A study on the Weekly Calendar Effect of Chinese Stock Market. Taking Guizhou Maotai as an Example

Transcription

1 Volume 04 - Issue 06 June 2018 PP A sudy on he Weekly Calendar Effec of Chinese Sock Marke Taking Guizhou Maoai as an Example Guang WU 1, Hong-guo SUN 1* 1 (Deparmen of Mahemaics and Finance Hunan Universiy of Humaniies Science and Technology Loudi, China) Absrac: Based on he basic heory of AR model, a reasonable AR model was esablished. The above guizhoumaoai index was aken as an example o conduc fiing predicion and empirical analysis of sock prices. Firs, using Eviews sofware, uni roo es is conduced on he original daa sequence o deermine wheher he original daa sequence is sable. If i is no sable, he original sequence needs o be reaed wih weekly rae of reurn differenial. Secondly, he idenified AR model is esimaed by using he model form of recogniion sequence of auocorrelaion graph and parial auocorrelaion graph, including he coefficien of esimaion model and he order of discriminan model. Finally, he model is used o predic he weekly closing price of guizhoumaoai index wih high precision, so as o predic he weekly calendar effec of he sock marke. The resuls show ha he fiing effec is good, indicaing ha he esablished AR model has cerain accuracy. Conclusion he AR model is more suiable for shor-erm daa fiing. A he same ime, combined wih Eviews sofware, he calculaion process can become simple and accurae. Sudy changes in he shor-erm in our weekly calendar effec on sock prices in he fuure rend and formulae invesmen sraegies have pracical significance, can provide reliable informaion service for invesors and policy makers and decision. Key words: AR model; Week calendar effec; The ime series I. Preface The weekly calendar effec is ha he average reurn or average volailiy of financial markes on one rading day of he week is significanly differen from ha of he res of he week. The research on he effec of he weekly calendar began wih he sudies of Osborne(1962) and Cross(1973). Since he 1980s, he weekly calendar effec of financial markes has been widely sudied. Alhough he calendar effec of research on financial marke in China began in he 1990 s, bu so far no many use he research mehods, from he domesic research in China calendar effec in he lieraure, such as Li-chengFeng(2003) [1], Guo-dongXu(2004),Hui Xu(2005),Xiao-guangHe(2006),Hua Cai(2006) mehod is adoped by he dummy variable regression. The weekly calendar effec on he sock marke analysis has imporan role for invesors, so his aricle is in China's guizhoumaoai, for example by using he ARCH of es analysis and AR model is esablished o sudy. This aricle mainly aims a guizhoumaoai index closing price every week during he period of he 2008, forecas problems, esablish guizhoumaoai index weekly closing price forecas model, by using he AR model in guizhoumaoai index closing price every week for high precision fiing predicion. The research resuls show ha he weekly closing price of guizhoumaoai index will mainain a seady rise in a shor period of ime, and here will be no sharp rise or fall. Sudy changes in he shor-erm in guizhoumaoai index closing price every week o undersand he sock marke week calendar effec change has pracical significance and invesmen decisions can provide reliable informaion service for invesors and policy makers and decision. The efficiency of he sock marke has been grealy improved. In counries such as he us and Ausralia, 46 Page

2 Volume 04 - Issue 06 June 2018 PP calendar effecs have reversed, suggesing ha financial markes are becoming more efficien. In China, financial markes already have some weak efficien marke characerisics, bu no enough o show ha he marke has really reached he weak efficien sage. The weekly calendar effec has some regional characerisics. Research shows ha among maure sock markes in he us, UK and Germany, he weekend effec is he lowes on Monday and he highes on Friday. Socks in he asia-pacific region, such as Ausralia, Malaysia and Hong Kong, had he lowes yields on Tuesday and he highes on Friday. A es of he weekly effec of he Shanghai sock marke is consisen wih ha of mos asia-pacific markes, wih yields generally rading a heir lowes on Tuesday and highes on Friday. The range of daa used o sudy he calendar effec is expanding and he mehod is updaing. Calendar effec research pay more and more aenion o he model and heory suppor and saisical significance es, considering he calendar effec on yield and he impac of marke risk, he research mehods are from he original simple analysis o he random walk model, he average of he ARCH model, GARCH model, and he rolling sample esing mehod, ec. The focus of furher research. Fuure research should srenghen he analysis of yield risk. A he same ime, along wih many conrols, Chinese sock marke is more and more specificaions, bu sill have some wih Chinese characerisics, so he characerisics of he sock marke in China should be more deailed and in-deph analysis. In addiion, many scholars abroad have found ha smaller companies have a significan calendar effec, a presen our counry abou he sudy of he relaionship beween company size and calendar effec is less, in he fuure should make full use of he daa of lised companies o srenghen he research in his field. II. The developmen Course of Weekly Calendar Effec 2.1. Foreign Developmen The sudy on calendar effec began in he 1930s. Bu he main findings focus on he pos-1970s.cross(1973) [2] and French(1980) sudied he yield of S&P500 index, and found ha on average, he average yield of Friday was higher han ha of Monday.French(1980) [3] found a differen week rading day afer he sock yields here is significan difference beween, many sudies have confirmed ha he differen ime inerval and differen sock index have weekly calendar effec.gibbons(1981) [4] and Keim(1984) [5] discovered ha he Dow Jones index had a negaive yield on Monday.Rogalski(1984) found ha he average negaive reurn beween Friday's close and Monday's close occurred during non-rading hours, and he average rading day reurn (from opening o closing) was consisen all days.jaffe(1985) [6] sudied four developed markes in Ausralia, Canada, Japan and he UK, and he resuls showed ha here was weekend effec in he counries sudied. However, David J.Kim (1998) found no weekly effec in he sudy of Korean and Thai markes.jaffe (1989) confirmed Monday's abnormal yield no only exiss in he securiies marke, bu also exis in many differen securiies, Flannery and Proopapadakis (1988) confirmed also exis in many differen varieies of securiies calendar effec Domesic Developmen The research on he calendar effec of financial marke in China is relaively lae compared wih ha in foreign counries. Qin Fan and Ming-shanZhang (2002) [7] based on he random walk model, use nearly 10 years of daa on China's securiies marke empirically es he exisence of he weekend effec, is conclusion is ha China's sock marke exiss he weekend effec, and Shanghai effec more apparen over he weekend, China's securiies 47 Page

3 Volume 04 - Issue 06 June 2018 PP marke is sill no reach he weak form efficien. Tong Liu(2003) [8] o sudy he recen Shanghai sock marke, he USES he basic saisical analysis and Kolmogorov Smirnov has inspecion (1) (K - S found ha Shanghai sock marke index disribuion does no obey normal disribuion, hen Levne es analyzes he variance of he reurns series, he Shanghai sock marke exiss on Tuesday and Friday effec conclusions.shao-fuzhouand Qi-anliChen(2004) [9] he uncondiional volailiy of correcing Levene es and GARCH model of he flucuaion of he Shanghai sock marke week effec of empirical research, he resuls show ha he Shanghai sock marke is significanly high flucuaions on Monday, hey are using he mixed disribuion model, furher research ha weekend he accumulaion of informaion may be one reason for he high flucuaions on Monday.Guo-dongXu,Xiang-linTian,Bing-gongL in (2004) [10] he use of he sandard K S nonparameric es and virual variable regression mehod, using 1993 o 2003, he sock index fromhree levels (monh/quarer/semi-annual) on he calendar effec of he Shanghai and shenzhen sock marke in China has carried on he comprehensive analysis and es. The resuls show ha here is a significan seasonal effec in Shanghai marke, bu no in shenzhen marke. The sudy also found ha boh Shanghai and shenzhen have significan December effecs, which are inseparable from he special policy and marke background of he Chinese sock marke. They hink ha he exisence of seasonal effec reflecs he inefficiency of China's sock marke from one perspecive, which is more obvious in Shanghai sock marke. Xuan Zhang and Mei Cai(2004) using l3l6 a-share index of Shanghai and shenzhen sock marke rading day he yield on he calendar effec of Shanghai and shenzhen sock marke are sudied, resuls show in Shanghai and shenzhen sock marke have significan posiive excess yields on Friday, here were significan effec of week, bu he effec is no obvious in Shanghai and shenzhen wo ciy, only show he weak January effec.xiu-juanzhao,qi-fangwuand Shou-yangWang(2004) [11] conduced an empirical es on he calendar effec of open-ended funds and closed-end funds in China's securiies marke and compared i wih he index benchmark. The resuls show ha he Chinese fund marke has a cerain degree of calendar effec. Wha's more, he Shanghai index and mos of he open-end funds had relaively higher yields on Monday. The average daily reurn for he firs half was lower han he average for he second half. Closed-end funds had higher reurns in March and lower reurns in Augus. III. Empirical Analysis of Weekly Closing Price of Guizhou Maoai Index AR model refers o he use of previous observaion value and curren inerference value and a cerain linear combinaion o predic and analyze. The mahemaical formula of AR model is: y y 1 1 y 2 2 y p p (1) Type: yis a saionary ime series, i ( i =1,2,,p) represens he undeermined coefficien of AR model, p represens he order of AR model, for he error. Find he hisorical daa of he weekly closing price of guizhoumaoai index on neease financial websie, from o Based on he modeling heory of AR model, he weekly closing price predicion model of guizhoumaoai index was esablished o sudy he shor-erm changes of weekly closing price of guizhoumaoai index. 48 Page

4 Volume 04 - Issue 06 June 2018 PP Sabiliy processing of raw daa Fig 1. The weekly closing price of guizhoumaoai Can be seen from he figure 1, guizhoumaoai index closing price every week period beginning in he , has been a seady flucuaions, prices have risen sharply since 2015, suggess ha his ime he company has a larger adjusmen, and promoe he rapid rise of he economy, herefore can roughly deermine he sequence of non-saionary ime series. Fig. 2 ADF es resuls of weekly closing price of guizhoumaoai Furhermore, ADF es was performed on he original daa sequence, and he es resuls were shown in figure 2. As can be seen from figure 2, under he condiion ha he significance level is 0.01, he uni roo exiss, so he original assumpion is acceped, ha is, he original daa sequence is non-saionary Conver of he original daa Fig 3. Linear graph of weekly yield ofguizhoumaoai 49 Page

5 Volume 04 - Issue 06 June 2018 PP We can see from figure 3, guizhoumaoai weekly reurn series R has obvious aggregaion, a high yield afer geing higher yields, a low yield afer geinglower yields. Fig. 4 ADF es resuls of weekly reurns of guizhoumaoai As can be seen from figure 3, he difference of weekly rae of reurn on he original daa may be sable. Is furher ADF es, as shown in figure 4, ADF es saisics is , he absolue value of more han 1% under he significan level of he absolue value of he criical value o , herefore does no accep he null hypohesis, weeks afer he yield difference sequence is smooh Auocorrelaion graph and parial auocorrelaion graph Fig5. Auocorrelaion and parial auocorrelaion of guizhoumaoai weekly rae of reurn As can be seen from FIG. 5: since boh he auocorrelaion coefficien and he parial auocorrelaion coefficien are 6 order railing, he AR (6) modelis esablished [12]. As shown in figure 6, he P value is less han 0.05, indicaing ha he coefficien of he model is significan. The following is he expression corresponding o he model: X 3.4. Heeroscedasiciy es ARCH es [13] is here any heeroscedasiciy (2) X 6 Fig. 6 heeroscedasiciy es of guizhoumouai weekly rae series As shown in figure 6, he P value is greaer han he significance level of 0.05, and he original hypohesis is acceped. There is no condiional heeroscedasiciy in he original sequence. 50 Page

6 Volume 04 - Issue 06 June 2018 PP Residual es of sequence model Fig7 residual correlaion diagram of guizhoumaoai weekly reurn rae series AR (6) The figure 7 shows: as he P value is greaer han 0.05, shows all he Q value is less han 0.05 card square disribuion under he es level of he criical value, he model of heremnans of difference as whie noise, here is no serial correlaion residuals. Therefore, i can be deermined ha hefiing effec of his model is very good. From formula 1-2, i can be seen ha: he average weekly reurn decreased by unis in he period when he weekly rae of reurn was increased by 1 uni in he period wih a lag. We know ha guizhoumouai week closing price is rising gradually, bu is weekly reurn wih lag, here is a weekly calendar effec, because of is shares [14] on Tuesday and Friday are generally have varying degrees of decline. This model fully highlighs his poin, indicaing ha he weekly calendar effec of China's sock marke is quie significan. IV. Conclusion Modeling heory, his aricle is based on AR model by using he AR model in guizhoumaoai week index closing price for high precision fiing and empirical analysis, he sudy of guizhoumaoai week index closing price shor-erm flucuaions, o mee, o verify he weekly calendar effec of he sock marke in China. Based on AR model (6) and esablished in his paper in guizhoumaoai index week close fiing predicion and analysis, combining our counry sock marke volailiy weeks weekly calendar effec principle, in ignoring he enerprise he managemen policy and governmen policy unchanged under he premise of can ge guizhoumaoai index in weeks despie he ups and downs, bu he overall rend is sill presen coninuous rose slighly. Therefore, in he sudy of China's sock marke invesmen decisions, we mus no ignore he weekly calendar effec of China's sock marke, someimes i can play a decisive role. In a word, he AR model o predic non-saionary ime series daa has he very good effec, a he same ime combined wih Eviews sofware for he esablishmen of he AR model and solving, can provide reliable informaion service for invesors and policy makers and decision. V. References [1]. Li-chengFeng. The weekly effec of China's sock marke[j]. Economic research , [2]. Cross F. The behavior of sock prices on Fridays and Mondays[J].Financial Analysis Journal,1973,29, [3]. French K.Sock reurns and he weekend effecs[j].journal of Financial Economics,1980,8, [4]. Gibbons,M.R. Day of he week effecs and asse reurns.journal of Bussiness.1981,(54), [5]. Keim D.B.A furher invesigaion of he weekend effecs in sock reurns[j]. Journal of 51 Page

7 Volume 04 - Issue 06 June 2018 PP Finance.1984,13, [6]. Jaffe J. The weekend effec in common sock reurns: The inemaional evidence[j]. Journal of Finance.1985, XL(2), [7]. Qin Fan, Ming-shan Zhang. Research on weekend effecs of China's securiies marke[j]. China managemen science , [8]. Tong Liu. Sudy on weekend effecs of Shanghai sock marke by non-parameric mehods[j]. Mahemaical saisics and managemen , [9]. Shao-fuZhou and Qian-liChen. The weekly calendar effec es of Shanghai sock marke volailiy[j]. Mahemaical saisics and managemen , [10]. Guo-dongXu, Xiang-xinTian, Bing-hongLiu. Empirical analysis of seasonal effecs of Chinese sock marke[d]. Journal of guangxi universiy of finance , [11]. Xiu-juanZhao, Qi-fangWu, Shou-yangWang. Has he growh rae of ne worh of open-ended funds been increased?---calendar effec of Chinese sock marke es[j]. Journal of managemen science in China , [12]. Ji-wenShi and Hao-ran Wu. Empirical analysis of he weekly calendar effec of China naural rubber fuures [J]. China business daily , [13]. Ming-yueFu. Research on sock marke risk value based on ar-garch model [D]. Suzhou universiy , Page