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The tab-delimited text file 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?
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(b) Suppose that the initial conditions are as follows: y0 = 0 and et = 0 for t= 0. Impose the initial conditions in order to find the general solution.
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