough he coefficien b. An unforeseen fall, which consiues bad news, will induce an increase in volailiy hrough he coefficien (b + c). Thus, a non-zero value of he coefficien c implies he asymmeric naure of he reurns, while a posiive value of c indicaes he presence of leverage effec. The exponenial naure of he condiional variance in he EGARCH model ensures ha exernal unexpeced shocks will exer a sronger influence on he prediced volailiy han hey would in he TARCH model. The EGARCH (1, 1) model is given as follows: r = µ + α r 1 + (6) = z ln ( ) = a + b c d ln ( 1 ) + w

5 Sunway Academic Journal, 1 1 (005) 5 As in he TARCH model, he non-zero value of c will indicae an asymmeric effec in he reurns and he presence of leverage effec is shown by is negaive value. The models are evaluaed in erms of heir abiliy o forecas fuure reurns. Several measures are used in comparing forecasing performance of differen models. The mos common measure is he mean squared error (MSE). Ofen he square roo of MSE (RMSE) is used so as o preserve he unis. The less popular, bu noneheless common, measures are he mean absolue error (MAE) and he mean absolue percenage error (MAPE). Anoher common crierion used in comparing performance of forecas models is he Theil inequaliy coefficien. Is value always lies beween zero and 1, where zero indicaes a perfec fi. These four forecas error saisics are compued as follows: RMSE: 1 0 T + 0 = T + 1 ( ) Pˆ P MAE: 1 0 T + 0 = T + 1 Pˆ P MAPE: 100 T ( = T + 1 Pˆ P P ) Theil Inequaliy T Coefficien: ( Pˆ P ) = T + 1 T + 0 Pˆ = T T + 0 P = T + 1 where T is he number of observaions in he sample for esimaion and he ex-pos forecass consiue observaions T + 1 o T + 0. P and Pˆ respecively denoe he acual and forecased daily closing values for he sock index of a marke in period. The bes model for forecasing for a paricular period, as indicaed by a paricular measure, is he one wih he smalles forecas value of ha measure. For each period, we rank he forecasing abiliy of he six models by ranking he magniudes of he forecas errors. RESULTS Six esimaion models are used in his sudy, namely, RW, OLS, GARCH (1,1), ARCH (1,1)-M, TARCH (1,1) and EGARCH (1,1) models. These models are esimaed for each of he five ASEAN markes for he pre-crisis, crisis and pos-crisis periods. These esimaed models are hen used for forecasing he values of he marke index for he las 0 days of each period of an ASEAN marke. The four saisical measures of forecas error RMSE, MAE, MAPE and Theil are compued for each forecas. The resuls of he RMSE and heir resulan rankings for hese six models are given in Table 1. The oher hree measures of forecas errors are no repored here as hey provide he same rankings as hose based on he RMSE. For he five ASEAN equiy markes, he magniudes of he forecas errors are he leas in he pre-crisis period and he greaes in he crisis period. In he pre-crisis period, he

6 6 Wong Y. C. and Kok K. L. RMSE values range from o They are he lowes (0.013 o 0.016) for Singapore and he highes (0.053 o 0.060) for Thailand. The forecasing abiliy of he models is raher poor in he crisis period. The forecas errors in each ASEAN marke are very much higher during his period of high volailiy. They range widely from o The forecas errors are he lowes (0.047 o 0.058) for he Philippines. Raher surprisingly, conrary o he resuls in he pre-crisis period, he RMSE values for Malaysia are excepionally high (0.376 o 0.436). Thus, he forecasing performance of he models for Malaysia during he crisis period has deerioraed. The forecasing abiliy of he models improves in he pos-crisis period and, generally, revers o ha during he pre-crisis period. As in he pre-crisis period, he forecasing performance is he bes for Malaysia and he wors for Thailand. From he rankings of he models in Table 1, no one single model is he bes for hese ASEAN markes. In he pre-crisis period, he TARCH model is he bes forecas model for Malaysia. The OLS model is he bes for Singapore and he Philippines, while he ARCH-M model is he bes for Thailand and Indonesia. In he crisis period, he bes forecas model for Malaysia, Singapore and he Philippines is he ARCH-M model, while for Thailand and Indonesia i is he RW model. In he pos-crisis period, he TARCH and EGARCH models, which capure he asymmerical marke reurns volailiy, are he bes forecas models. The TARCH model is he bes for Malaysia and Thailand, while he EGARCH model is he bes for he oher hree ASEAN markes. Thus, our findings show ha he bes forecas model for an ASEAN marke is differen for each period excep for Malaysia, where he TARCH model is he bes in boh he pre-crisis and pos-crisis periods. The esimaed models for he ASEAN markes are given in Table. The F-saisics in Panel A for he pre-crisis period show ha he models are significan in all counries excep Singapore. The curren reurns are posiively correlaed wih he previous-day reurns and, again, he correlaion is significan excep for Singapore. The resuls of he LM es for he presence of ARCH effecs show ha he OLS model used for Singapore and he Philippines is inadequae. However, he LM es resuls are no significan for he differen varians of he GARCH model used for Malaysia, Thailand and Indonesia. The and erms in he TARCH model for Malaysia and in he ARCH-M model for Thailand and Indonesia are significan, hereby highlighing he salien feaures of he ime-varying volailiy of sock reurns in hese counries. The 1 ξ 1 erm in he TARCH model for Malaysia is significan, hereby indicaing evidence of asymmerical impac of good/bad news on sock reurns in he Malaysian equiy marke. The risk-reurns rade-off of he ARCH-M model is no significan for boh Thailand and Indonesia. In he crisis period, he F-saisics in Panel B show ha he models are significan for Singapore and he Philippines bu no for Malaysia. The curren reurns are again posiively correlaed wih he previous-day reurns and he correlaions are significan for hese hree markes. The resuls of he LM es show he presence of ARCH effecs in he RW model for Thailand and Indonesia bu no in he ARCH-M model for he oher hree ASEAN counries. Similarly, he ime-varying reurns volailiy is highlighed by he significance of 1 and 1 erms in he ARCH-M model for hese hree equiy markes. Likewise, he risk-reurns rade-off of he ARCH-M model is no significan in hese hree markes. 1 1

7 Sunway Academic Journal, 1 1 (005) 7 Table 1. Measures of Forecas Errors (RMSE) and Rankings of he Six Models for he ASEAN Equiy Markes Pre-crisis period Crisis period Pos-crisis period Malaysia RW [] [] [5] OLS [3] [3] [3] GARCH [4] [6] [6] ARCH-M [5] [1] [4] TARCH [1] [5] [1] EGARCH [6] [4] [] Singapore RW [] [3] [4] OLS [1] [4] [5] GARCH [3] [] [3] ARCH-M [6] [1] [6] TARCH [5] [5] [] EGARCH [4] [6] [1] Thailand RW [] [1] [5] OLS [4] [] [] GARCH [3] [5] [4] ARCH-M [1] [3] [3] TARCH [5] [6] [1] EGARCH [6] [4] [6] Indonesia RW [6] [1] [5] OLS [3] [] [6] GARCH [4] [6] [3] ARCH-M [1] [5] [4] TARCH [5] [3] [] EGARCH [] [4] [1] Philippines RW [] [4] [4] OLS [1] [3] [6] GARCH [3] [] [3] ARCH-M [4] [1] [5] TARCH [5] [5] [] EGARCH [6] [6] [1] The numbers in [ ] indicae rankings of he models in each period for each equiy marke, [1] having he lowes RMSE.

8 8 Wong Y. C. and Kok K. L. Table. The Bes Esimaed Models for he Five ASEAN Equiy Markes in he Pre-crisis, Crisis and Pos-crisis Periods Malaysia Singapore Thailand Indonesia Philippines Panel A. Pre-crisis Period Model TARCH OLS ARCH-M ARCH-M OLS Mean Equaion Variance Equaion c r ** ** ** 0.016** c ** ** ** ** 0.18** ** ξ ** ** ** 0.609** F-saisic (pvalue) ARCH-LM 5 lags (p-value) 10 lags Panel B. Crisis Period Model ARCH-M ARCH-M RW RW ARCH-M Mean Equaion Variance Equaion c * * r ** ** 0.030** c ** * ** ** 0.** ** 0.798** ** F-saisic (pvalue) ARCH-LM (p-value) 5 lags lags

9 Sunway Academic Journal, 1 1 (005) 9 Table (coninued) Malaysia Singapore Thailand Indonesia Philippines Panel C. Pos-crisis Period Model TARCH EGARCH TARCH EGARCH EGARCH Mean Equaion c r ** ** 0.137** Variance Equaion F-saisic (pvalue) ARCH-LM (pvalue) c ** * **.4404** 0.708** ** ** * ξ ** 0.760** ** 0.56** ** ** ** ** 0.999** ln lags lags * Significan a 5% level. ** Significan a 1% level. The significance es is based on he Newey-Wes s (1987) heeroscedasiciy consisen sandard errors for he OLS model and he quasi-maximum likelihood sandard errors due o Bollerslev and Wooldridge (199) for he oher models. The F-saisic is for esing he significance of he model. ARCH-LM refers o he Engle (198) LM es for he presence of ARCH effecs. In he pos-crisis period, where he bes models are TARCH and EGARCH, he F- saisics in Panel C are significan for Malaysia, Indonesia and he Philippines bu no for he oher wo ASEAN markes. Similarly, he correlaion beween he curren reurns and he previous-day reurns is significanly posiive for he same hree ASEAN markes. The non-significance resuls of he LM es show ha he TARCH and EGARCH models fully accoun for he ARCH effecs. The presence of he ime-varying reurns volailiy in Malaysia and Thailand is indicaed by he significance of he 1 and TARCH models. The bu no in Thailand. The 1 1 erms in he ξ erm confirms significan asymmeric reurns in Malaysia 1 1 and ln ( 1 1 ) erms in he EGARCH model are significan

10 10 Wong Y. C. and Kok K. L. 1 for Singapore, Indonesia and he Philippines. Bu he erm is only significan for he 1 Philippines, hereby indicaing asymmeric reurns in his counry only. CONCLUSION This sudy examines six models for forecasing he values of he leading marke indices of five ASEAN equiy markes in he pre-crisis, crisis and pos-crisis periods. The forecass are he mos reliable in he pre-crisis period and he poores in he crisis period. The forecas abiliy of he models in he pos-crisis period revers o ha in he pre-crisis period. No one single forecas model is found o be he bes for hese ASEAN equiy markes. Insead hree models, TARCH, OLS and ARCH-M, are found o be he bes for he ASEAN markes in he pre-crisis period. In he crisis period, he bes models found are ARCH-M and RW, while in he pos-crisis period he bes models are TARCH and EGARCH, which capure he asymmeric volailiy in he marke reurns. In he pre-crisis period, he resuls of he bes esimaed models show ha he models are significan wih posiive relaionship beween he curren reurns and he previous-day reurns excep for Singapore. The TARCH and ARCH-M models are adequae in capuring he ime-varying reurns volailiy and he asymmeric reurn volailiy, while he OLS model is inadequae for his purpose. In he crisis period, he bes models ARCH-M and RW are significan excep for Malaysia. The curren reurns and he previous-day reurns have a significanly posiive relaionship. The varying reurns volailiy is adequaely capured in he ARCH-M model bu no in he RW model. Finally, in he pos-crisis period, he bes models, TARCH and EGARCH, are significan for only hree of he five ASEAN markes. Similarly, he relaionship beween he curren reurns and he previous-day reurns is significanly posiive for he same hree equiy markes. These models no only adequaely capured he varying reurns volailiy in he five markes bu also he asymmeric reurns in Malaysia and he Philippines. The risk-reurns rade-off is no significan in he markes in he pre-crisis and crisis periods modelled by he ARCH-M model. In a way, he findings from his sudy esify ha he bes forecasing model is relaed o he marke condiions, and also possibly o he differen sages of developmen of he markes. For any marke, no one single model should be used o forecas fuure sock reurns. In order o be as accurae as possible, albei wihin he limiaions of empirical sudies, one has o work ou he bes forecasing model for a paricular marke and in accordance o he prevailing marke condiions. REFERENCES Akgiray, V. (1989). Condiional heeroscedasiciy in ime series of sock reurns. Journal of Business, 6, Bollerslev, T., & Wooldridge, J. M (199). Quasi-maximum likelihood esimaion and inference in dynamic models wih ime-varying covariances. Economeric Reviews, 11,

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