According to the data downloaded from the website, it involved some information about the all ordinaries index. For instance, it covered the date, open, high, low, close, and volume and adjust close. In the question, it defined date 1 as the first trading day of the study period. Date 0 which is one day before the first trading day Date 1. First of all, using excel to set up the time index column to arrange the date of the trading day. The range of the data is from date 0 to 1087. In order to calculate the daily return for the all ordinaries index, the formula could be used.
is the return for each day, stands for the all ordinaries index at a specific date t and is the data of the all ordinaries index that one day before the date t. In addition, the adjust close is the appropriate data selected to calculate the daily returns. Referring back to the given data, the daily return for date 0 could not be computed since the data of adjust close before date 0 is unavailable. Therefore, the daily return will be calculated from date 1 to 1087. For example, the daily return on date 1 can be calculated as following: R1= = = -0.10%.
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The descriptive statistics data of the daily return that calculated by excel are following: Mean 0. 04% Standard Error 0. 03% Median 0. 08% Mode -0. 16% Standard Deviation 0. 010444 Sample Variance 0. 000109 Kurtosis 1. 102023 Skewness -0. 23502 Range 0. 077052 Minimum -0. 04209 Maximum 0. 034966 Sum 0. 4047 Count 1087 Among all the 1087 date, the returns of all ordinaries index have the mean of 0. 04%, median of 0. 03% and the most frequent data of -0. 16%. Also, the range of these returns is 0. 077052. The maximum and minimum return of all ordinaries index are 0.034966 and -0. 04209 respectively. The descriptive statistics data of the daily return can form a histogram through the excel as well. Display like following: Task 2 Basing on the question, the data has been divided into two separate groups. The first group contains all the positive daily return Rt of all ordinaries index. On the other hand, the second group is made up of all the negative returns. As a result of the two groups of data, it is obvious that the two sample hypothesis test should be chosen to perform the statistical test.
The t- test is chosen to perform the two sample hypothesis test because the population standard deviation is unavailable. Additionally, because of the changeable variances, choosing unequal variance is more suitable. Moreover, it is essential to calculate the sample mean and sample standard deviation of these two groups of data before the statistical test. According to the excel result, the sample means of group1 and group2 are 1169918868 and 1144404303 respectively. On the other side, the sample standard deviations are 357047870.
To compute the 90% prediction interval for all trading days during the study period, the formula ( , ) can be used. Referring to the question equals 0. 1 and equals 0. 05. Task 4 In conclusion, the returns of the all ordinaries index are not very good during the study period. Furthermore, it seems unlikely that the variations of the time index will have any impact on the change of the all ordinaries index. Nevertheless, the prediction of the all ordinaries index are almost not influencing by the variation of the time index.