Suppose that a researcher has observations on the log stock price indexes of Korea (), Japan () and Singapore (). Each stock price index series is I(1). The researcher also has data on the yield to maturity of 3-month US treasury bills. The series is denoted 3 and it is I(0).
o) Suppose P1t is the stock price index for country 1 and P2t is the stock price index for country 2 . The researcher believes that the stock price indexes are determined as: P1t=P1t1+tP2t=0.5P1t+vt where t and vt are white noise. (i) Does the researcher believe that P1t and P2t are, respectively, I(1) series? Justify your answer. (1 mark) (ii) Does the researcher expect that P1t and P2t are cointegrated with each other? Justify your answer. (1 mark) (iii) The researcher obtains data on the two stock price indexes (i.e., on P1t and P2t ) and decides to test whether there is a cointegrating relationship between them using the method of Engle and Granger. For this method, write down the null and alternative hypotheses, the ADF regression with one lag, the test statistic and the decision rule using a 5% significance level. (2 marks) (For your information, the 5% ADF critical value is 2.861 and the 5% Engle-Granger critical value is 3.398 ). (iv) The test statistic was found to be 2.98. What do you conclude? Are the researcher's beliefs justified? (1 mark) o) Suppose P1t is the stock price index for country 1 and P2t is the stock price index for country 2 . The researcher believes that the stock price indexes are determined as: P1t=P1t1+tP2t=0.5P1t+vt where t and vt are white noise. (i) Does the researcher believe that P1t and P2t are, respectively, I(1) series? Justify your answer. (1 mark) (ii) Does the researcher expect that P1t and P2t are cointegrated with each other? Justify your answer. (1 mark) (iii) The researcher obtains data on the two stock price indexes (i.e., on P1t and P2t ) and decides to test whether there is a cointegrating relationship between them using the method of Engle and Granger. For this method, write down the null and alternative hypotheses, the ADF regression with one lag, the test statistic and the decision rule using a 5% significance level. (2 marks) (For your information, the 5% ADF critical value is 2.861 and the 5% Engle-Granger critical value is 3.398 ). (iv) The test statistic was found to be 2.98. What do you conclude? Are the researcher's beliefs justified? (1 mark)
