MA3518: Applied Statistics Page 1
Department of Mathematics
Faculty of Science and Engineering
City University of Hong Kong
MA 3518: Applied Statistics
Assignment 1
Question 1: Consider the following data set containing the daily close values for a market portfolio:
Date / Close14 Sep 03 / 918.63
15 Sep 03 / 814.81
16 Sep 03 / 829.32
17 Sep 03 / 925.97
18 Sep 03 / 1018.38
19 Sep 03 / 1033.16
22 Sep 03 / 1012.12
23 Sep 03 / 1033.03
24 Sep 03 / 889.38
25 Sep 03 / 906.27
(a) Create a SAS data set with name ‘Portfolio’ using the ‘CARDS’ command and print it on the SAS Output Window
(b) Print the mean, the standard deviation and 95% confidence interval for the mean of the data on the SAS Output Window
(c) Compute the skewness and the excess kurtosis of the data and comment on the degree of symmetry and the tail behavior of the distribution for the data
(5 marks)
Question 2: Consider the following data set containing the daily open, high, low, close values and trading volumes of NASDAQ from 22 Sep 03 to 3 Oct 03 (Data Source: Yahoo Finance) :
Date / Open / High / Low / Close / Volume3-Oct-03 / 1864.54 / 1891.62 / 1864.54 / 1880.57 / 20145800
2-Oct-03 / 1828.94 / 1842.55 / 1823.64 / 1836.22 / 16040900
1-Oct-03 / 1797.07 / 1832.25 / 1796.09 / 1832.25 / 18217400
30-Sep-03 / 1812.81 / 1812.81 / 1783.46 / 1786.94 / 18642400
29-Sep-03 / 1801.55 / 1824.59 / 1786.57 / 1824.56 / 16669300
26-Sep-03 / 1816.75 / 1821.57 / 1792.06 / 1792.07 / 18415300
25-Sep-03 / 1849.39 / 1856.22 / 1817.20 / 1817.24 / 20330600
24-Sep-03 / 1903.81 / 1904.13 / 1843.43 / 1843.70 / 22079700
23-Sep-03 / 1877.44 / 1901.73 / 1875.15 / 1901.72 / 18688000
22-Sep-03 / 1881.42 / 1881.42 / 1866.88 / 1874.62 / 17200800
(a) Create a SAS data set with name ‘NASDAQ’ using the ‘CARDS’ command and print the first ten observations of the data
(b) Display the descriptive statistics for each of the variables ‘Open’, ‘High’, ‘Low’ ‘Close’ and Comment on the degree of symmetry and the tail behavior of the distribution for each of the variables
(c) Suppose o and c denote the average daily open values and the average daily close values for the Index, respectively. Perform a paired-t test on the hypotheses H0: o = c against H1: o c at 5% significance level
(5 marks)
Question 3: Consider the following data for the annual percentage returns from Portfolio A and Portfolio B
Portfolio A 8.5 10.3 12.1 8.6 7.3 11.3 12.1 11.6 10.8 8.6 8.2
Portfolio B 6.2 6.8 7.1 8.6 10.2 6.8 8.1 7.5 6.5 10.2 11.7
(a) Create a SAS data set called ‘Performance’ with variables A and B corresponding to the annual percentage returns from Portfolio A and Portfolio B, respectively
(b) Perform a statistical test for the hypothesis that there is no difference in the means of the annual percentage returns from the two portfolios at 5% significance level
(5 marks)
Question 4:
Download a data set containing the daily high, low and close values for S&P500 Index from 27 February 1993 to 27 February 1997 (Remember to quote the source of the data set) and import the data set directly to the SAS work library.
(a) Fit a simple linear regression model for predicting the daily squared returns of the Index from its daily ranges and write down the fitted regression model
(b) Does the regression model fit the data well based on the value of the coefficient of determination?
(c) Perform a F-test for the full model and a t-test for each of the individual parameters at 5% significance level
(5 marks)
Question 5:
Download a data set containing the daily high, low, close values and trading volumes for S&P500 Index from 27 February 1995 to 27 February 2003 (Remember to quote the source of the data set) and import the data set directly to the SAS work library.
(d) Fit a multiple linear regression model for predicting the daily squared returns for the Index from its daily logarithmic returns, daily price ranges and its daily trading volumes and write down the fitted regression model
(e) Does the regression model fit the data well based on the value of the coefficient of determination?
(f) Perform a F-test for the full model and a t-test for each of the individual effects at 5% significance level
(5 marks)
~ End of Assignment 1~