Stock Prices and Dividends in Taiwan's Stock Market: Evidence Based on Time-Varying Present Value Model. Abstract

Transcription

1 Sock Prices and Dividends in Taiwan's Sock Marke: Evidence Based on Time-Varying Presen Value Model Chi-Wei Su Deparmen of Finance, Providence Universiy, Taichung, Taiwan Hsu-Ling Chang Deparmen of Accouning and Informaion, Ling Tung Universiy, Taichung, TAIWAN Yahn-Shir Chen Deparmen of Accouning, Naional Yunlin Universiy of Science and Technology Absrac In his sudy, we use he newly developed momenum hreshold uni roo and coinegraion ess advanced by Enders and Granger (998), and Enders and Siklos (00) o invesigae if here is any asymmeric adjusmen in long-run prices and dividends in Taiwan s sock marke during June 99 o February 005. The empirical resuls indicae ha long-run prices and dividends coinegraion relaionship holds for he majoriy of Taiwan s sock marke, bu ha adjusmen mechanism is asymmeric. The resuls for mos indusries from he M-TAR coinegraion ess aes o he absence of raional bubbles in Taiwan s sock marke. These resuls have imporan policy implicaions for invesors. Ciaion: Su, Chi-Wei, Hsu-Ling Chang, and Yahn-Shir Chen, (007) "Sock Prices and Dividends in Taiwan's Sock Marke: Evidence Based on Time-Varying Presen Value Model." Economics Bullein, Vol. 7, No. 4 pp. - Submied: March, 007. Acceped: March 7, 007. URL: hp://economicsbullein.vanderbil.edu/007/volume7/eb-07g0003a.pdf

2 . Inroducion This sudy invesigaes wheher raional bubbles were presen in Taiwan s sock marke during June 99 o February 005. Financial heory poins ou ha in a well-funcioning capial markes, prices and dividends should be relaed (Brealey and Myers, 986); he presen value of he share should be equal o he dividend sream discouned by he reurn earned on securiies of comparable risk. The occurrence of raional bubbles signifies ha no long-run relaionship exiss beween sock prices and dividends. In pursui of deermining if sock prices and dividends are coinegraed, empirical sudies have, for he mos pars, employed coinegraion echniques. According o he presen value model, sock prices are fundamenally deermined by he discouned value of heir fuure dividends, which derive heir value from fuure expeced earnings (e.g., see Campbell, Lo, & Mackinlay, 997; Cochrane, 00). Empirical sudies of he validiy of presen value models have been exensively conduced in he coinegraion framework in wo approaches. One is based on he assumpion of a consan discoun rae, prediced ha sock prices and dividend levels are araced o each oher in he long-run. I means ha hey are heoreically coinegraed. If sock prices and dividends follow inegraed processes of order hen ransversaliy condiion holds (Campbell & Shiller, 987). Alernaively, if he presen value model is valid, he ime-varying discoun rae can be applied insead of a consan one. As a resul, he log difference beween dividends and prices follows a saionary process (Campbell & Shiller, 988a, 988b). From a heoreical perspecive, here is no sound reason o assume ha economic sysems are inrinsically linear (Barne and Serleis, 000). In fac, numerous sudies have empirically demonsraed ha financial ime series, such as sock prices, exhibi nonlinear dependencies (see, Hsieh, 99; Abhyankar e al., 997). Recen research has mosly advocaed ha he relaionship beween sock prices and dividends may bes be characerized by using a nonlinear model. For example, heoreical models for he ineracion beween arbirage raders and noise have generally suggesed ha small and large reurns may very well exhibi differen dynamics. For example, arbirageurs mus consanly be wary of he possibiliy of noise raders driving reurns furher away from equilibrium before correcion. Oherwise, from a mehodological poin of view, if we ake he long-run validiy of he presen value model, he low power of uni roo ess in paricular, non-lineariies, srucural breaks and/or ouliers are possible candidaes for mixed findings. Consequenly, convenional inegraion and coinegraion mehods are no appropriae because hey assume ha a uni roo is he null hypohesis and a linear process under he alernaive. Therefore, we apply Momenum Threshold Auoregressive (M-TAR) model proposed by Ender & Granger (998) and Enders & Siklos (00). These models are equipped o provide he requisie empirical evidence favorable o he validiy of he presen

3 value by permiing shor-run asymmeric sock price adjusmen or error correcion mechanisms. Pas empirical research show ha raional bubbles exis in Taiwan s sock marke (Chang, 988; Lin and Ko, 993; Sheng and Chang, 000). Mos of hem use radiional linear Dickey-Fuller uni roo and Engle-Granger coinegraion es o improve raional bubbles. This presen empirical sudy conribues significanly o his field of research because, firsly, i deermines wheher raional bubbles exis in Taiwan s sock marke for which we use he M-TAR model of Ender & Granger (998) and Enders & Siklos (00). Second, we rely in our paper on a presen value model wih ime-varying expeced reurns and a general class of processes o model bubble-like deviaions from he long-run equilibrium. Third, o he bes of our knowledge, his sudy is he firs of is kind o apply he M-TAR echnique, which allowing us o draw conclusions in he long-run validiy of he presen value model and, hence, addresses he quesion of wheher Taiwanese sock prices adhere o fundamenals in he long-run. Finally, invesigaing he shor-run dynamics under he M-TAR approach provides a es concerning he imporance of bubble-like processes in sock prices. The framework of he remainder of his paper is as follows. In secion, we provide he heoreical background. Secion 3 briefly describes he M-TAR uni roo and coinegraion es of Enders and Siklos (00). Secion 4 presens he daa we use in our sudy and our empirical resuls are shown in Secion 5. Finally, Secion 6 concludes he paper.. Presen Value Model This paper invesigaes wheher a long-run relaionship exiss beween dividends and prices using a coinegraion mehodology. The framework for our sudy is a presen value model which relaes he real sock price, P, o is discouned expeced fuure real dividends, D, using eiher a consan or a ime-varying expeced reurn (or discoun rae). In paricular i has been applied o es presen value models for sock prices: P = E ( P D ), 0 < ( R) < () ( R) where E denoes he condiional expecaions operaor, P denoes he real price a ime, D is he ime real dividend, R is he expeced real reurn (assumed consan). If he ransversaliy condiion holds, hen he real sock price is equal o he fundamenal value. Following Campbell and Shiller (987), i implies: P i D P = E ΔD i R R i= R () where Δ denoes firs differences. If boh (real) sock prices and dividends are non-saionary, hen under a no-bubbles assumpion such ha he righ-hand-side of () is

4 saionary (I(0)), P and D will be coinegraed wih he coinegraing vecor equal o [,/ R]. When he relaion beween prices and reurns are nonlinear, sock price behavior should be ime-varying. If we sill use he assumpion of consan reurn, i will yield esimaed errors. Campbell and Shiller (988a, 988b) proposed a log-linear approximaion of he presen value framework, which enables he invesigaion of sock prices behavior under any model of expeced reurns. I leads o he following presen value equaion: φ = i p E λ (( λ) d i r i ) (3) λ i= where p denoes he log of real sock price, d he log of he dividend paymen, and he log of he ime-varying discoun rae. φ and λ are linearizaiom parameers. Rewriing Eq. (3) in erms of he log dividend-price raio, we yield: φ = i d p E λ ( Δd i r i ) (4) λ i = Given ha changes in he log dividend and he discoun rae follow process, hen he log sock price and he log dividends are coinegraed wih he coinegraing vecor [, ] and he log dividend-price raio is a saionary process (see Cochrane & Sbordone, 988; Craine, 993). When expeced reurns vary over ime, he presen value model does no generally imply he exisence of a saionary relaionship beween he inegraed level variables and D. In conras, coinegraion ess ha rely on he log dividend-price raio are valid in he presence of ime-varying expeced reurns. If here are no long-run relaionships beween sock prices and dividends, i means here exis raional bubbles in Taiwan s sock marke Taiwan s sock marke may have raional bubbles. Consequenly, our empirical invesigaion is based on he esable implicaions of he presen value model (4) wih ime-varying expeced reurns. Moreover, he findings conained in Ender and Granger (998) and Enders and Siklos (00) demonsrae he low power properies of convenional es approaches in he presence of asymmeric deparures from he long-run equilibrium. The findings make clear ha M-TAR s design capured cerain ypes of asymmeric adjusmen behavior needed o obain deeper insighs ino he characerisics of he log dividend-price raio and sock price behavior. 3. Tesing for Threshold Adjusmen 3. M-TAR uni-roo ess and dividend-price raio The sandard Dickey-Fuller (979) es assumes a uni roo as he null hypohesis and a symmeric adjusmen process under he alernaive. However, he implici assumpion of linear adjusmen is problemaic. If adjusmen o he long-run value of log r P 3

5 dividend-price raio is asymmeric, he sandard uni-roo es and is corresponding error correcion represenaion may enail a misspecificaion error. A formal way o quanify an asymmeric adjusmen process as a generalizaion of he Dickey-Fuller es is given by he MTAR model proposed by Ender & Granger(998) and Enders & Siklos (00): Δ( d p) I ( d p) ( I ) ρ ( d p) γ iδ( d p) i i= = I ρ ε where he indicaor variable is defined as:, if Δ ( d p ) τ I = { 0, if Δ ( d p ) τ (6) where ε is a whie-noise disurbance and he residuals, I is he Heaviside indicaor funcion such ha I = if Δ( d p) τ and I = 0 if Δ( d p) τ, where τ is he hreshold value. A necessary condiion for { Δ( d p) } o be saionary is: < ( ρ, ρ ) < 0. If he variance of ε is sufficienly large, i is also possible for one value of ρ j o be beween and 0 and for he oher value o equal zero. Alhough here is no convergence in he regime wih he uni-roo (i.e., he regime in which ρ j = 0 ), large realizaion of ε will swich he sysem ino he convergen regime. Enders and Granger (998) and Enders and Siklos (00) boh poin ou in eiher case, under he null hypohesis of no convergence, he F-saisic for he null hypohesis ρ = ρ = 0 has a nonsandard disribuion. The criical values for his non-sandard F-saisic are abulaed in heir paper. Enders and Granger (998) also showed ha if he sequence is saionary, he leas squares esimaes of ρ and ρ have an asympoic mulivariae normal disribuion. According o Enders and Granger (998), his model is especially valuable when adjusmen is asymmeric such ha he series exhibis more momenum in one direcion han he oher. This model is ermed Momenum-Threshold Auoregressive Model (M-TAR). The M-TAR model allows he auoregressive decay o depend on Δ( d p). As such, he M-TAR represenaion can capure sharp movemens in a sequence. In he mos general case, he value of τ is unknown, i needs o be esimaed along ( 5 ) wih he value of ρ and ρ. By demeaning he ( d p) sequence, he Enders and Granger (998) es procedure employs he sample mean of he sequence as he hreshold esimae of τ. However, he sample mean is a biased hreshold esimaor in he presence of asymmeric adjusmens. For insance, if auoregressive decay is more sluggish for posiive deviaions of Δ d p) from τ han for negaive deviaions, he sample mean ( esimaor will be biased upwards. A consisen esimae of he hreshold τ can be obained by using Chan s (993) mehod of searching over possible hreshold values o minimize he residual sum of squares from he fied model. Enders and Siklos (00) 4

6 applied Chan s mehodology o a Mone Carlo sudy o obain he F-saisic for he null hypohesis of ρ = ρ 0 when he hreshold τ is esimaed using Chan s procedure. = The criical values of his non-sandard F-saisic for esing he null hypohesis of ρ = ρ 0 are also abulaed in heir paper. As here is generally no presumpion as o = use M-TAR model, he recommendaion is o selec he adjusmen mechanism by a model selecion crierion such as he AIC. The M-TAR model ses up he null hypohesis of a uni roo in he log dividend-price raio, ha is, H ρ 0, H ρ 0, and H ρ = ρ 0. The disribuions for hese 0 : = 0 : = 0 : = saisics are non-saisics and non-sandard. Enders & Granger (998) and Enders & Siklos (00) used simulaion o ge criical values. If he null hypohesis is rejeced, he null hypohesis of symmeric adjusmen is H : ρ = ρ 0. If we canno rejec he null hypohesis H : ρ = ρ 0, we can conclude in favor of a linear and symmeric adjusmen in he log dividend-price raio. 3. M-TAR Coinegraion Tess In his paper, we employ he hreshold coinegraion echnique advanced by Enders and Siklos (00) o es for sock index price and dividends wih asymmeric adjusmen in Taiwan Sock Exchange Capializaion Weighed Sock Index (TAIEX) and seven indusries. This es involves a wo-sage process. In he firs sage, we esimae a long-run equilibrium relaionship of he form: P = α 0 αd u (7) where P and D represen he logarihm of sock price index and dividends respecively, and u is he sochasic disurbance erm. The second sage focuses on he OLS esimaes of ρ and ρ in he following regression: Δu = I ρ l u I ) ρ u γ iδu i i= ( ε where ε is a whie-noise disurbance and he residuals, μ, in (7) are exraced o (8) o be furher esimaed. I is he Heaviside indicaor funcion such ha I = if Δu τ and I = 0 if Δu τ, where τ is he hreshold value. For he case of coinegraion, * le φ and φ be he F-saisics for esing he null hypohesis of ρ = ρ = 0 under he * M-TAR represenaion. The disribuion of φ and φ are deermined by he number of variables in he coinegraing relaionship. Enders & Siklos (00) and Enders & Dibooglu * (00) showed ha he power of φ es exceeds ha of he Engle-Granger es for a reasonable range of asymmery, while he power of φ -saisic increases relaive o Engle-Granger (987) es when he degree of asymmery increases. 4. Daa (8) The indusries are included Cemen, Foods, Plasics & Chemicals, Texile, Elecric & Machinery, Consrucion and Finance. 5

7 We analyze he monhly daa for sock price index ( P ) and dividends ( D ) aken from Taiwan Economic Journal (TEJ) daabase during he June 99 o February 005 period. The daa begin from June 99 since dividend daa are available from his period. Our empirical analysis focuses on Taiwan s group sock price indices, which are TAIEX, Cemen, Food, Plasics & Chemicals, Texile, Elecric & Machinery, Consrucion and Finance. Oherwise, we use Consumer Price Index (CPI) o deflae sock price index and dividends. The purpose is ha we can ge real price and dividends. 5. Empirical Resuls As a firs sep, we es TAIEX and seven indusries log dividend-price raio using he M-TAR specificaions using he hreshold τ = 0, respecively repored in Table. Diagnosic saisics and he values of he AIC are used o selec appropriae lag changes. From Table we can only find ha he Texile indusry is esimaed wih adjusmens using M-TAR. I means ha in oher indusries, prices do no follow heir fundamenal values. Bu in Table using he Chang (993) mehod o find he hreshold τ, we can find he null hypohesis of no convergence is rejeced because he log dividend-price raio is saionary wih asymmery adjusmen. The indusries include TAIEX, exile, elecric & machinery, consrucion and finance. Hence, our empirical evidence generally suppors he majoriy of all indusries wih long-run validiy of he presen value model wih ime-varying expeced reurns for he Taiwan s sock marke. Furhermore, he majoriy of cases shows ha ρ and ρ are saisically significanly mixed. The absolue value of parameer ρ is higher compared o he esimaed ρ coefficien, excep he Consrucion and Finance indusry. The F-saisic rejecs he null hypohesis of symmeric adjusmen, expec for he cemen indusry. Hence, i is reasonable o conclude ha he log dividend-price raes are saionary, and he adjusmen mechanisms are asymmeric. Table Esimaed adjusmen equaions using momenum hreshold uni es wih zero hreshold Indusry ρ ρ Φ μ ρ = ρ AIC Lags Q(4) Asymmeric adjusmen wih τ = 0 TAIEX ** Cemen Foods Plasics & Chemicals Texile 0.04** ** 4.4** 8.08*** Elecric & Machinery Consrucion Finance Noe: *, **, *** indicae significance levels a 0%, 5% and % respecively. Enries in his column are he F-saisics for he null hypohesis ρ = ρ = 0. This es follows a non-sandard disribuion so he es saisics are compared wih criical values repored by Enders and Granger (998). 6

8 he numbers repored in his column are F-saisics of symmeric adjusmen. Table Esimaed adjusmen equaions using momenum hreshold uni es wih consisen esimae of he hreshold Indusry ρ ρ Asymmeric adjusmen wih τ =hreshold Φ μ ρ = ρ AIC Lags τ Q(4) TAIEX 0.0** ** 3.97** 7.943*** Cemen Foods * Plasics & Chemicals * ** Texile 0.057*** *** 0.807***.339*** Elecric & Machinery *** 3.79** 7.37*** Consrucion ** * 5.0** Finance 0.049* -0.08* 3.05* 5.93*** Noe: *, **, *** indicae significance levels a 0%, 5% and % respecively. Enries in his column are he F-saisics for he null hypohesis ρ = ρ = 0. This es follows a non-sandard disribuion so he es saisics are compared wih criical values repored by Enders and Granger(998). he numbers repored in his column are F-saisics of symmeric adjusmen. Table 3 repors he applicaion of he Engle-Granger procedure o equaion (7). For each indusry he lag lengh was seleced using he Akaike Informaion Crieria (AIC). The Engle-Granger coinegraion es resuls indicae ha he null of no coinegraion can be rejeced. The oucome is he same as claiming raional bubbles are exisen in he Taiwan sock marke (Chang, 988; Lin and Ko, 993; Sheng and Chang, 000) when hey used radiional linear Dicky-Fuller es. The absence of a long-run relaionship beween prices and dividends in hese iniial ess migh be aribued o he employmen of linear ess for mean reversion. There are in fac asymmeries in any adjusmen oward fundamenal values wih respec o posiive and negaive shocks. Moreover, hese ess for symmeric coinegraion have low power agains a background of asymmeric adjusmens. Therefore, we pursue hreshold coinegraion ess. The resuls of he hreshold coinegraion es wih zero hreshold are shown in Table 4. The null hypohesis of ρ = ρ 0 can be rejeced for five indusries. These resuls indicae ha raional = bubbles do no exis for mos indusries. Thus, he relaionship beween prices and dividends generally fails, assuming linear adjusmen or allowing for asymmeric adjusmen using a hreshold value of zero. Given he presence of measuremen errors and/or adjusmen coss, here is no reason o presume ha he hreshold is equal o zero. As shown in Table 5, widespread suppor for he heory is found when Chan s mehod is used o obain a consisen esimae of hresholds. The MTAR model uses he AIC model 7

9 o selec crierion. We find here is srong evidence of no raional bubbles beween he prices and dividends, excep in foods and finance indusries. A major difference from he resuls previously repored in Table 3 indicaes ha he case for coinegraion is subsanially srenghened when asymmeries are accouned for. In addiion, whenever raional bubbles do no exis, he null hypohesis of symmeric adjusmen is also rejeced. The ess suppor he predicion under ime-varying presen value models ha he following five indusries are coinegraed: TAIEX, Cemen, Plasics & Chemicals, Texile, Elecric & Machinery and Consrucion. In addiion, in mos cases (7 ou of he oal 8 indusries) here is evidence ha ρ < ρ implying ha he speed of adjusmen oward fundamenal values is faser in he case of a negaive shock wih respec o μ. For example, he rae of he exile indusry converges o is fundamenal value, τ, a he rae of 9.3% for a posiive deviaion and 5.7% for a negaive deviaion. Table 3 The esimaed adjusmen equaions using he sandard coinegraion es Indusry ρ AIC Lags Symmeric adjusmen TAIEX ( ) Cemen (-3.807) Foods (-.9906) Plasics & Chemicals (-.9666) Texile (-3.97) Elecric & Machinery (-3.409) Consrucion (-.965) Finance (-.734) Noes: The criical vales of -saisics for he null hypohesis = 0 ρ wih hree variables in he coinegraing relaionship are -4.73, -4., and a he %, 5% and 0% significance levels respecively. Table 4 Esimaed adjusmen equaions using momenum hreshold coinegraion es wih zero hreshold Indusry ρ ρ Φ μ ρ = ρ AIC Lags Q(4) Asymmeric adjusmen wih τ = 0 TAIEX ** ** 5.969** Cemen -0.46** -0.*** 7.6** Foods Plasics & Chemicals -0.69*** * Texile *** 6.48**

10 Elecric & Machinery -0.07** ** 5.484* Consrucion ** Finance * Noe: *, **, *** indicae significance levels a 0%, 5% and % respecively. Enries in his column are he F-saisics for he null hypohesis ρ = ρ = 0. This es follows a non-sandard disribuion so he es saisics are compared wih criical values repored by Enders and Siklos(00). he numbers repored in his column are F-saisics of symmeric adjusmen. Table 5 Esimaed adjusmen equaions using momenum hreshold coinegraion es wih consisen hreshold Indusry ρ ρ Asymmeric adjusmen wih τ =hreshold Φ μ ρ = ρ AIC Lags τ Q(4) TAIEX -0.88*** ** 8.07** 3.94** Cemen -0.37** -0.94*** 8.443**.86* Foods ** Plasics & Chemicals -0.09*** * 3.995** Texile ** -0.57*** 7.9** 3.79* Elecric & -0.09** -0.93* 6.79* Machinery Consrucion *** 8.844*** 0.964*** Finance -0.34** Noe: *, **, *** indicae significance levels a 0%, 5% and % respecively. Enries in his column are he F-saisics for he null hypohesis ρ = ρ = 0. This es follows a non-sandard disribuion so he es saisics are compared wih criical values repored by Enders and Siklos(00). he numbers repored in his column are F-saisics of symmeric adjusmen. Having found evidence supporing asymmeric adjusmen, an asymmeric error-correcion model can be used o invesigae he movemen of variables o he long-run equilibrium relaionship. We esimae he following sysem of asymmeric error-correcion models for each indusry: ΔP ΔD = α 0 = α 0 K i= K i= α ΔP i i i α ΔP i K i= K i= β ΔD i i i β ΔD i γ P γ Z D where Z = I μ and Z = ( I ) μ, μ is he residual from equaion (7), I = if Δu τ and I = 0, oherwise. The choice of he appropriae lag lengh is based on he mulivariae AIC. The choice of non-zero hreshold follows he same procedure oulined earlier. The esimaed asymmeric error-correcion models wih consisen esimae of hresholds are shown in Table 6. The esimaed coefficiens of and Z γ P γ Z D Z ε ε Z (9) Z 9

11 deermine he speed of adjusmen for posiive and negaive deviaions from fundamenal values, respecively. We found ha posiive deviaions from values are eliminaed quicker han negaive deviaions and he price (no he dividends) is responsible for mos of he adjusmens. The resuls repored in Table 6 highligh more generally he roles played by price adjusmen. Furhermore, we found ha he speed of adjusmen coefficiens on dividend levels end o be small in magniude and saisically insignifican. For comparison purposes, we also esimae symmeric error-correcion models for each indusry. Bu, resuls repored in Table 6 indicae ha he dividend (no he price) is responsible for mos of hese adjusmens. Table 6 The esimaed asymmeric error-correcion models Linear ECM Threshold ECM Indusry ρ Lags ρ ρ TAIEX Δ p (.435) Δ d *** (-3.733) Cemen Δ p 0. 04* (.783) Δ d -0.9*** (-4.08) Plasics & Chemicals Δ p * (.700) Δ d *** (-.859) Texile Δ p *** (.389) Δ d -0.7*** (3.6) Elecric & Machinery Δ p *** (.996) Δ d (-0.87) Consrucion Δ p (.337) Δ d -0.08*** (-.86) -0.39*** (-.746) ** (-.40) * (-.77) (.63) *** (-3.99) * (-.897) ** (-.563) (-.407) ** (-.54) * (-.797) * (-.9) (-0.) (-.4) ** (-.75) (-.638) 0. 68*** (3.64) (-0.93) (-0.49) (-0.865) (-0.774) -0.4*** (-.934) (-0.30) (-0.55) 0. *** (.954) τ Noe: -Saisics are in parenheses,. *, **, *** indicae significance levels a 0%, 5% and % respecively 0

12 6. Conclusions The purpose of his paper is o invesigae wheher raional bubbles exis in Taiwan s sock marke. A large par of he curren debae on Taiwan sock price behavior concenraed on he quesion of wheher sock prices are driven by fundamenals. We found ha he presen value model wih ime-varying expeced reurns (Campbell & Shiller, 988a, 988b) provides an empirically valid descripion of Taiwan sock price behavior. We apply he momenum hreshold auoregressive (MTAR) mehod by Enders & Granger (998) and Enders & Siklos (00) for Taiwan s sock marke. Compared o convenional coinegraion approach, his echnique produces more convincing evidence of he ime series properies of he dividend and price, because i is flexible enough o capure non-linear adjusmen paerns. These findings suppor he exisence of sock price increases relaive o is fundamenals. Hence, hese resuls reveal ha sock prices adhere o dividends and raional bubbles were nonexisen in Taiwan s sock marke during June 99 o February 005. References Abhyankar, A. H., L. S. Copeland and W. Wong (997) Uncovering Nonlinear Srucure in Real Time Sock Marke Indexes: he S&P 500, he DAX, he Nikki 5, and he FTSE 00 Journal of Business and Economic Saisics, 5, -4. Barne, W.A. and A. Serleis (000) Maringales, Nonlineariy, and Chaos Journal of Economic Dynamics and Conrol, 4, Brealey, R. A. and S. C. Myers (986) Principle of Corporae Finance, McGraw Hill, London. Campbell, J. Y., and R. J. Shiller (987) Coinegraion and ess of presen value models Journal of Poliical Economy, 95, Campbell, J. Y., and R. J. Shiller (988a) The dividend-price raio and expecaions of fuure dividends and discoun facors Review of Financial Sudies,, Campbell, J. Y., and R. J. Shiller (988b) Sock prices, earnings, and expeced dividends Journal of Finance, 43, Campell, J. Y., A. W. Lo and A. C. MacKinlay (997) The Economerics of Financial Markes, Princeon Universiy Press, Princeon NJ. Chan, K.S. (993) Consisency and Limiing Disribuion of he Leas Squares Esimaor of a Threshold Auoregressive Model The Annals of Saisics,, Chang, L. H. (990) Tesing he Exisence bubbles in Taiwan Sock marke Securiy Managemen, 8, 6-0. Cochrane, J. H. (00) Asse pricing, Princeon Universiy Press, Princeon NJ. Cochrane, J. H. and A. M. Sbordone (988) Mulivariae esimaes of he permanen componens of GNP and sock prices Journal Economic Dynamics and Conrol,, 55-96

13 Craine, R. (993) Raional bubbles. A es Journal Economic Dynamics and Conrol, 7, Enders, W. and S. Dibooglu (00) Long-run purchasing power pariy wih asymmeric adjusmen Souhern Economics Journal 6, 0-0. Enders, W. and C.W.F. Granger (998) Uni-Roo Tess and Asymmeric Adjusmen Wih an Example Using he Term Srucure of Ineres Raes Journal of Business Economics & Saisics, 9, Enders, W., and P. L. Siklos (00) Coinegraion and hreshold adjusmen Journal of Business and Economic Saisics 9, Engle, Rober and C. W. J. Granger (987) Coinegraion and Error Correcion: Represenaion, Esimaion, and Tesing Economerica, 55, Hsiao, Cheng (979) Causaliy in economerics Journal of Economic Dynamics and Conrol, 4, Lin, U. and S. T. Ko (993) The empirical evidence of bubbles heory in Taiwan sock marke: esing he exisence and characerisics of bubbles Journal of Taiwan Economics and Finance, 9, Sheng, S. L. and U. C. Chang (000) Tesing he Exisence of Speculaive Bubbles in Sock Price of Financial Indusry Journal of Indusry Economics, 06,