Question 3 (a) Suppose that Yt follows the moving average process Yt = ut +0.3ut-2, = where errors ut are independent an

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Question 3 A Suppose That Yt Follows The Moving Average Process Yt Ut 0 3ut 2 Where Errors Ut Are Independent An 1 (342.84 KiB) Viewed 25 times

Question 3 (a) Suppose that Yt follows the moving average process Yt = ut +0.3ut-2, = where errors ut are independent and identically distributed with E (ut) = 0 and var (u) = 0.4. Compute the mean, variance and the first three autocovariances of Yt. (6 marks) (b) Suppose the time series Y follows the random walk model and suppose we observe sample Y₁,..., Y. Write down the model. What is the best forecast of YT+1 given the observed data? (3 marks) (c) In order to determine whether the US unemployment time series contains a unit root, the following regression has been estimated by OLS for quarterly data from 1965 to 2005, AUS Unempt = 0.21 0.038US Unempt-1+0.64AUS Unempt-1, (0.08) (0.013) (0.06) R² = 0.41, where the number of lags was selected using the Bayes information criterion (BIC). The values in parentheses are the standard errors of coefficient estimates. Does the series US Unempt have a unit root? Explain your answer. (5 marks) (d) In order to determine whether the Japanese GDP time series contains a unit root, the following regression has been estimated by OLS for quarterly data from 1965 to 2005, A ln (Japanese GDPt) = 0.014 0.00031t (0.026) (0.00006) +0.0031 In (Japanese GDPt-1), (0.0026) R² = 0.47, where the values in parentheses are the standard errors of coefficient estimates. Does the series In (Japanese GDPt) have a unit root? Ex- plain your answer. (5 marks) (e) A regression of US unemployment on Japanese GDP was estimated by OLS for quarterly data from 1965 to 2005, US Unempt = 2.69 +0.27 In (Japanese GDPt), R² = 0.05. (0.81) (0.07)
Is the coefficient on Japanese GDP statistically significant? What is the conclusion about the relationship between US unemployment and Japanese GDP? How would you explain this phenomenon? (6 marks)