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Weak form efficiency of chinese stock markets

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China, in the last 30 years, has shown the spectacular growth rate in economy. By the end of 2010, China' GDP ranks the second in the world. Compared with the stable growth of China's economy, the performance of Chinese stock markets is also a limelight. The stock markets have improved with an expansion in the number of the list companies and the total amount of stock trading. China has two major stock exchanges-Shanghai and Shenzhen Stock Exchanges. Shanghai Stock Exchange (SHSE) was founded in December 1990 and Shenzhen Stock Exchange (SZSE) started its trading in July 1991. Two types of shares are traded in China's Stock Exchanges, which are named type "A" and type "B" shares. In China, type "A" shares are available to Chinese nationals only and these shares are traded by Chinese Yuan. Type "B" shares, in Shanghai Stock Exchange, are traded by U.S dollars, while in Shenzhen Stock Exchange those are denominated in Hong Kong dollars (Martin Laurence, Francis Cai and Sun Qian 1997). Particularly, type "B" shares are only available to investors from Hong Kong, Taiwan, Macau and other countries before 19th February 2001. After this date, individual investors in China's Mainland are able to purchase type "B" shares. By the end of 2010, the number of listed companies on SHSE is 901 and on SZSE is 1169. In the Shanghai exchange, there are 891 A-shares and 54 B-shares. The Shenzhen Exchange has 1195 A-shares and 54 B-shares. Chinese stock markets are the emerging stock markets, since they are relatively young compared with stock markets in some developed countries. Many external and internal aspects and policies lead to the specific features of China's stock markets. One of the features is the structure of a listed company. A listed company's ownership structure can be divided into five categories: stated-owned shares, employee shares, legal-person shares, tradable A-shares and shares only available to overseas investors. To distinguish them in a more detailed way, stated-owned shares, employee shares and legal-person shares are classified as non-negotiable shares which cannot be traded on the two exchanges. The listed companies are financed with non-negotiable shares that account for 60 percent of the companies' equities (Qiet al. 2000, Wei and Varela 2003). Chinese Stock Exchange, in addition, exhibits that a majority of the individual investors are regarded as the gambler. Many investors treat the stock trading like a casino with the fact that they do not pay much attention to the information, finance and announcements about the listed companies (Ma 1996, Nam et al. 1999, Kang et al. 2002, Girardin and Liu 2003). Polices carried out by China's central government affect China's stock markets at a significant extent. The indexes of China's stock markets may not be consistent with the economic growth of China. The government has macro-economic control over the stock markets, which interferes the decisions made by investors. Thus China's government makes the stock markets a tool of raising finance. Except for the aspects mentioned above, the efficiency of Chinese stock markets is essential to the investors and regulators since it relates to how information in the market can be reflected by the stock price. Efficient-Market Hypothesis (EMH) developed by Eugene Fama (1970), mainly, has three forms of market efficiency. In Weak-form efficiency, people cannot predict the stock prices in the future though they collect and analyze the information contained in the past prices. In addition, excess returns in long term cannot be made by using historical stock prices and other historical data. Some techniques can provide excess returns to investors in some cases. But the excess returns may not be consistently produced by the technical methods. Stock price in the future follow a random walk since it is predicted by the information not contained in the past prices, and no serial dependencies exist between these prices. Dimson and Mussavian (1998) defined efficient capital market in a similar way. In an efficient capital market, all information must be reflected in the financial assets' prices and the prices changes should be consistent with the new information. An efficient capital market, of course, cannot be identical with a perfect market. Basically, the definition of a perfect market is with several assumptions. Investors in a perfect market can obtain all of the relevant information immediately and simultaneously. Also, the information provided is costless. Moreover, investors in such market are rational and the market should be presumed to be frictionless. In the real world, there is no perfectly efficient market and no completely inefficient market. This report mainly focuses on testing the weak-form market efficiency of Chinese stock markets. In this study, three statistical techniques are employed. Dickey-Fuller test for unit root test is firstly provided and then employing the non-parametric runs test. In addition, Lo-Mackinlay Variance Ratio test is presented. Section 2 presents some tests ealier employed by other people. The data description and the research methodology will be discussed in Section 3. Section 4 contains the empirical results, and Section 5 then provides the summary and conclusion.

Literature Review

Various previous market efficiency tests findings (Liu, X., H. Song and P. Romilly 1997, Laurence, M., F. Cai and S. Qian 1997 and Lima and Tabak 2004 for A-shares markets in both SHSE and SZSE, and Long, D.M., J.D. Payne and C. Feng 1999 for A- and B-shares markets in SHSE) reveal that Chinese stock markets are significantly speculative to the investors. Due the fact that Chinese stock markets are speculative, many noise traders who regard the stock trading as a casino may make the stock returns serially correlated. Previously De Long, J.B., A. Shleifer, L.H. Summers and R.J. Waldmann (1990) employed a theoretical model to indicate the effect of noise traders in the stock markets. This model finally shows that if noise traders expect to find positive returns when they trade, the price stress will give rise to autocorrelations between positive returns during a relative short time. However, Kang et al. (2002) reported that abnormal profits exist in the A-shares market given certain short-horizon and intermediate-horizon strategies. Random walk was employed by Abrosimova and Linowski (2002) when they examined the weak-form efficiency of the Russian Stock Exchange. They found that if the monthly data was used, random walk could not be rejected. However if daily data was used in the test, random walk could be rejected. Balaban (1995) carried out an experiment of testing the weak-form efficiency of Istanbul Securities Exchange, and he performed a random walk test on this market. Tian et al. (2002) reported that 412 technical rules were useful in predicting the movements of stock price in Chinese stock markets, which making traders pursue excess profits in 1990s. In addition to the aforementioned researches which apply the well-known and conventional tests, many other studies related to this topic aim at avoiding some defects in the previous tests. For instance, run tests employed by Laurence (1997) and Mookerjee and Yu (1999) enable them to reach the conclusion that stock markets are in the weak-form efficiency. Besides, Liu (1997) and Seddighi and Nian (2004) used unit root tests to conduct their analyses. Lo and MacKinlay (1988) applied variance ratios tests to detect the serial correlations between the stock returns, and then asserted that random walk could be rejected using a sample of 1,216 observations of firms in NYSE-AMEX during 1962-1985. K.A. AI-Abdulqader et al. (2007) used two conventional tests to examine the weak- form efficiency of Saudi stock market. One of them is the filter rule test, and the other one is moving average strategy. Fliter rule is proposed by Alexander (1961, 1964). According to the opinion of Fama and Blume (1966), Alexander's filter rule detects whether prices changes are consistent to the new information. This research applied various filters to the data, and then assessed the filters' effect on the rule's profitability. This filter rule strategies finally obtained the conclusion that rule profits, in minority of cases, could not exceed the profits from the buy-and-hold strategy. Accordingly, if profits of the strategy are more than the profits from a buy-and-hold strategy, it could provide evidence against the weak-form efficiency. To compare the conclusion from the filter strategy, a moving average strategy was also employed in their research. This strategy relates to the buying (selling) at the short-term average price moves above (below) the long-term average price during k days. In this research they adopted four different moving average strategies: (1, 50, 0), (1, 50, 1), (1,150, 0), (1, 150, 1). For example, (1,150, 0) demonstrate that length of short-term is 1 day, the length of long-run is 150 and the bandwidth is 0. Bandwidth reflects the minimum change made before a signal is identified. The conclusion from the results of the moving average strategy indicated that though this strategy outperformed a buy-and-hold portfolio much more significantly, the ability of predicting changed according to the moving average strategies applied. Pakistan stock market is an emerging stock market like Chinese stock markets. Research conducted by Madhlimita Chakraborty (2006) investigated the weak-form efficiency of the Pakistan stock market. He employed the Lo-Mackinlay variance ratio test (1988) in addition to the traditional serial correlation test and runs test. The variance ratio test requires the precondition that the random walk increments' variance is linear between the experiment samples. Therefore, if a random walk process is presented, the q-differences' variance must be q multiplies the first differences' variance. Also, the Box-Jenkins Technique (1978) was applied to his research. In context of Chinese stock markets, several studies have been done. In this report, three typical researches are presented. The reason for taking these reports into consideration is that they performed the distinct tests in their investigations and separately reached the dissimilar conclusions. Martin Laurence et al. (1997) tested the behavior of the share price, weak-form market efficiency and causality of the Shanghai and Shenzhen stock markets. Also, they examined the causality of the Chinese stock markets with the Hong Kong and U.S. stock markets. The data were from four Chinese stock market indices, one Hong Kong Index and one U.S. Index. The four indices are Shanghai 'A', Shanghai 'B', Shenzhen 'A' and Shenzhen 'B'. Dow Jones News Retrieval Services and Datastream International provided the research data. First of all, they performed a unit root test for the six stock indices, and the test was based on an augmented Dickey-Fuller (1979, 1981) model. After that, they employed bivariate cointegration tests for comparing every pair of stock indices, which involved the method of the Phillips and Ouliaris (1990). This method is used for estimation through the Ordinary Least Square of the regression model. Apart from the above two tests, the serial correlations and Ljung and Box test (1978) were used. The presence of serial correlation was significant in form of daily returns. But it can be viewed as a violation of the weak-form market efficiency, because investors are able to take advantage of serial correlation for making excess return. Lastly, with the purpose of investigating lead-lag relationships among the six market indices, Granger's (1969) causality tests are performed. They, eventually, obtained the consequence that Chinese stock markets were getting closer to a weak-form efficient market. The results from causality tests indicated that Chinese stock markets were related to the global market to a great extent. At the beginning of the 21th century, Ma and Bames (2001) completed their report about testing the weak-form efficiency of the Shanghai and Shenzhen stock markets. They employed serial correlation, run tests and variance ratio tests. The data collected for this report was based on daily, weekly and monthly returns. They collected stock returns from December 1990 to April 1998 for Shanghai stock exchange, and employed stock returns from April 1991 to April 1998 for Shenzhen stock exchange. To be more detailed, the numbers of A-share taken from Shanghai and Shenzhen stock markets were 375 and 348, and the amount of B-share employed from the two markets were 49 and 51. They found that stock returns between the two stock exchanges were correlated significantly, but the daily returns were much more correlated than the return of weekly and monthly. Considering the daily returns of individual A-share and B-share of the Shanghai exchange and daily returns of individual B-share of the Shenzhen exchange, generally, they did not follow a random walk. They also concluded that individual shares exhibited more efficient than stock indices, and the Shenzhen market showed more evidence than the Shanghai market. Generally, B-share typically violated the random walk. That is, prices of B-shares were more easily predicted than prices of A-shares. To explain this, they asserted that thin trading could result in the B-shares' inefficiency. If according to the theory of Fama's (1965), Chinese stock markets were in weak-form efficiency. Nevertheless, they finally reported that Chinese stock markets were not determined to be as a weak-form efficient market, since many professionals argued that Fama's (1965)' theory of defining the efficient markets was not correct to some extent. Seddighi and Nian (2004) conducted an investigation about the Shanghai exchange indices and 8 listed shares in this market. The data contained the stock returns from January 2000 to December 2000. The listed shares were randomly selected from 8 companies involved in 8 sectors. In their research, three tests were used, i.e. the Lagrange Multiplier test, Dickey-Fuller test and ARCH test. From the result of the Lagrange test, they concluded that 6 of the target companies were not related to autocorrelation. Random walk was asserted to be present in the Shanghai stock market as a result of Dickey-Fuller test. However, unit root was not found in 2 of the listed shares series. Finally, they reported that the Shanghai stock prices did not follow a random walk. That is, Chinese stock market did not perform weakly efficient.

3. Data and Methodology

3.1 Data description

The data, in this study, is daily price index for Shanghai and Shenzhen stock exchanges. These price indices are obtained from the Datastream, and the observation period ranges from January 3, 2000 to December 31, 2010. To examine Chinese market efficiency, this study employes daily data of closing prices for four Chinese stock indexes: Shanghai A-share Index, Shanghai Composite Index, Shenzhen A-share Index and Shenzhen Composite Index. The data in Table 1 (see Appendix), obtained from Datastream, are collected on basis of the daily closing prices for weekdays between January 03, 2000 and December 31, 2010. Shanghai A-share Index, Shanghai Composite Index, Shenzhen A-share Index and Shenzhen Composite Index are denominated in Chinese Yuan (CNY). These four stock indices reflect the statistical data related to domestic investors and the overall stock market, but the indices used by overseas are excluded since domestic investors account for the majority and the composite indexes could reflect the overall market daily prices. Time series plots are exhibited below:

Figure 1. Time Series Plots for Chinese Stock Indices

Shanghai A Index

Shanghai Composite Index

Shenzhen A Index

Shenzhen Composite Index

Apparently, Shanghai A-share Index approximately has the identical distribution of return compared with that for Shanghai Composite Index. Shenzhen A-share Index, also, has the identical time series compared with that for Shenzhen Composite Index. Both of Shanghai indices and Shenzhen indices reached the peak level in the year of 2007. Between 2007 and 2008, the Shanghai Composite Index experienced the highest level of price which is around 6000, and Shenzhen Composite Index had almost reached at the level of 1600. From 2000 to 2007, all of the four indices series did steadily fluctuate with relative small range. After 2007 these indices ascended sharply until the financial crisis arrived. In the following year of 2008, the four indices descended dramatically due to the financial crisis. Overall, Shanghai and Shenzhen indices have the identical fluctuation before 2009, whereas in the following years, Shenzhen indices has higher increase in index prices compared with Shanghai indices. That is, Shenzhen stock market is considered to be in better condition than Shanghai stock market after 2009. All indices series returns are calculated by the following formula: Where stands for the closing price for the index at time t and is natural logarithm.

3.2 Methodology

To test the weak-form efficiency of Chines stock markets, the main approach is to examine whether Chinese stock markets follow a random walk. Generally, it is necessary to indicate that logarithmic market returns follow a random walk. However, there are two assumptions in the theory of random walk. That is, the continuous price changes are independently distributed and the price changes follow some probability distribution (Fama 1965). The random walk hypothesis requires the price increments to be independently and identically distributed (IID). The equation below shows the dynamics of share prices: where and IID distributed Statistically, we need to define the hypothesis as the following: H0: Chinese stock markets follow a random walk, i.e. follow the weak-form efficiency H1: Chinese stock markets do not follow a random walk, i.e. do not follow the weak-form efficiency Therefore, to examine the null hypothesis of the random walk, three statistical tests including unit root test, non-parametric runs test and variance ratio test are employed. The tests are performed on the entire sample. The unit root test was mainly based on the the Dickey-Fuller test. This test determines whether the stock returns series is non-stationary since it is an essential condition for random walk. Lo and Mackinlay (1988) developed the variance ratio test which may be a more proper test for a random walk hypothesis.

3.2.1 Unit root test

The unit root test was developed by Dickey and Fuller (1981), which examines the stationarity of the time series. If unit root is found in the series, then it can be defined as non-stationary which shows the presence of random walk. Commonly, Dickey-Fuller test is proper to examine whether a unit root exists in a series. With the purpose of testing the weak efficiency of Chinese stock markets, therefore, the Dickey-Fuller test is provided. Equation (1), basically, is a simple unit root form. In this equation, only by the fact that slope coefficient is equal to 1 can we exhibit that the current price is totally explained by the lagged term of the market price. Then the current price is explained by the constant or drift. (1) Where is independently and identically distributed with the mean 0 and the constant variance . The error increment is called white noise, and all of the error terms are uncorrelated. Nevertheless, Dickey-Fuller (1981) showed that under the null hypothesis that , the standard t-ratio does not have a t-distribution since corresponds to a non-stationary process which invalidates the standard results on the distribution of the OLS (Ordinary Least Square) estimator . Then Dickey and Fuller transformed the equation (1) to the equation below: (2) Dickey and Fuller replaced by , which is realized by deducting in both sides of the equation. Accordingly, the actual return has been changed to the change in return, as well as the hypothesis should be transformed to: (Non-stationary or unit root) against (Stationary or no unit root) In equation (2), the last termcan also be assumed to be white noise. Denoteas the OLS (Ordinary Least Square) estimator andas the usual OLS standard error. To test the hypothesis thatwe can use standard 't-statistic' given by: With the value of to be more be negative, the more significant the t-value might be to reject the null hypothesis and the returns are stationary which do not follow a random walk. In other words, if the null hypothesis is not rejected, that the series follow a random walk. To examine whether the stock prices in Chinese stock markets follow a random walk, Dickey-Fuller test,significantly, provides the effective evidence.

3.2.2 Runs Test

Runs test provides another method to the random walk. To distinguish runs test with the other two tests, it is presumed that the returns would not be required to follow a normal distribution. Specifically the non-parametric runs test, unlike the general runs test, it tests the independency of the successive price changes. The non-parametric runs test is under the assumption that only if the observed number of runs in the series is close to the expected number of runs can the returns of price in the series follow a random walk. A sequence of successive price changes with the same sign is described as a run. The non-parametric runs test, actually, is proper to examine the randomness for the successive of returns; hence, it provides adequate evidence on whether price returns in Chinese stock markets are possible to be predicted. The first stage of the test is observing the number of runs which is defined as the total number of the sequence of consecutive prices changes with the same sign: positive, negative or no change. Then assigning equal weight to every corresponding change and distinguishing direction of the successive changes, which must be based on the rule that classifying each change in return according to the mean return. That is to say, the positive change is obtained when the price return is larger than the mean return, and the negative change is obtained when the price return is less than the mean return and no change when the return is equal to the mean return. The run test is employed by taking the actual runs (R) and the expected runs (m) into account. To perform the test, comparing the actual returns and the expected returns is required. Since the distribution of the number of runs is assumed to converge to a normal distribution, the expected number of runs can be calculated as equation (3) below: (3) Where N is the number of observations,denote the signs of positive, negative and zero,denotes the number of price changes of each sign. If the total number of observations N is greater than 30, the expected number of runs m is normally distributed with a standard deviation as the equation below (4): (4) The standard normal Z-statistic is: Z~ N(0,1) (5) Where R is the actual number of runs, (1/2) denotes the correction factor for continuity adjustment (Ma and Bames 2001), where the sign is plus if Rm, and is negative if Rm. The null hypothesis can be described as the following: If null hypothesis can be rejected at a certain significance level (1%, 5% and 10%), then it indicates that the series does not follow a random walk at that significance level. Furthermore, a positive serial correlation is implied by a negative Z value, and a positive Z value implies a negative serial correlation.

3.2.3 Variance Ratio Test

The variance ratio test designed for random walk testing was proposed by Lo and MacKinlay (1988). Basically it is assumed that there is a linear relationship between the variance of random walk increments. Accordingly, if a random walk exists, the variance of its differences should be times the variance of its first differences. Consequently, when we have observations () of the log of stock returns and obtain these log returns at the intervals with equal space (is an integer larger than 1), the ratio of of the variance to the variance of is equal to 1. The variance ratio test is employed under assumptions of homoscedastic and heteroskedastic random walks. Then some important equations in this test are presented: (6) Where is the variance of the difference and is the variance of the first differences. (7) where (8) and (9) where and is the number of observations Under the assumption of homoscedasticity, the modified (Liu and He 1991) is in the form of the formula below: Where (asymptotic variance of the variance ratio) If the null hypothesis of no autocorrelation coefficient is rejected, there is no random walk under the case of homoscedasticity. Commonly, heteroscedasticity and autocorrelation might lead to the rejection of random walk under homoscedasticity (Worthington and Higgs 2004). In addition, Campbell et al. (1997) reported that the variance ratio would be close to unity even in under the assumption of heteroscedasticity if returns are not correlated. Lo and MacKinlay (1988) introduced the standard normal test : where (standard error term) and Under the null hypothesis, the variance ratio is equal to 1. That is, the series follows a random walk. If random walk is rejected under the assumption of heteroskedastic, evidently, there is the presence of autocorrelation. Under the case of autocorrelation, a negative serial correlation exists if variance ratio is less than 1 and a positive serial correlation is presented if variance ratio is larger than 1.

4. Empirical Results

4.1 Descriptive Statistics

An overview of descriptive statistics for Shanghai and Shenzhen stock indices are provided in Table 2 (see Appendix). The total number of observations for each stock index is 2870. All of the four series have the positive means. Shenzhen Composite Index has the highest mean of returns of 0.000406, while Shanghai A Index has the lowest mean of returns of 0.000246. The maximum returns obtained from Shanghai A Index and Shanghai Composite Index, obviously, exceed these obtained from Shenzhen A Index and Shenzhen Composite Index; nevertheless, Shanghai A Index has the lowest minimum return of -0.092608. Due to th fact of high return with high risk, the two Shenzhen indices incorporate with the highest standard deviations even though they have higher average returns than these of two Shanghai indices. Therefore, daily returns for two Shanghai indices are less volatile than returns of two Shenzhen indices and Shenzhen indices has higher returns compared with Shanghai indices on the average. Daily compounded indices statistics for Shanghai and Shenzhen stock markets are provided in this table. The returns are given by , where is the series price at time t. "μ" is the mean of returns and "σ" is the standard deviation for the series of returns.

4.2 Unit Root

Basically it is essential to use Dickey-Fuller test without time trend to examine whether Shanghai and Shenzhen stock indices follow a random walk. This test model composites of the constant or drift, coefficient slope and white noise. The results for Dickey-Fuller test without time trend is given in Table 3 (see Appendix). This table presents the results for Shanghai and Shenzhen Index prices between 2000 and 2010. The estimated slope coefficient is represented by and the standard error for is. The critical value is 3.51 at 2% significance level, 3.17 at 5% significance level and 2.58 at 10% significance level. ***, ** and * indicate the slope coefficient is statistically significant at the 2%, 5% and 10% level. Results in table 3 (see Appendix) indicate that indices series in Shanghai and Shenzhen are non-stationary or unit root under the significance level of 2%, 5% and 10%. Currently the result shows the random walk of the Chinese stock markets, but testing results may vary with some changes of this model. In this model, on the one hand, time trend is not taken into consideration. In some cases, we may have to consider a statistical model which can include a deterministic time trend. It is particularly necessary when the series exhibit either upward or downward trend. The reason is that if a series shows significant time trend it is non-stationary. Considering a trend-stationary process, if the process is not accounted for in the regression model, it is likely that a unit root test would fail to reject the null hypothesis, even though the process is trend-stationary. On the other hand, unit root may exist in high-order AR model. In this report, only AR(1) has been employed, which may not be the correct specification. If we use an AR(1) when the correct specification would be a higher-order AR process, we may misleadingly reject the null hypothesis of a unit root because of the misspecification of the model. Thus Augmented Dickey-Fuller Test can provide further analysis to examine the existence of random walk. Overall Dickey-Fuller test without time trend can provide solid evidence that Chinese stock markets follow a random walk.

4.3 Runs Test

Table 4 (see Appendix) indicates the results of non-parametric runs test for four stock indices in Shanghai and Shenzhen between 2000 and 2010. The total number of observations is represented by N and total number of runs is denoted by R. The amount of observations below mean is denoted by <mean, whereas >=mean indicates the number of observations larger than or equal to the mean. The critical value for Z statistics is given by: Z=1.285 at 10% significance level, Z=1.645 at 5% significance level and Z=2.33 at 1% significance level. ***, ** and * denote the statistical significance at 1%, 5% and 10% levels. The results of the non-parametric runs tests for Shanghai and Shenzhen market indices are presented in Table 4 (see Appendix). The estimated Z-values for returns on Shenzhen A-share Index and Shenzhen Composite Index are significant at 5% level, and both of returns on Shanghai indices are significant at 10% level. Accordingly the null hypothesis can be rejected under some significance level, which implies that both of Shanghai and Shenzhen stock markets are not weak-form efficient. Nevertheless Shanghai stock market can only be determined as weak-form inefficient in the case of 10% significance level, which may not provide adequate evidence ensuring the weak-form inefficiency of this market. Shenzhen stock market is determined as weak-form inefficient even at 5% significance level. The negative Z-values for daily returns on the four stock indexes, indeed, imply the positive serial correlation. Anyway Chinese stock markets can not determined as wear-form efficient using the non-parametric runs test.

4.4 Variance Ratio Test

The results of variance ratio test for the Chinese stock markets are presented in table 5 (see Appendix) and the time period is 2000-2010. N denotes the total amount of observation and q is the equal-spaced interval of the observation. In this test, q is equal to 2, 4, 12 and 20, respectively. VR(q), Z(q) and Z*(q) are the estimations of the corresponding statistics. VR(q) is the estimate of variance ratio, and Z(q) and Z*(q) are the Z test statistics of homoscedasticity and heteroscedasticity, respectively. *, ** and *** denote the statistical significance at 10%, 5% and 1% level. The outcomes of variance ratio test for Shanghai and Shenzhen stock indexes are provided in table 5 (see Appendix). VR(q) is the estimate of variance ratio, and Z(q) and Z*(q) denote the Z test statistics under homoscedasticity and heteroscedasticity, respectively. The q-difference is assigned as 2, 4, 12 and 20 for all four indexes. For Shanghai A-share market, apart from the interval of 20 days, the null hypothesis cannot be rejected at all three significance levels under both of homoscedasticity. The results of variance ratio for Shanghai Composite Index are similar with these obtained for Shanghai A-share Index. For variance ratio test conducted for Shanghai Composite in 20-day interval, the null hypothesis of random walk is only rejected at 5% and 10% significance level under the assumption of homoscedasticity and heteroscedasticity, respectively. However, the null hypothesis of random walk for Shenzhen stock market is strongly rejected under the presumptions of homoscedasticity and heteroscedasticity in all the q intervals. The rejection of random walk can be realized even at 1% significance level. Under homoscedasticity, the reason for rejection of the null hypothesis of random walk could be the autocorrelation in stock returns. Nevertheless the null hypothesis is also rejected under heteroscedasticity, which indicates that the rejection of the null hypothesis under homoscedasticity is exclusively attributed to the autocorrelation in the series returns. According to the results obtained from all of the statistics about variance ratio test, Shanghai stock market is weak-form efficient and Shenzhen stock market is weak-form inefficient. The findings of Shenzhen stock market indicate that the autocorrelation in returns may completely reject the random walk of this market. Overall the Chinese stock markets represent inconsistency between the Shanghai and the Shenzhen stock markets. Compared with the findings of runs test, Chinese stock markets may not be weak-form efficient.

5. Conslusions

Examining the weak-form efficiency of Chinese stock markets presents the relevant information behind the market series returns. The definition of Efficient-market Hypothesis (EMH) is developed by Eugene Fama (1970), which defines that in weak-form efficient market investors cannot make excess returns though historical stock prices and data, and the stock prices follow a random walk because the past price would not provide any related information to predict the future price. Based on the theoretical interpretation about the weak-form efficient market, some research has been conducted in the context of Chinese stock markets. As the empirical evidence obtained in the previous studies, they cannot reach a consensus on whether Chinese stock markets are weak-form efficient. Some studies asserted that Chinese stock markets did not follow a random walk, however other empirical findings subscribed to the opinion that Chinese stock markets are weak-form efficient. This study focuses on testing the weak-form efficiency of Shanghai and Shenzhen stock markets, and two major indexes in each market are examined. Daily price from the time period 2000 to 2010 for each index is collected in order to examine the hypothesis of the random walk, and A-share index and composite index in Shanghai and Shenzhen stock markets are used. Statistical methodologies have been used in many empirical studies testing the random walk hypothesis. Considering the features of each statistic method, three statistical methods are employed. Dickey-Fuller is used to find the unit root of the returns series of stock indices, a non-parametric runs test aims at finding the independence among the returns for each stock index, and the variance ratio test examines the linear relationship between the variance of the random walk increments. Except for the empirical results of the Dickey-Fuller, the findings of the other two statistical methods indicate that Chinese stock markets do not perform consistently with the hypothesis of random walk, consequently implying that Chinese stock markets are weak-form inefficient. The results of Dickey-Fuller test ensure the existence of the unit root in the return series, which determining Chinese stock markets as weak-form efficient. Generally speaking, Chinese stock markets are not typically consistent with the hypothesis of weak-form inefficiency since no consensus has been reached among the three statistical methods. This results seem to be similar to the conclusion of the previous studies. A significant number of studies reported that the emerging stock markets might not has the unique features of the weak-form efficient markets because of the characteristics of the domestic polices and economies and etc. Even though Chinese stock markets are found untypical under the assumption of weak-form efficient market, it is still rational to believe the Chinese stock markets to behave like an market of informational efficiency in the following years since the development in Chinese financial world is significant. Investors in Chinese stock markets cannot get a sufficient historical information from the current stock prices, which indicates some investors may acquire excess returns by some techniques. Inefficient markets may benefit the investors who can get access to the inner information or information about the patterns of the movements of the stock prices. To improve this study, firstly, it is proper to employ weekly or monthly data and to employ Shanghai B-share index and Shenzhen B-share index. Secondly, further researches could use Augmented Dickey-Fuller test with time trend instead of Dickey-Fuller test in this study. Besides, the whole time period could be divided into some sub-intervals, which proving more detailed analysis. At last studies employing four or more statistical methods might present adequate evidence on this topic.
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