Relationship between stock return and trading volume in vietnam's stock market

luận văn, khóa luận, chuyên đề, đề tài

MINISTRY OF EDUCATION AND TRAINING UNIVERSITY OF ECONOMICS HO CHI MINH CITY

-

ĐỖ NGỌC HOÀNG YẾN

RELATIONSHIP BETWEEN TRADING VOLUME AND STOCK RETURN IN VIETNAM’S STOCK MARKET

Major : FINANCE – BANKING Code : 60.31.12

MASTER THESIS

Instructor: Dr HỒ VIẾT TIẾN

HO CHI MINH CITY, SEPTEMBER 2011

ABSTRACT

This thesis investigated the relationship between return and trading volume in the Vietnam’s stock market in the context of Granger causality test and GARCH model test The sample, including two market indices and thirty seven largest market capitalization listed companies during the period since they firstly traded through July

2011, was used The dynamic relation as marked by lead –lag relationship from return

to volume was confirmed at both market level and firm level I also found the evidences supported the interaction between two exchanges in Vietnam When testing the mixture distribution hypothesis, the results indicated that volume was not a good proxy for information arrival in the stock market due to the persistence of volatility remained in most of the cases This finding was similar to other emerging markets which less agreed with the mixture distribution hypothesis

CONTENTS

Abstract i

Contents ii

List of Tables iv

Chapter 1: Introduction 1.1 Introduction 1

1.2 Research background 1

1.3 Problem statement 3

1.4 Research objectives and questions 4

1.5 Research methodology and scope 5

1.6 Thesis structure 5

Chapter 2: Literature Review 2.1 Theoretical background 7

2.2 Empirical studies 2.2.1 Studies on volume- price change relation 9

2.2.2 Studies on volume- volatility relation 11

Chapter 3: Research Methodology 3.1 Hypotheses 15

3.2 Data Description 15

3.2 Econometric Methodology 3.2.1 Stationary and Unit Root test 16

3.2.2 Cointegration 17

3.2.3 Granger Causality tests 19

3.2.4 ARCH models 21

3.2.5 GARCH models 23

3.2.6 Threshold GARCH models 23

Chapter 4 Empirical results 4.1 Market level analysis 4.1.1 Descriptive statistic for markets 25

4.1.2 Unit root test and Granger causality test 26

4.1.3 GARCH(1,1) test and TGARCH (1,1) test 27

4.2 Firm level analysis 4.2.1 Descriptive statistic 29

4.2 2Granger causality test 30

4.2.3 Restricted and unrestricted GARCH(1,1), TGARCH (1,1) test 33

Chapter 5 Conclusion and Implication 5.1 Main findings 35

5.2 Implications 35

References 37

Appendix 1 41

LIST OF TABLE

Table 4 1 Descriptive statistics of two market indices 25

Table 4 2 Stationary test for market indices 26

Table 4 3 Cointegration test (Unit root test for residuals) 26

Table 4 4 Granger causality test at market level 27

Table 4 5 ARCH effect test for indices 28

Table 4 6 GARCH (1,1) model and TGARCH (1,1) model for indices 29

Table 4.7 Granger causality test at firm level 31

Table 4.8 ARCH effect test for firms 33

Table A1 Descriptive statistics of firms 41

Table A2 Unit root test for return and volume of firms 43

Table A3 Cointegration test at firm level 44

Table A4 GARCH (1,1) model with and without volume for firms 45

Table A5 TGARCH(1,1) model with and without volume for firms 47

Table A6 List of 37 sample firms with their symbol 48

CHAPTER 1: INTRODUCTION

1.1 INTRODUCTION

This chapter explains why the link of volume, return and volatility is worth investigating in the case of the Vietnamese stock market In particular, this chapter divides into six sections The first section summarizes the structure of the chapter The second one provides evidences that tell us why the return – volume relationship becomes a concern for market participants and policy makers From this background information, the third section raises the problem necessary to make clear for the case of Vietnam The fourth section covers the research objectives and research questions The fifth section describes the methodology and scope The last one ends with description about the structure of the thesis

1.2 RESEARCH BACKGROUND

The relationship between return, volatility, and volume has met the interest of many researchers over the past years The motivation comes from the attempt to measure and model the volatility of financial assets return Volume is evidenced to be an important part of pricing financial assets under influence of information arrival Due

to new information arrival, investors may adjust their expectations and this is the main source for price and return movements However, the stock return may remain unchanged if some investors recognize the information as good news whereas others find it to be bad news Clearly, it is necessary to examine the dynamics of stock return, volatility and trading volume so that it would improve the understanding

of the microstructure of the stock market and then help the participants and policy

makers in their own strategies

Most previous researches followed two leading theories (hypotheses), the mixture of distribution hypothesis (MDH) and the sequential information arrival hypothesis (SAI), to examine the information arrival process in financial markets In general,

between volume and absolute return and assume a symmetric effect for price changes As pointed out in MDH, volume of trade can be a proxy of new arrivals [Clark (1973), Epps and Epps (1976)] Clark (1973) implies that the value of price change and trading volume are distributed independently from each other Also, the number of information arrivals per time period varies Lamoureux and Lastrapes (1990) shows that a serially correlated mixing variable measuring the rate at which information arrives to the market helps explain the generalized autoregressive conditional heteroskedasticity (GARCH) effect in the return According to them, volume that is considered as an explanatory in the conditional variance equation eliminates the GARCH effects Sharma et al (1996) extend Lamoureux and Lastrapes (1990) work by bringing out two main forms: (1) the ability of daily trading volume data to fully capture the information flow on the market return would partly rest on the degree of market efficiency, and (2) both firm – specific factors and market – wide factors (which affect volume) can generate volatility This makes volume a good or poor proxy for news arrival that contributes to conditional heteroskedasticity However, Najand and Yung (1991) and Bessembider and Seguin (1992, 1993) present evidence against MDH In addition, Bessembider and Seguin (1992, 1993) suggest that the volatility –volume relation in the financial markets depends on the type of trade

On the other hand, the sequential arrival of information hypothesis (SAI) suggests gradual popularization of information According to Grammatikos and Saunders (1986, p.326), the implication of SAI is that the information is sequentially observed

by each trader in the market Under SAI framework, McMillan and Speight (2002) argue that past absolute return provides information on current volume, and past volume contains information on current absolute return In other words, this dynamic relationship is helpful and important to forecast return and volatility by using trading volume information

1.3 THE PROBLEM STATEMENT

The stock market in Vietnam, which is supervised and managed by the State Securities Commission, has developed rapidly since established in July 2000 With

289 firms listed on Hochiminh Stock Exchange and 384 firms listed on Hanoi Stock Exchange up to May 2011, the market is considered as a channel for companies to raise medium and long capital Regarding capitalization value, it is recorded to grow considerably from VND270 billions in 2000 (approximate 0.28% GDP) to VND740,433 billion in 2010, approximate 45.2 percent of Vietnam GDP The number of securities trading accounts has reached at 1,103,184 at April 30th 2011, increasing 25.4 percent compared to one year before On average, total trading volume of two exchange is 81,312,559 shares and fund certificates and VND2,534.93 billions trading value per day is recorded in 2010

During ten years, Vietnam‟s stock market has shown the ups and downs of a developing market In the first five years, the market did not attract the public attention and made very little distribution to the economy due to the lack of merchandise and unattractive small listed companies Since 2006, it has attracted more foreign and domestic investors with lively trading activities in two listed exchanges It showed an excellent performance in 2006 when the market capitalization increased fifteen times, the Vnindex of Hochiminh Stock Exchange (HOSE) grew 144% and the Hnindex of Hanoi Stock Exchange (HNX) grew 152.6% only in one year After reaching the highest peak of 1170.67 points in March 2007, Vnindex went down rapidly under effects of the global recession The index fell as low as 239.69 points in February 2009 Since then, the index rose nearly 2.6 times to 530 points at the beginning of 2010 As being affected by the changes of the world finance and the difficulties inside the economy, the stock market of Vietnam continues to perform quietly during the 2010 and the first half of

2011

For a young stock market, Vietnam‟s market clearly contains weaknesses Firstly, this is an immature market with a weak legal environment and lack of capital The Government strictly controls the rules and actively intervenes in stock trading Accordingly, investors tend to speculate, and thus cause high market volatility Secondly, the lack of transparency is widely known as a biggest problem facing the traders Reporting requirements are not well-defined and public information disclosure is not clear and unreliable From that reasons, it is harder for investors to build up a good portfolio in an inefficient market which contains lots of confusing information

It is the fact that while most of previous studies focused on developed markets, little empirical evidences for emerging markets have been found, especially in Vietnam This analysis allows us to answer the important question of whether the linkage of volume, return and volatility in the case of Vietnam market at both market level and firm level exists

1.4 RESEARCH OBJECTIVES AND QUESTIONS

To solve the research problem, this study has following objectives:

 To explore the causal relationship of stock return and trading volume

 To find out the trading volume effect on the return volatility

The research problem defined above leads to the following research questions:

 Is there any long run relationship between the trading volume and stock return in Vietnam?

 Does the causal relationship between stock return and trading volume exist in Vietnam‟s stock market? If yes then, what is direction and extent

of relationship between these variables?

 Does ARCH effect exist in stock return of two indices? If yes then, is this ARCH effect weaker when trading volume is added as an explanatory variable in GARCH equation?

 Does ARCH effect exist in individual stock return? If yes then, does this effect reduce when trading volume is included as an explanatory variable

in GARCH equation?

1.5 RESEARCH METHODOLOGY AND SCOPE

The Granger causality and ARCH/GARCH effect tests are employed to test the proposed hypotheses Theoretically, these tests are only appropriate when the variables analyzed, including stock price, the index and trading volume, are stationary and co-integrated Therefore, it becomes necessary to conduct various prior tests of integration and cointegration In so doing, this thesis will apply the unit root test (specifically the augmented Dickey-Fuller tests) Following previous studies, this thesis will employ the Akaike Information Criterion (AIC) and Schwarz Information Criterion (SIC) to determine the optimal lag lengths

Data used in Granger causality and GARCH models are collected from two official sources, namely, Hochiminh Stock Exchange and Hanoi Stock Exchange during the May 2006 to July 2011 period I also use the stock price of 37 large size (sorted in market capitalization) companies as my sample Similar to most previous studies, this thesis will use the daily data to meet the required observations in GARCH models More details in handling variables will be discussed in chapter three

1.6 THESIS STRUCTURE

In terms of structure, the thesis has five chapters After defining the research problem, questions for the study in chapter one, chapter two reviews previous researches related to relationship between volume and price change Chapter three discusses in detail about the methodology including the data collection and analysis methods, and

hypothesis testing to support the model Data analysis and findings are presented in chapter four This chapter presents descriptive results of return –volume and volatility – volume relation in the aspect of market index and firms Chapter five ends with conclusion and implications

CHAPTER 2: LITERATURE REVIEW

2.1 THEORETICAL BACKGROUND:

Mixture of distritbution hypothesis

The mixture of distribution hypothesis in finance proposes that the net price change

X(t) over period t is the sum of (t) incremental inter – period steps, giving

X((t)) = Xt,i (2.1) Accordingly, the heavy tails fluctuation X(t) can be explained by inserting the

number of economic time (randomized time) or the number of information arrivals

that traders meet during t, typically associated with trading volume V(t) The

resulting convolution X((t)) has a mixed distribution that can capture

leptokurtosis, expound heterogeneity, including conditional heteroscedasticity, and

improve model fitting similar to nonparametric

The mixture has statistical foundation from Probability theory, which concerned

with analysis of random variables, stochastic processes, and events If y(t):=  X(t)

has density  y (y ;) and economic time (t)≥0 has density (), then the observed

convolution y ((t)) has a density mixture

 y ()(y) = 0 y (y:  )  (  ) d  (2.2) Clark (1973) provides evidence showed that the standard Central Limit Theorem,

which maintains only when the number of random variables added is unchanged

over time, is violated in the case of speculative markets He proposes the opposite

theorem in which the limit distribution of price changes is subordinate to the normal

distribution In an attempt to exploit Bochner‟s and Feller‟s work on subordinated

Gaussian processes, Clark builds a model of asset return as following:

Denote by µ y,, ²y and Ky respectively the mean, variance, and kurtosis of y , and

yz (t) is the conditional variance give random z If X(t)≡ X(t): -∞ < t < ∞

is a stochastic process and (t), :N→|R+ is a “driving process” then the stochastically indexed X((t)) is subordinated to X(t) If (t) is stationary and independent with mean µ >0, and X(t) (0, X), then the subordinated fluctuation X((t)) are stationary and independent, and distributed as following  X (  (t ) ) (0, µ  x  X ) (2.3)

For µ reflects the arrival of new information, only the average amount of new information affects the scatter of imbedded return X If price fluctuations are normally distributed X(t) N(0, X) and  < ∞ and (t) are independent

of X(t), then price fluctuations have kurtosis K larger than 3, thus, they are considered to be heavy – tailed The tails of price fluctuations grow heavier as the variance of information flow raises Further, if iid (t) are lognormal with parameters c ,v²  then

 X  (t) =  V (t), where  ,  > 0 (2.6)

In short, the mixture distribution hypothesis creates the framework, in which the distribution of price change is subordinate to a normal distribution and the positive relationship between volume traded (in lognormal distribution) and equity return is concerned Since Clark‟s (1973) work, a large amount of studies has attempted to support it

2.2 EMPIRICAL STUDIES

2.2.1 Studies on volume – price change relation

The most cited and excellent review of research is Karpoff‟s work (1986,1987) According to his articles, the main reasons for studying the price changes –volume relation were (i) insight into structure of financial market, (ii) benefit for event studies which use the volume and price data to reach inferences, (iii) critical time to the debate over the empirical distribution of speculative markets, and (iv) important implications to the studies of futures market In the discussion of two sets of hypotheses, the mixture of distribution and the sequential arrival of information (SAI), Karpoff generaled previous studies into empirical conclusion which suggested the positive and contemporaneous correlation between volume and price variability

Clark (1973), Harris (1983), Tauchen and Pitts (1983) and Andersen (1996) among others, explained the positive correlation between volume and squared value of price change with daily data on securities For instant, Clark (1973) assumed volume, which distribution was lognormal, could be a proxy for price data that were generated by a conditional normal stochastic process with a changing variance parameter Using the same assumption, Harris (1983), Harris (1986), Harris (1987) and Tauchen and Pitts (1983) showed that a mixture of bivariate normal distributions could model the joint distribution of daily price changes and volume

These two variables were assumed to be conditioned by the rate of information which is uncorrelated and random They also used maximum likelihood analysis to estimate the model in the assumption of lognormal distribution for the mixing variable

With less agree to earlier studies, Anderson (1996) added a volume component which was not information sensitive and a conditional Poisson distribution for the trading process in order to modify the MDH model He suggested the modified model significantly outperformed the standard model

Studying nine international markets (Canada, France, Hongkong, Italy, Japan, Netherlands,Switzerland, UK and US), Chen, Firth, and Rui (2001) also found the positive correlation between absolute value of stock price changes and volume Besides the MDH models and SAI models, they explained the relation with another two models, the rational expectation asset pricing (REAP), and the differences of opinion (DO) Using daily volume and return data from 1973 -2000, they concluded that EGARGH models could represent for return of stock index data

Malabika, Srinivasan and Devanadhen (2008) also confirmed the positive and contemporaneous relationship between absolute price changes and volumes in six markets (Hongkong, India, Indonesia, Malaysia, Korea, Tokyo and Taiwan) Based

on VAR model and EGARCH (1,1) model, the dataset in the period from 1stJanuary 2004 to 31st March 2008 showed the feedback system in Indonesia, Hongkong, Malaysia and Taiwan The evidence indicated stronger return causing volume than volume causing return They also found that return variance and lagged trading volume has positive association for most of Asia – Pacific stock markeits with the stable coefficient over the time This finding is similar to results of Pyun Lee and Nam (2000) for Korean market, Bohl and Henke (2003) for Polish market, and Lucey (2005) for the Irish stock market

In recent years, many researches focused more on Granger causality relationship between volume- return to contribute the literature During the decade of the 1990s data, Kamath, et al (2005) examined the return –volume relation in four merging markets and found the strong positive correlation between magnitudes of return and volumes In Malaysia and Indonesia, they found that causality run in both direction

On the other hand, in Thailand and South Korea, they found that only return cause the volume

Another study of Kamath and Yi Wang (2006) showed similar results in six developing Asian equity markets during the period from January 2003 and October

2005 In Malaysia, Singapore, South Korea, and Taiwan, they provided evidence indicated that the market increase was accompanied by rising volume and vice versa Moreover, they also found that the correlation between positive return and volume

to be positive and correlation between negative return and volume to be negative The absolute return – volume relation was found to be statistically significant positive in most of six markets, except the Indonesian market The Granger causality tests were employed to detect the causal direction between return and volume While in Taiwanese market, volume was found to Granger cause return, in the South Korean market, they found return Granger causing volume Meanwhile, the absence of causality between two variables was supported by evidence in case

of Hongkong, Indonesia, Malaysia, and Singapore

2.2.2 Studies on volume- volatility relation

Another distributions examine the effect of trading volume to the market return by using generalized autoregressive conditional heteroskedasticity (GARCH) model in hope of broaden the work of Lamoureux and Lastrapes (1990) The trading volume

is included as an explanatory variable in the conditional variance equation in GARCH model It is found to positively affect on conditional volatility

Hiemstra and Jones (1994), Gallant et al (1993) and Tauchen et al (1996) presented a positive correlation between trading volume and volatility by using VAR, Granger causality test and GARCH models Testing the data from Australian Stock market in the period 24 April 1989 to 31 December 1993, Brailsford (1994) presented a diminution in GARCH effect and in the persistence of variance when trading volume was used Similarly, in another study of Brailsford (1996), trading volume - stock return volatility and trading volume – conditional volatility relationship was also examined in Australian stock market He found that the result from GARCH (1,1) model was insignificant when the volume was taken into consideration

Sharma et al (1996) studied the GARCH effects in the NYSE The paper showed how the volume explained the GARCH effects in market return From that reason, the authors considered a simple GARCH (1,1) model with and without daily volume, and assumed the conditional normality and conditional t – distribution The data covered the period 1986-1989 The results implied that the introduction of volume did not eliminate the GARCH effects However, they found that the coefficient of volume was positive and statistically significant For market index data of nine countries, Arago and Nieto (2005) also found that volume effects did not cancel out GARCH effects at the country index level

Ragunathan and Pecker (1997) considered the relationship between volume and price variability for the Australian futures markets over the return series of the contracts in the period January 1992 to December 1994 Applying models developed by Schwert (1990), and Bessembinder and Seguin (1993), they suggested that unexpected volume affected greater on volatility than expected volume

Hogan et al (1997) used daily data from 3 January 1988 to 31 December 1991 of the S&P 500 cash and CME S&P 500 near zero term futures contracts to examine the relationship between trading volume and market volatility The results from

Using GMM and Original least square regression method (OLS), Wang and Yau (2000) continued paying attention to the interesting relationship in futures markets Based on two financial futures contracts (S&P 500 and DM) and two metal futures contracts (gold and silver), the data set covered the period 2 January 1990 to 29 April 1994 The results provided evidence of positive relationship between trading volume and price volatility, and negative relationship between price volatility and lagged trading volume

Applying the model of Bessembinder and Seguin (1993), Wanatabe (2001) found a considerably significant and positive relationship between price volatility and unexpected volume for the Nikkei 225 stock index futures The sample period was from 24 August 1990 to 30 December 1997 The results also showed that there was

no relationship between volatility and volume when the regulation increased gradually

In the work of Illueca and Lafuente (2003), link between spot volatility and trading volume was not found in the Spanish stock index futures market However, Pilar and Rafael (2002) provided evidence of a decrease in the volatility and increase in trading volume in the Spanish stock market by using a GIR model with a dummy variable

Applying VAR model with five lags in addition to a GARCH model to examine the lagged volume and volatility effects for the two indexes of China, Lee and Rui

(2000) explored interesting results It was evident to note that trading volume did not Granger cause the stock market return in Chinese markets However, when testing the cross – market effects, they found that the US and Hongkong return help predict return of Shanghai A and B stocks while US and Honkong volume did not affect on volume in Chinese markets They also discovered the feedback relationship of return within the markets in China Shenzen B return was Granger caused by Shanghai A volumes, and Shanghai B stock return could be predicted by Shenzen B volume

Investigating the GARCH effect on the China‟s stock markets, Wong et al (2005) found that it completely disappeared when trading volume was added and the persistence of volatility decreased gradually in most cases They also found that the number of transaction and the turnover affected positively on the conditional volatility of the Chinese stock market

In the paper of Jinliang et al (2009), they emphasized the interaction of GARCH and volume effects, and the impact of firm size and trading volume on these effects for individual stocks of the Australian All Ordinaries Index They concluded the volume could be a good proxy of information flows and replace the GARCH effect

in the model Furthermore, they confirmed that the elimination was higher for the largest trading volume stocks and largest market capitalization stocks Their results also showed a stronger volume – volatility relationship for actively traded stocks Meanwhile, the thin trading stocks and small firms were found to lead a high persistence of volatility of GARCH effect in estimated model

Yet there has been very little research about this issue in the case of Vietnam so far

in both market level and firm level

Hypothesis 1: Return does not Granger cause the volume

Hypothesis 2: Volume does not Granger cause the volume

- Regarding the effect of volume on return volatility, many previous researches proposed an explanatory power of volume in the conditional variance equation So, the hypothesis is:

Hypothesis 3: Trading volume does affect the volatility and make the

persistence of variance reduce significantly

In more detail, the study would use the Granger causality to test the first two hypotheses The last one is investigated with GARCH and TGARCH models

3.2 DATA DESCRIPTION

The data set consists of daily price and trading volume data for HOSE and HNX indexes as well as 37 largest market capitalization listed companies The sample period for the market indices begins from 20th May 2006 and ends at 14th July 2011 Meanwhile, the firms are tested during the period from their first traded day until

14th July 2011 In fact, these firms hold around 80% of total market capitalization Due to market index counting method in Vietnam, these 37 companies trading activities may affect considerably to the market movement However, not all of them have the large trading volume It may, therefore, be informative to focus on

as VOLt = log (Vt / Vt-1) where V denotes the number of shares trading at day t All data is available on official website of HOSE and HNX

3.3 ECONOMETRIC METHODOLOGY

3.2.1 Stationary and Unit Root test

This research design is completely based on the time series data, which is usually trended According to Gujarati (2003), if a time series is not stationary, we can study its behaviors only in one time period under consideration, thus, we cannot generalize all other periods In regression analysis, it leads to the invalidity of the forecasting results that are usually called as spurious regression phenomenon From this reason, testing whether a set of time series is stationary appears to be the first task of any analysis

In stationary time series, shocks will be temporary and over time, their effects will

be eliminated as the series revert to their long-run means values On the other hand, non-stationary time series will necessarily contain permanent components Therefore, the mean and/or the variance of a non-stationary time series will depend

on time, which leads to cases where a series (a) has no long-run mean to which the series return, and (b) the variance will depend on time and will approach infinity as time goes to infinity

Most academic studies are applying the widely approved unit-root test methods, introduced by Dickey-Fuller (1979) In statistic language, if a time series have a unit root, it is called “non-stationary” In this thesis, I concentrate on the augmented Dickey-Fuller (ADF) test As the error term is unlikely to be white noise, Dickey

and Fuller extended their test procedure suggesting an augmented version of the test which includes extra lagged terms of the dependent variable in order to eliminate autocorrelation The lag length on these extra terms is either determined by Akaike Information Criterion (AIC) or Schwarz Bayesian/Information Criterion (SBC, SIC),

or more usefully by the lag length necessary to whiten the residuals (i.e., after each case, we check whether the residuals of the ADF regression are autocorrelated or not through LM tests and not the DW test

The three possible forms of the ADF test are given by the following equations:

t i t i 1

t i t i 1

3.2.2 Cointegration

In the case of having two non – stationary variables, we can consider an error as a combination of two cumulated error processes According to Asteriou and Hall (2007), these processes are called stochastic trends and their combination is expected to produce another non – stationary process Suppose that, if two

variables, say X and Y, are really related, the two stochastic trends would be very similar to each other, and then their combination may be eliminate the non – stationary In this special case, the variables are cointegrated Cointegration becomes an overriding requirement for any economic model using non-stationary time series data If the variables do not cointegrate, we usually face the problems of spurious regression and econometric work becomes almost meaningless On the other hand, if the stochastic trends do cancel to each other, then we have cointegration

Suppose that, if there really is a genuine long run relationship between Yt and Xt, although the variables will rise overtime (because they are trended), there will be a common trend that links them together For an equilibrium, or long run relationship

to exist, what we require, then, is a linear combination of Yt and Xt that is a stationary variable (an I(0) variable) A linear combination of Yt and Xt can be directly taken from estimation the following regression:

Yt = 1 + 2Xt + t (3.4) and taking the residuals:

t

Y andX t, and thus they are cointegrated In other words, Y t and X t are I(1) variables and u t is I(0), which implies that Y tand X t are cointegrated and β2 is the cointegrating parameter

According to Asteriou (2007), Engle and Granger proposed a straightforward method to testing for cointegration However, EG approach just examines the long run relationship of two variables

3.2.3 Granger Causality Tests

A simple test developed by Granger (1969) that examines causality between two variables has been widely applied in economic policy analysis Following the VAR model, the Granger causality test concerns about the ability of one variable to predict the other If a variable Xt can be predicted with larger precision by using past values of the Yt variable rather than not using such past values, all other terms remaining unchanged, it is said to be Granger – caused by variable Yt

In Granger causality test, they found three cases of relationship between two variables Before that, it involves the estimation of VAR model: (3.6)

Case 2 The lagged R terms in equation (3.7) are statistically different from zero as

a group, and the lagged V terms in equation (3.7) are not statistically different from zero In this case, we have that Rt causes Vt

Case 3 Both sets of V and R terms are statistically different from zero as a group in

equation (3.6) and equation (3.7), so that we have bi- directional causality

Case 4 Both sets of V and R terms are not statistically different from zero in

equation (3.6 ) and equation (3.7), so that Vt is independent of Rt

The Vector Autoregressive (VAR) method used for estimation and model with four lags is selected based on SchwarzBayesian (SBC) Criteria

s j j







Step 4 Calculate the F statistic for the normal Wald test on coefficient

restrictions given by:

) k N /(

RSS

m / ) RSS RSS

( F

u

U R

where N is the included observations and k = m+n+1 is the number

of estimated coefficients in the unrestricted model

Step 5 If the computed F value exceeds the critical F value, reject the null

hypothesis and conclude that X t causes Y t Similarly, we conduct the

same procedure to test if Y t causes X t and so on In this thesis, instead

of comparing F values, we compare the chi-square statistic to reach conclusions

3.2.4 ARCH models

The autoregressive conditional heteroskedasticity (ARCH) model was developed by Engle (1982) Before its introduction, many specifications considered only the mean return in efforts to forecast future return As the innovation of ARIMA model, this model supposes that the variance of error terms (the unpredictable part of return) at time t depends on squared error terms at previous periods Engle suggested that variance of data series should be modeled simultaneously with the mean when it is doubted to vary over time The equation is specified as following:

shock occurs at period t-1, then ut value would be larger It means that when u²t-1 is big (small), the variance of ut is big (small) either The parameter 

1 has to be positive because variance is always positive In fact, the conditional variance may depend on several lags The ARCH(q) model is given as following:

Testing for ARCH effects

In order to consider the existence of conditional heteroskedasticity (which is known

as ARCH effect (Tsay, 2005)), the squared residual series ε²t are conducted This paper employs the Ljung Box approach with 12 lags for formally ARCH effect The Ljung-Box Statistic Q(m) proposed by McLeod and Li (1983) The null hypothesis

is that the first m lags of ACF of the squared residuals series ε²t are equal to zero The Q-statistics are significant at all lags, indicating significant serial correlation in the residuals The first step of the test is to estimate the mean equation:

and follow a  ² distribution with q degree of freedom This procedure was suggested

by Engle (1982) If the value of test statistic is greater than the critical value from

the  ² distribution (F > ²m () ) or the p value of F is less than  , then reject the null