CHAPTER III METHODOLOGY 3.1 Description In this chapter, the calculation steps, which will be done in the analysis section, will be explained. The theoretical foundations and literature reviews are already explained in Chapter II. The explanation started from the data collection method, and ended in the calculation to achieve the result. 3.2. Data Collection Data on this research is taken based on the criteria that the stock used in this observation has more than one period to be traded at lower limit of trading price in the observation period from finance.yahoo.com at 27/6/2012. The closing time is 4.00 PM GMT +7, and the closing price is based on the last transaction price in the given day. 3.3 Calculation Methodology Below are the calculation methodology used on this report. The calculation will start with gap analysis and linear interpolation on the stock price, and end with back-testing of the portfolio on the given trading strategy. 15
16 Figure 3.1 Calculation Step
3.3.1 Return Calculation Return of the data is calculated using continuous compounded return based on equation (2.2). This method is used since the characteristic of the financial assets, which is fluctuated over the time and not directly observable in the data, which only containing the closing price. Another reason in using geometric rate of return is the time difference between the markets closing bell. In order to minimize the problems above, continuous compounded return is give more accurate measurements compared to arithmetic return. The calculation in this section will be calculated in Eviews 7 software. 3.3.2 Descriptive statistics and Visual Observation Descriptive statistics and Visual Observation helps the observant to get the basic information of the data characteristics, such as trend, distribution characteristic, and prejudgment of stationarity and heteroskedasticity of the data. The calculation and graph in this section will be calculated and plotted in Eviews 7 software. 3.3.3 Augmented Dickey-Fuller Test As one of the method to detect the stationarity, Augmented Dickey-Fuller test is essential to detect the stationarity of the data, which is based on the result of the test, as explained in Chapter II section 2.1.7. The critical value, which will be used as the decision criterion is 5%. The data is stationer if the result of t-statistic value is smaller than the t-statistic value of 5%. Eviews7 software will be use to test the Augmented Dickey-Fuller. 3.3.4 Heteroskedasticity Test Classical linear regression is based on the assumption that the data is homoskedastic. Because of that reason, test of heteroskedasticity is one of the crucial points for meeting the criteria of classical linear regression. To detect the heteroskedasticity, White Heteroskedasticity test as explained in Chapter II section 2.1.6 is used. The data is heteroskedastic if the test result is below the probability value of the F-statistic and R- squared is below the critical value, which is 5%. All of the calculation in this section will be done in Eviews 7 software. 17
3.3.5 Autocorrelation Other criteria for the classical linear regression are the independency of the data. To test the independency of the data, Ljung-Box probability value and visual observation from the correlogram can help to detect the correlation of the data, which is a sign of the dependency of the data with the data from past period. The method of calculation is already explained in Chapter II section 2.1.5. The data has an autocorrelation if the Ljung-Box test statistic probability is less than critical value, which is 5%. The calculation and graph will be done in Eviews 7 software. 3.3.6 GARCH Model Building Based on the information from the previous test, a normal GARCH model for the data is selected. Significant autocorrelation on the model is also taken into account in deciding the model. Model selection is based on several criteria listed below based on the priority of the criteria: 1. The model is statistically significant 2. No autocorrelation in the residual 3. Residual is homoskedastic 4. If several model are fitted with the criteria above, the model is chosen based on AIC and BIC ratio as explained in Chapter II section 2.1.11 5. Simplicity of the model The calculation and model building in this section will be done in Eviews 7 software and based on the look-likelihood function. 3.3.7 Residual Analysis After the model is built, and the coefficient is significant, the remaining residual should be checked. ARCH-LM test, as a tool to check the heteroskedasticity is being used, with 5% rejection criteria. The residual is also being tested in order to make sure that there are no remaining autocorrelation in the residual. 18
3.3.8 Critical Value Calculation Based on the conditional variance and forecasted return from GARCH model explained above, critical value is calculated based on equation (2.29) for normal distribution, and equation (2.30) for GARCH with t-student distribution. The degree of freedom is defined based on GARCH with t-student modification degree of freedom calculation result. 3.3.10 Model Back-Testing To obtain the result of the back testing, the comparison between the actual return and the critical value is compared. To obtain the result, below is the methodology, which are used to measure the back testing result 1. Count the number of observations, which are lower than the lower critical value, or higher than upper critical value. 2. Divide the result with the number of observation. 3. Compare the result from stage 2 to the given 1- confidence interval. 4. The model is under-confident if the result from stage 2 is higher than 1- confidence interval, and the model is over-confident if the result from stage 2 is lower than 1-confidence interval. 5. Calculate Z value based on equation (2.31) 6. Reject the model as the unbiased estimator if the calculated Z value excess Z value of 1-confidence interval divided by 2. 3.3.11 Portfolio Back-Testing To measure the indicator performance, back-testing on trading strategies is used. Below is the methodology to obtain the result of back-testing. 1. Calculate the indicator of buying and selling point for each of the trading strategies 2. Calculate actual return produced by the portfolio by equation (2.2) 19
There are several assumptions in back-testing on the trading strategies in this research, which are: 1. There are no trading commission and fee for each of transactions. 2. Jakarta Stock Exchange is being used as a benchmark of portfolio. 3. The closing price and the next opening price is the same. 4. Back-testing assumes that the researcher is being able to buy and sell at the next day opening price of the buying and selling signal. 20