CHAPTER III

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CHAPTER III

RESEARCH METHOD

3.1 Data Data that will be used in this research are daily exchange rates and composite price index of equity markets for period January, 1999 through December, 2004 because of providing more robust and updated results. The data sample will be divided into two periods that are the pre-Euro period and the post-Euro period. The pre-Euro period of time is started from January, 1 1999 to December, 31 2001. A reason chooses date for the pre-Euro period because the Indonesians economy has become stable from Asian financial crisis and has adopted the floating exchange rates. The post-Euro period of time is started from January, 1 2002 to December, 31 2004. A reason chooses date for the post-Euro period because the banknotes and coins of Euro firstly were introduced in the world market in January, 1 2002.Data of exchange rates that are employed for this research are daily closing observations on the nominal exchange rate for US Dollar, and Japan Yen. Because US Dollar and Yen are primary currencies in the world are used to the international trade. And many Indonesian companies use debt services denominated in US Dollar. Besides the debt, many subsidiaries of US and Japan companies are established in Indonesia which have operating transaction by US Dollar and Yen, and local companies have mainly exporting and importing activity to target countries such as US, and Japan. Data of composite indices that are employed for this research is daily closing observations for each of countries such as Indonesia, US, and Japan. For Indonesia, employs LQ45 Index in Jakarta Stock Exchange. The US employs Standard&Poor500 Composite Price Index. According to Fratzscher (2001), the indices are denominated in local currencies because using a common currency would mitigate the effect of exchange rate changes and uncertainty. Finally, Japan employs Tokyo Nikkei225 Composite Price Index. Reasons choose S&P500 Index and Nikkei225 Index because they are the largest capital market in the world and have active transaction of share. In addition, almost companies in US and Japan which are listed in their indices usually have subsidiary company in Indonesia. Whereas a reason chooses LQ45 Index because the companies which are listed in stock exchange have active transaction of share every day and almost of companies are susceptible with US Dollar debt service. There are at least two difficulties arise in investigating stock market interdependencies across countries. The first one is the missing observation problem due to different stock market holiday. Since the study extensively incorporates lags in the regressions, missing data is particularly troublesome. Thus, it is desirable to fill in estimate-based information from an adjacent day. Rather than using a sophisticated interpolation, this study follows the studies of Jeon and Von (1990), and Hirayama and Tsutsui (1998) by adopting the method of Occam's razor (just fill in with the previous day's price). Simplistic as it may be, this study justifies this method on the premise that a closed stock exchange does not produce any information on bank holidays. Since no new information is revealed, the previous day's information is carried over to the subsequent day. Method of collecting data is practiced in doing research that is library research. Data that is used in this research is secondary data which is collected by Jakarta Stock Exchange Daily Statistics. 3.2Variable

Variables that will be used in this research are:

1. Dependent variable is changes of Jakarta Composite Index for period 1999-2004 that will be calculated with: R.LQ45 =.

2. Independent variables are changes of abroad stock markets (S&P500 Index, and Nikkei225 Index) and changes of foreign exchange rates (US Dollar, and Japan Yen) that are calculated with:

R.S&P500 =, R.Nikkei =,

R.US$ =, and R.Yen =.

3.3 Descriptive Statistics

Firstly, analysis that is practiced in this research is analyzing of data descriptive statistics. Component of descriptive statistics are sample mean, deviation standard, skewness coefficient, and kurtosis of data sample. Mean sample is used to know central data, while standard deviation is used to spread data sample. From skewness and kurtosis, describe about form of data distribution.3.4 Unit Root Test of Time Series Data

Stationary is concept of data stability toward effects innovation of variable. In time series, stability means that stable mean, and variance toward innovation of time. Data of time series is collecting data that is ordered based on sequence specified time. Ordered time in time series is very important because moment of data distribution always is influenced by innovation of time. According to Mukherjee et al. (1998), moment of data distribution is mean, variant, and other data distributions.

The study finds that all stock indices and exchange rates contain a unit root, implying that the null- hypothesis of the presence of a unit root at level cannot be rejected even at the 1% significance level. Since the indices and exchange rates are found to be non-stationary at levels, the first differences for whole models are taken. The same tests are applied to the first differences of the indices and the results show that all the indices and exchange rates become stationary after differencing once. If the result indicates that all index levels are integrated of order one, I(1) and, therefore, we can proceed to the cointegration analysis and error correction model by two step Engle-Granger with these indices and exchange rates because they are all integrated in the same order as required for cointegration.

Co-integration test of two or more data that is proved non-stationary also is necessary done. Two or more data is called cointegration if linear combination of both data is stationer data. In bivariate analysis, two data must have same order of integration that is called cointegration. Cointegration shows that non-stationary data has tendency to move together convergent in long period. If data is used in regression model that is non-stationary data, and cointegration, the model should be repaired to catch dynamic in short period.

Suppose {} and {} are time series I(1), and {} relation to and is wanted to be analyzed. Because {} and {} are non-stationary, model can be used to analysis this linkage is model using differential of {} and {}, are:

, with ~

But, if {} and {} is cointegrated, this above model is not accurate. Cointegration {} of and {} is shown with linear combination that is stationer.

If {} and {} is cointegrated, the accurate model to analysis linkagetoward and is:

, with ~, and is first lag from error correction variable. Variable is residual of regression to regression. =- A- B with A and B is coefficient regression to.

Unit root test is used to examine is a time series stationer toward time, or not. And this test assumes that the errors are statistically independent and have a constant variance. Unit root test that is used in this research is Dickey-Fuller Test. Firstly, stationary of composite indices data will be tested by unit root Dickey-Fuller. Some steps that are necessary done in this testing are:1. Regression to uses ordinary least square (OLS) model, so formed linear regression model is: . Taking estimation of , and standard deviation of .2. Calculate of DF statistics:

Value of DF is compared with critical value on level of significant.3. Using hypothesis of non-stationary and .If DF , hypothesis of data non-stationary can not be rejected on level of significant. A data is called stationer on level of significant if DF . Critical value of and .Steps of testing hypothesis of non-stationary above also are used on other variables such as Japan Yen, US Dollar, LQ45 Index, S&P500 Index, and Nikkei225 Index. 3.5Analysis of Akaikes Final Prediction Error (FPE)

In this research, vector auto regression (VAR) model is used to examine hypothesis of non-causality Granger. FPE analysis is used to determine lag optimum that is number of lags minimize error caused by inconsistency and inefficient of parameter estimation in VAR model. Standard recommendations for the selection of the appropriate lag length is to choose the number of lags to be long enough to ensure that the residuals are white noise, but not too long since the estimates can become imprecise. The lag length is therefore often selected somewhat arbitrarily.

Linkage x variable Granger causes y variable will be tested with using VAR model that is:

,

With and are optimum lag for y and x variables. If y and x are non-stationer variables and non-cointegration, variable that will be used in VAR model is differential from y and x, are and .

Some steps determine optimum lag and with using FPE analysis (Zhou,1997).1. Determines maximum lag of M and N for y and x variables.

2. With using model of OLS linear regression and sets N=0, regress y on lag 1 y, lag 2 y,, lag m y, for m=1,2,3,,M.

Equation of regression is , for m=1,2,3,,M.

3. Calculate FPE of VAR equation on second step as following:

, for m=1,2,3,,M.

(3.1)SSR(m) is sum of squared residuals.

4. Choosing that can minimize FPE(m), for m=1,2,3,,M.So FPE() FPE(m), for all of m=1,2,3,M.5. Next, setting m = , doing linear regression (OLS) that fulfills linear model:

, for n=1,2,3,,N.6. Calculate FPE for VAR equation on fifth step as following:

, for n=1,2,3,,N.

(3.2)7. Choosing that can minimize FPE(,n), for n=1,2,3,,N.So FPE(,) FPE(,n), for all of n=1,2,3,,N.Lag and that are obtained from step number of four and seven above, are optimum lag used in VAR model. To test is x variable Granger cause y.

8. If FPE(,) FPE(), This FPE analysis can detect that indicating x variable Granger cause y variable.

Steps number 1-8 above will be used in all of couple of variables in this research. After determining optimum lag that will be used to test Granger Causality in each of couple variables, the next step is to test significant Granger Causality.

3.5.1 Testing of Non-Causality Granger HypothesisGranger causality is tool of causal test that always is used to two variables of time series. According to Granger (1969), X granger causes Y if Y is better predicted using X data history, compared with only using Y data history (Zhou, 1997). Formally, X granger cause Y if mean square error (MSE) of Y prediction model uses X history data and Y is smaller than MSE that comes from Y prediction model without X history data (Chen, 2001). Testing of non-causality Granger hypothesis in a couple variables is practiced through vector auto regression (VAR) that represents linkage both variables.

Suppose will be practiced testing direct causality from time series variable X = {} and Y = {}. Generally, VAR model that will be used to test direct Granger causality is:

(3.1)

(3.2)With residual of and of VAR model is not autocorrelation.

According Oxley (1998), equation (3.1) and (3.2) of VAR model can be used in couple of and variables that are stationer, even couple of and variables are non-stationer, and cointegration. If couple of and variables are non-stationer data but no cointegration, couple of and variables must be differentiated first.

VAR model that is accurate used to test direct Granger causality in couple of and variables is non-stationer and no cointegration:

(3.3a)

(3.4a)

Beside VAR (3.1) and (3.2) model, VAR (3.3b) and (3.4b) model also can be used to test direct Granger causality of couples of and variables that are non-stationer, and cointegration.

(3.3b)

(3.4b)

With and are first lag of error correction variable for each of VAR models. Whereas is differential symbol. According to Granger (1969) show that if both of time series {} and {} also cointegrated, causal relation will be existed in one direct.

After determined through FPE analysis, optimum lag will be used in VAR model to examine hypothesis of non-causality Granger in all of couple of variables. VAR model that will be used to examine is x variable Granger cause y variable:

With and are optimum lag for y and x variables. Lagrange Multiplier (LM) test will be used to examine hypothesis of non-causality Granger in equation of VAR. Statistic test of LM distributes chi-square and strong to heteroskedastial residual. In testing hypothesis of non-causality Granger is assumed VAR model that does not consist residual autocorrelation.

Some steps that are necessary done to test is x variable Granger cause y variable significantly on level of significant:

1.With using optimum lag and from result of FPE analysis, determines equation of OLS regression in VAR model applying backward method. Backward method purposes to eliminate variable that is not significant based on OLS and to exclude in VAR model.

VAR model above is called unrestricted model that has been simplified. Backward method only is used in unrestricted model. For other regressions, used OLS applies selection method of enter. With using unrestricted model, hypothesis of non-causality Granger:

will be tested.

2.From unrestricted model, form of restricted VAR model as following:

Variable that is included into restricted model is equal with included into unrestricted model. OLS results with backward method. In this restricted model, takes residual.3.Regression each of variables that correspond with to all of variables are corresponding with.

, for some j.Takes for some j. Notes, independent variable of and are took from VAR unrestricted model on first step.

4.Creates new variable, called a, with , for some j.5.Regressing constant 1 to all of variables that are obtained from fourth step, without using intercept constant in regression equation. Takes is sum of squared error that is obtained from this regression.

6.Calculates based on Woolridge (2000). T is total of observations that are analyzed. Under, LM distributes chi-square with degree freedom q that is total of variables in simplified unrestricted VAR model. Thus, can be calculated using Microsoft Excel. Statistic function of Excel that is used to calculate is CHIDIST (LM,q). 7.Hypothesis of non-causality Granger is rejected on level of significant if < .

Step of 1-7 are implemented in all of couple of variables in this research that examines linkage Granger causality. 3.5.2 Error Correction Model by Two Step Engle-GrangerError correction model is used to examine whether relationship between stock markets and exchange rate has short term. It means that the expectation from economic analyst is not same with exist truly. So to repair this problem is needed the model which corrects error in disequilibrium is called as Error Correction Model (ECM).For instance, interaction between Y and X Variables that is. If Y has equilibrium spot to X Variable, equilibrium between two variables X and Y can be fulfilled based above equation. But in economic, generally equilibrium is seldom to be found. If has value which is different with equilibrium value, difference left and right sides are. This difference is called as disequilibrium error. Thus if is null, surely Y and X have equilibrium condition.

Because Y and X Variables are seldom in equilibrium condition, they will only do observation of short term relationship with including lag Y and lag X. To describe this problem, we have an equation that is

0