Testing for the Random Walk Hypothesis and Structural Breaks in International Stock Prices

Transcription

1 Universiy of Wollongong Research Online Faculy of Business - Economics Working Papers Faculy of Business 200 Tesing for he Random Walk Hypohesis and Srucural Breaks in Inernaional Sock Prices S. Chanchara Universiy of Wollongong A. Valadkhani Universiy of Wollongong, abbas@uow.edu.au Publicaion Deails Chanchara, S and Valadkhani, A, Tesing for he Random Walk Hypohesis and Srucural Breaks in Inernaional Sock Prices, Working Paper 0-, Deparmen of Economics, Universiy of Wollongong, 200. Research Online is he open access insiuional reposiory for he Universiy of Wollongong. For furher informaion conac he UOW Library: research-pubs@uow.edu.au

2 Universiy of Wollongong Economics Working Paper Series 200 hp:// Tesing for he Random Walk Hypohesis and Srucural Breaks in Inernaional Sock Prices Surachai Chanchara and Abbas Valadkhani WP 0- Ocober 200

3 Tesing for he Random Walk Hypohesis and Srucural Breaks in Inernaional Sock Prices Surachai Chanchara and Abbas Valadkhani * School of Economics, Universiy of Wollongong, NSW 222 Ausralia Absrac This paper examines wheher sock prices for counries are rend saionary or follow a random walk process using he (Zivo and Andrews, 992) and (Lumsdaine and Papell, 99) ess and monhly daa (98:2-200:2). Wih one srucural break, he ZA es resuls provide evidence in favour of random walk hypohesis in counries. However, when wo endogenously-deermined srucural breaks are considered, his hypohesis was rejeced for only five counries, suggesing a robus conclusion regarding he non-saionariy of sock prices world wide. In addiion, he daes of srucural break in mos cases poin o he Asian crisis in he period JEL Classificaion: G, G, C22 Keywords: sock marke, random walk, srucural break * Abbas Valadkhani (corresponding auhor), abbas@uow.edu.au.

4 . INTRODUCTION Vibran sock markes are imporan o promoe economic growh. The essenial funcion of sock markes is o allocae funds from savers o invesors, leading o more efficien allocaion of resources and economic prosperiy. However, sock markes can rouble he economy as a whole oo. Previous sudies in financial lieraure found ha an inefficien marke canno serve he economy as much as an efficien marke (Ma, 200). Therefore, he efficien marke hypohesis has been widely invesigaed in numerous financial sudies. There are several approaches o esing he efficiency of sock markes. However, he random walk hypohesis has been broadly used by a large number of financial analyss. The issue of wheher sock prices can be characerized as random walk or rend saionary process has been widely invesigaed. If sock prices follow a random walk process, any shocks o sock prices will be permanen and fuure reurns canno be forecased by using informaion on hisorical prices. Neverheless, if sock prices follow a rend saionary process, he price level reurns will rever o is rend pah over ime and fuure reurns can be prediced by using hisorical prices (Chaudhuri and Wu, 200). The erm random walk describes he movemens of sock prices canno be prediced because hey can change wihou fronier in he long run. Alhough he subjec of random walk in sock prices has been sudied before, however, here is no consensus among analyss due o he inconclusive resuls in he lieraure. Fama (90) and Fama and French (988) firs found ha he US sock prices are rend saionary. In addiion, using variance raio ess, Lo and MacKinlay (988) and Poerba and Summers (988) also offered some evidences of rend saionary in he US sock prices. On he oher hand, more recenly Kim, Nelson and Sarz (99) and McQueen (992) demonsraed ha he resuls of rend saionary in US sock prices are no robus o ouliers or alernaive disribuional assumpions. A number of sudies have also invesigaed he rend saionary propery for inernaional sock prices. However, evidence of random walk or rend saionary process in sock prices is quie mixed (Urruia, 99; Zhen, 998; Malliaropulos and Priesley, 999; Balvers, Wu and Gilliland, 2000). The issue of srucural breaks in macroeconomic ime series has been subjec o an exensive invesigaion. Srucural breaks manifes hemselves in he ime series daa for a number of reasons for insance economic crises, policy changes and regime shifs. Perron (989) argued ha if srucural breaks are no deal wih appropriaely, one may obain spurious resuls. However, here are few sudies which have incorporaed srucural breaks in esing for uni roos in sock prices. Chaudhuri and Wu (200) employed one srucural break proposed by Zivo and Andrews (992), hereafer ZA, o es he random walk hypohesis in sock prices of emerging markes. They found evidence of rend saionary for en ou of eigheen sock markes. Narayan and Smyh (200) invesigaed he exisence of random walk for OECD counries using he ZA es. Similar o he presen sudy, heir findings also provided srong suppor for he random walk hypohesis. The major objecive of his paper is o invesigae he random walk hypohesis in sock prices of counries for which we could obain consisen and comparable ime series daa. We firs begin wih he convenional uni roo ess which do no consider any srucural breaks in he daa, i.e. he Augmened Dickey-Fuller (ADF) and Phillips-Perron (PP) ess. We hen employ more relevan uni roo ess which allow one srucural break, ZA es, and wo srucural breaks (Lumsdaine and Papell, 99, hereafer LP) o examine he significance Gujarai (200) argues ha he erms random walk, uni roo and nonsaionariy can be used inerchangeably. However, while every random walk is an I() process, he reverse is no always he case. 2

5 of srucural breaks. These wo ess will empirically deermine he mos significan srucural break in he daa. The remainder of he paper is srucured as follows. Secion 2 discusses briefly he empirical mehodology uilized in he analysis. Then Secion describes he summary saisics of he daa employed. Secion presens he empirical economeric resuls as well as policy implicaions of he sudy. The paper ends wih some concluding remarks. 2. METHODOLOGY We perform he ADF uni roo es o examine he ime series properies of he daa wihou allowing for any srucural breaks. The ADF es (Dickey and Fuller, 99) is conduced using he following equaion: y = µ + β+ αy + c y + ε k i i () i= where y denoes he ime series being esed, is he firs differen operaor, is a ime rend erm, k denoes he number of lagged erms and ε is a whie noise disurbance erm. In his paper, he lowes value of he Akaike Informaion Crierion (AIC) has been used as a guide o deermine he opimal lag in he ADF regression. These lags augmen he ADF regression o ensure ha he error is whie noise and free of serial correlaion. In addiion, he PP es proposed by Phillips and Perron (988) has been used as an alernaive nonparameric model of conrolling for serial correlaion when esing for a uni roo. By using he PP es, one can ensure ha he higher order serial correlaions in he ADF equaion have been handled properly. In oher words, he ADF es correcs for higher order auocorrelaion by including lagged differenced erms on he righ-hand side of he ADF equaion, whereas he PP es correcs he ADF -saisic by removing he serial correlaion in i. This nonparameric correlaion uses he Newey-Wes heeroscedasiciy auocorrelaion consisen esimae and is robus o heeroscedasiciy and auocorrelaion of unknown form. An imporan shorcoming associaed wih he ADF and PP ess is ha hey do no allow for he effec of srucural breaks. Perron (989) argued ha if a srucural break in a series is ignored, uni roo ess can erroneous in rejecing null hypohesis. Perron (989) proposed models which allow for one-ime srucural break in Equaion (). Moreover, ZA (992) have developed mehods o endogenously search for a srucural break in he daa. We employed model C which allows for a srucural break in boh he inercep and slope in he following equaion: y k = µ + β+ θdu + γdt + αy + c y + ε (2) i= i i where DU = if > TB, oherwise zero; TB denoes he ime of break, DT = TB if > TB, oherwise zero. As Ben-David, Lumsdaine and Papell (200) argued, if here are wo srucural breaks in he deerminisic rend, hen uni roo ess wih one srucural break will also lead o a misleading conclusion. LP (99) argued ha uni roo es ha accoun for wo srucural breaks is more powerful han hose, which only accommodae for one srucural break. They inroduced a new procedure o capure wo srucural breaks as an exension of model C by including wo endogenous breaks in Equaion (). Consequenly, model CC can be represened as follows:

6 y = µ + β+ θdu + γdt + ωdu 2 + ψdt 2 + αy + c y + ε () where DU = if > TB, oherwise zero; DU 2 = if > TB2, oherwise zero; DT = TB if > TB, oherwise zero; DT 2 = TB2 if > TB2, oherwise zero. Two dummy variables (i.e. DU and DU2 ) are indicaors for srucural breaks in he inercep a TB and TB2, respecively. However, he oher dummy variables (i.e. DT and DT2 ) are indicaors for srucural breaks in rend a TB and TB2, respecively. Following Hall (99), we se k max = 2 in he es procedure. The rimming region, in which we have searched for TB and TB2 cover he 0.T-0.8T period. We have seleced he break poins (TB and TB2) based on he minimum value of he saisic for α. k i= i i. THE DATA Sample daa included in his paper are sock prices from he following counries: Argenina (AR), Ausralia (AU), Brazil (BA), Germany (GE), Hong Kong (HK), Indonesia (IN), Japan (JA), Korea (KO), Malaysia (MA), he Philippines (PH), Russia (RU), Singapore (SG), Taiwan (TA), Thailand (TH), he Unied Kingdom (UK) and he Unied Saes (US). Seven of hese markes are caegorized as developed marke (e.g. Ausralia, Germany, Hong Kong, Japan, Singapore, he UK and US) and he remainder is regard as emerging marke. Monhly daa span from December 98 o December 200 wih a base value of 00 in December 98, excep for he sock price index of Russia which covers he period December 99 o December 200 wih a base value of 00 in December 99. This differen base year has been modified accordingly. All sock indices were obained from Morgan Sanley Capial Inernaional. Table presens he descripive saisics of he daa. Sample means, medians, maximums, minimums, sandard deviaions, skewness, kurosis as well as he Jarque-Bera saisics and p-values are presened. The highes mean reurn is 0 per cen in Russia and he lowes is 000 per cen in Japan. The sandard deviaions range from 0 per cen (he leas volaile) o 0.88 per cen (he mos volaile). The sandard deviaions of sock reurns are lowes in developed economies (i.e. he US, UK, Ausralia, Germany, Japan and Singapore), and he mos volaile in Russia, Brazil, Argenina, Indonesia, Thailand and Taiwan. All monhly sock reurns, Ln(P /P - ), have excess kurosis which means ha hey have a hicker ail and a higher peak han a normal disribuion. The calculaed Jarque-Bera saisics and corresponding p-values are used o es for he normaliy assumpion. Base on he Jarque-Bera saisics and p-values, his assumpion is rejeced a any convenional level of significance for all sock reurns, wih he only excepions being he monhly sock reurns in Ausralia, Japan and he UK.. EMPIRICAL RESULTS AND POLICY IMPLICATIONS As menioned earlier, we firs used he ADF and PP ess o deermine he order of inegraion of he sock prices sudied in his paper. The lowes value of he AIC has been used o deermine he opimal lag lengh in he esimaion procedure. These lags augmen he relevan ADF regressions o ensure he error erm is whie noise and free of any serial correlaion. Based on he resuls of he uni roo ess presened in Table 2, he ADF and PP ess rejec he random walk hypohesis for sock prices in Taiwan a he and per cen, respecively. However, for all oher counries boh uni roo ess canno rejec he random walk hypohesis.

7 We hus concluded ha almos all sock prices employed in his paper are I(), in oher words, hey follow a random walk. In he second sage, we subjec each variable o one and wo srucural breaks. For each series, we hen esimaed model C and repored he resuls in Table. As menioned earlier, he ADF and PP es resuls reveal ha mos sock prices examined in his paper followed a random walk, whereas he resuls of he ZA es show ha sock prices for wo counries (i.e. Malaysia and Russia) are now saionary. The remaining foureen counries sill conain a uni roo in he daa. The esimaed coefficiens µ and θ are saisically significan for all variables excep for µ in case of Russian sock prices. Thus a leas here has been one srucural break in he inercep during he sample period for all sock prices. The esimaed coefficiens for β and γ are saisically significan in 0 ou of counries, implying he sock price series exhibi an upward or downward rend and here exis a leas one srucural break in rend in hese en counries. The repored TBs are endogenously deermined in he ZA es and presened in he second column of Table 2. I is no surprising o noe ha mos imporan srucural break in hese sock prices occurred in he Asian crisis period , see TBs for Hong Kong, Indonesia, Korea, Malaysia, he Philippines, Russia, Singapore, Thailand, he UK and US.

8 Table Descripions of he Daa Employed Variable Mean Median Maximum Minimum Sandard deviaion Skewness Kurosis Jarque-Bera p-value AR = AU = BA = GE = HK = IN = JA = 82e KO = MA = PH = RU = SG = TA = TH = UK = US = Source: Morgan Sanley Capial Inernaional. Noe: Daa employed covering he period December 98-December 200 excep for he sock price index of Russia December 99 o December 200.

9 Table 2 Uni Roo Tes Resuls: y = µ + β+ αy + c y + ε ADF es PP es Variable Consan and Consan and Opimal lag Bandwidh rend rend AR = AR = - *** 0-0 *** 2 2 AU = AU = -902 *** - *** 2 2 BA = BA = -.92 *** *** GE = GE = -. *** 0 -. *** 2 HK = HK = -0 *** 0-0 *** IN = - * IN = -0 *** -2 *** JA = JA = -. *** 0 -. *** 8 KO = KO = - *** 0 - *** 9 8 MA = MA = -.82 ** 0-2 *** PH = PH = -.9 *** 0-0 *** 0 RU = RU = -8. *** -9.9 *** 2 SG = SG = -.9 *** *** 2 TA = -.9 ** -8 *** TA = - *** 0 -. *** 2 TH = TH = -. *** -.9 *** UK = UK = -. *** -.8 *** 9 US = US = -.80 *** ** Noes: (a) Daa employed covering he period December 98-December 200 excep for he sock price index of Russia December 99 o December 200. (b) *, ** and *** indicaes ha he corresponding null hypohesis is rejeced a he 0, and per cen significance level, respecively. k i= i i

10 Table The Zivo and Andrews Tes Resuls: Break in Boh Inercep and Trend: 8 y = µ + β+ θdu + γdt + αy + c y + ε Variable TB µ β θ γ α k Inference AR = 99:02 (.8) ** (0.) (22) ** (-0) (-.) AU = 200:02 (.92) *** (.9) *** (-) *** (.) *** (-.) BA = 99:2 (88) *** (-) (2.82) *** (.) (-.) GE = 200:02 (.8) *** (.9) *** (-0) *** (0.9) (-.80) HK = 99:08 (.8) *** (.9) *** (-) *** (-2.) ** (-.9) IN = 99:08 (0) *** (0.8) (-) *** (.92) * (-) Random walk JA = 200:0 (.) *** (-.) (-2.8) *** (2.989) *** (-.) Random walk KO = 99:09 (.8) *** (-99) (-282) ** () *** (-.) MA = 99:0 () *** () *** (-) *** (-) * (-.8) *** 2 Saionary PH = 99:0 () *** (29) ** (-) *** (-.8) * (-.) Random walk RU = 998:0 (-8) () *** (-9) *** (-.) *** (-.90) *** Saionary SG = 99:0 (8) *** (2) ** (-2) *** (-2) (-.) TA = 99:0 (.890) *** (-2.8) *** (.) *** (2.) ** (-.) 2 Random walk TH = 99:0 (.8) *** (.8) * (-.8) *** (-0) (-.) 2 Random walk UK = 99:08 () *** (2) ** (2.) ** (-2.8) *** (-8) 2 Random walk US = 99:0 (.9) *** () *** (2.) ** (-) *** (-.9) Noes: (a) Daa employed covering he period December 98-December 200 excep for he sock price index of Russia December 99 o December 200. (b) *, ** and *** indicaes ha he corresponding null hypohesis is rejeced a he 0, and per cen significance level, respecively. (c) Criical values for α a he 0,, and per cen are -.82, -8 and -., respecively (Zivo and Andrews, 992). k i= i i

11 Table presens he resuls of he LP es allowing for he wo mos significan srucural breaks. The resuls show ha sock prices for counries (i.e. Argenina, Indonesia, Korea, Malaysia and Russia) become saionary now. The esimaed coefficiens for θ, γ, ω and ψ are significan for sock prices of Argenina, Brazil, Germany, Hong Kong, he Philippines, Russia, Thailand, he UK and US, indicaing ha srucural changes a TB and TB2 have impaced on boh he inercep and rend. In he case of Indonesia, Japan and Singapore, while γ, ω and ψ are significan, θ is no, suggesing ha he second srucural break occurred a TB2 for his sock price has affeced boh he inercep and slope bu he firs one exered a significan change in rend only. Finally based on he magniudes of -raios for θ, γ, ω and ψ, while he firs srucural break in Korea shifed boh he inercep and slope, he second one had no significan effec. On he oher hand, he second srucural break in Taiwan changed boh he inercep and rend whereas he firs one had no significan effec. Figure shows he log and he monhly reurn of each of he sock prices employed as well as heir corresponding srucural breaks--he hick dashed line denoes TB for he ZA es and he solid and hin dashed lines are used o show TB and TB2 in he LP es, respecively. The TBs and TB2s are presened in he second and hird column of Table. The resuls are quie consisen in idenifying srucural breaks in mos sock prices. TB in he ZA es is he same as ha of eiher TB or TB2 in he LP es for counries (i.e. Hong Kong, Indonesia, Korea, Malaysia, Russia, Singapore and he UK). In order o faciliae he cross model comparison, he imes of srucural breaks obained by he ZA and LP ess are presened in Table. As menion earlier, he resuls from boh ess are quie consisen. The mos significan break occurred during various monhs in he period for 0 and 9 counries in he ZA and LP ess, respecively. Two oher imporan breaks across various markes occurred in and , which coincided wih wo world-wide recessions. Based on he ZA es, in counries he srucural break occurs in and he same number in On he oher hand, he LP es resuls in Table show ha in counries he firs break occurred in 99-99, and for 2 counries he second break was idenified in Apar from he Asian crisis and he above wo global recessions, hese have been several oher counry-specific evens which caused jiers in financial markes (See Table ).. CONCLUDING REMARKS The main purpose of his empirical analysis is o examine he random walk hypohesis in sock prices of counries for which here were consisen monhly daa available. The resuls of he ADF and PP ess sugges ha here is a uni roo in almos all sock prices; supporing a random walk hypohesis. However, afer incorporaing one srucural break in he daa, he ZA es found evidence in favour of random walk hypohesis for counries. By applying he LP es, which allows for wo endogenously deermined srucural breaks in each series, similar o he resuls repored in he lieraure we have also found mixed resuls concerning he random walk hypohesis. Tha is o say, while monhly sock prices in Argenina, Indonesia, Korea, Malaysia and Russia were I(0), he sock prices in he res of counries coninued o follow a random walk process. According o he weak form of he efficien marke hypohesis, sock prices compleely reflec he informaion conained in he daa and consequenly no one can devise an invesmen sraegy o obain abnormal profis on he basis of an analysis of pas price paerns. In his paper we found some empirical evidence ha suppors previous saemen. In oher words, majoriy of marke prices evolve according o a random walk and as such hey canno be prediced using hisorical daa despie considering up o wo significan srucural breaks in he daa. 9

12 Table The Lumsdaine and Papell Tes Resuls: Break in Boh Inercep and Trend: y = µ + β+ θ DU + γ DT + ωdu 2 + ψ DT 2 + α y + c y + ε i i i= Variable TB TB2 µ β θ γ ω ψ α k Inference AR = 99: :0 (.) *** (.8) *** (.) *** (-.) *** (-.98) *** (.8) *** ** (-2) 2 Saionary AU = 99: 2002:0 (.8) *** (0.90) (2.8) ** (-0.8) (-.80) *** (0) *** (-.9) BA = 998: :0 (0) *** (.80) *** (.8) * (-2.) ** (-.) *** (.) *** (-9) 2 Random walk GE = 998: :0 (.928) *** () *** (29) *** (-9) *** (-) *** (.80) *** (-.8) 9 Random walk HK = 99:0 2002:0 (.822) *** (.8) *** (208) ** (-) *** (-2) ** (28) * (-.) IN = 99:08 200:02 (.8) *** (.9) (00) (-2.8) ** (-.88) * (2) ** (-9) * 8 Saionary JA = 99:0 2002:0 (22) *** () *** (-0) (2.8) ** (-.) *** () *** (-) 9 Random walk KO = 99: 99:0 (.90) *** (-) *** (0.8) (0.8) (-.9) *** (.8) *** ** (-2) Saionary MA = 99:0 99:08 (.) *** (2.9) *** (.90) * (-0.922) (-9) *** *** (0.8) (-) 2 Saionary PH = 99: 2002:0 () *** (.) *** () *** (-.89) *** (-.) *** (.) *** (-.80) 2 Random walk RU = 99:0 998:08 () *** (.9) *** (8) *** (-9) *** (-0) *** (.8) *** ** (-) 0 Saionary SG = 99:0 2002:0 (.) *** (.98) *** (.8) (-2.9) *** (-.) *** (2.89) *** (-92) 2 Random walk TA = 990: :09 (80) *** (2.) *** (0.9) (-2.) ** (-0.9) (-0) (-.9) 9 Random walk TH = 99:0 2000:0 (.8) *** (9) (.9) *** (-.) *** (-.9) *** (.9) *** (-99) 2 Random walk UK = 99:0 2002:0 () *** (.) *** (.88) *** (-.92) *** (-9) *** (.9) *** (-) 2 Random walk US = 99: :09 (.8) *** (0) *** (-.) *** (.) *** (2.) ** (-2.9) *** (-) Noes: (a) Daa employed covering he period December 98-December 200 excep for he sock price index of Russia December 99 o December 200. (b) *, ** and *** indicaes ha he corresponding null hypohesis is rejeced a he 0, and per cen significance level, respecively. (c) Criical values for α a he 0,, and per cen are -.9, -.82 and -., respecively (Lumsdaine and Papell, 99). 0 k

13 Figure Plo of Sock Price Indices Reurn of AR Ln(AR) 8 Reurn of AU Ln(AU) Reurn of BA Ln(BA) 8 Reurn of GE Ln(GE) Ln(AR) Reurn of AR Ln(AU) Reurn of AU Ln(BA) Reurn of BA Ln(GE) Reurn of GE Reurn of HK Ln(HK). Reurn of IN Ln(IN) Reurn of JA Ln(JA) Reurn of KO Ln(KO) Ln(HK) Reurn of HK Ln(IN) Reurn of IN Ln(JA) Reurn of JA Ln(KO) Reurn of KO Reurn of MA Ln(MA). Reurn of PH Ln(PH) Reurn of RU Ln(RU) Reurn of SG Ln(SG) Ln(MA) Reurn of MA Ln(PH) Reurn of PH Ln(RU) Rrurn ofru Ln(SG) Reurn of SG Reurn of TA Ln(TA). Reurn of TH Ln(TH) Reurn of UK Ln(UK) Reurn of US Ln(US) Ln(TA) Reurn of TA Ln(TH) Reurn of TH Ln(UK) Reurn of UK Ln(US) Reurn of US Source: Morgan Sanley Capial Inernaional.

14 Table Comparing he Time of Srucural Breaks for he Zivo and Andrews Tes and Lumsdaine and Papell Tes Resuls Zivo and Andrews es Lumsdaine and Papell es Variable TB Possible causes for TBs TB Possible causes for TBs TB2 Possible causes for TB2s AR = 99:02 - Global recession :08 - Global recession :0 - Global recession AU = 200:02 - Global recession : - Global recession :0 - Global recession BA = 99:2 - Global recession :08 - Asian crisis 2002:0 - Global recession GE = 200:02 - Global recession :02 - Asian crisis 2002:0 - Global recession HK = 99:08 - Asian crisis 99:0 - Asian crisis 2002:0 - Global recession IN = 99:08 - Asian crisis 99:08 - Asian crisis 200:02 - Domesic even JA = 200:0 - Global recession :0 - Global recession :0 - Global recession KO = 99:09 - Asian crisis 99: - Asian crisis 99:0 - Asian crisis 8 MA = 99:0 - Asian crisis 99:0 - Asian crisis 99:08 - Asian crisis 9 PH = 99:0 - Asian crisis 99: - Domesic even 2002:0 - Global recession RU = 998:0 - Asian crisis 99:0 - Asian crisis 998:08 - Asian crisis SG = 99:0 - Asian crisis 99:0 - Asian crisis 2002:0 - Global recession TA = 99:0 - Global recession :02 - Domesic even 2000:09 - Global recession TH = 99:0 - Asian crisis 99:0 - Global recession :0 - Global recession UK = 99:08 - Asian crisis 99:0 - Asian crisis 2002:0 - Global recession US = 99:0 - Asian crisis 99:02 - Domesic even 2000:09 - Global recession Noe: Daa employed covering he period December 98-December 200 excep for he sock price index of Russia December 99 o December

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