1 The tab-delimited text file C359A1S1Q2.txt contains daily stock prices for the Brazilian petroleum company Petrobras from 31 December 2008 to 31 December 2009. The data were obtained from yahoo finance.
a) Calculate the continuously compounded annual return for the Petrobras stock for 2009. Calculate the simple annual return for 2009.
b) Open the data in Eviews and generate the series of daily log returns. Calculate the sample mean, variance, skewness and kurtosis of the daily log returns. Comment on the results.
c) Explain the Jarque-Bera (J-B) test. Using this test, what conclusion can you make about the distribution of daily log returns? Is this result to be expected?
d) Explain the Ljung-Box Q*-test. Use the Ljung-Box Q* statistic to test the null hypothesis that there is no serial correlation in the daily log returns.
e) Square the daily log returns and then apply the Ljung-Box Q*-test to the squared daily log returns. Can you reject the null hypothesis of no serial correlation in squared daily log returns? Is this result to be expected?
2 The tab-delimited text file C359A1S1Q2.txt contains daily prices for the South Korean Stock Exchange Index (KOSPI) from 4/7/2006 (observation
1) to 11/6/2010 (observation 977). Although this is daily data, the data are presented as a sequence of 977 undated observations. The data were obtained from yahoo finance.
a) Build an AR/MA/ARMA model for the daily log returns, explaining the reasons for your choice of model specification. In your answer, present and explain the steps you take to develop the model; present and interpret the estimated model for the final specification you choose; and present and explain the results of any diagnostic testing you consider is appropriate.
b) Is Least Squares (LS) regression suitable for estimation of the model you obtain in Q2a? Explain your answer. If LS is not suitable, what estimation method do you suggest is suitable, and why?
c) Use the ARMA model to produce forecasts for the final 30 days of the sample for the process you obtain in Q2a. Evaluate the forecast performance of your model.
(Assignment Guidance: You will need to re-estimate the chosen model over a shorter estimation period, excluding the final 30 observations. Then use this estimated model to obtain forecasts for the forecasting sample of 30 days. In Eviews, please select the Option Dynamic in the forecast window).
Please ensure that your assignment is properly referenced. Further information on referencing (i.e. the Harvard system) is available in the Studying at a Distance textbook by Talbot and on the OSC: CeFIMS Quick Links/Student Support/Academic Honesty and Plagiarism/What is Plagiarism?