Suppose that a researcher has observations on the log stock price indexes of Korea (kt), Japan (jt) and Singapore (st). 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 y3t and it is I(0). (i) Suppose the researcher estimates the following regression by OLS: st=0+1jt+ut and finds that the autocorrelation function of the estimated residuals has the value of 0.5 at lag one and thereafter declines towards zero. How would you describe the movement of st and jt over time relative to one another? Explain your answer fully. (1 mark). Would you recommend the researcher estimate the regression st=0+1jt+ut as well? Justify your answer. (1 mark) (ii) Suppose the researcher estimates the following regression by OLS: kt=0+1jt+ut and finds that the autocorrelation function of the estimated residuals is indistinguishable from one at all lags. How would you describe the movement of kt and jt over time relative to one another? Explain your answer fully. (1 mark). Would you recommend the researcher estimate the regression kt=0+1jt+ut as well? Justify your answer. (1 mark) (iii) Suppose the researcher estimates the following regression by OLS: jt=0+1y3t+ut and finds the autocorrelation function of the estimated residuals. What pattern (if any) would you expect to see in the autocorrelation function of the estimated residuals? Justify your answer. (1 mark) Suppose that a researcher has observations on the log stock price indexes of Korea (kt), Japan (jt) and Singapore (st). 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 y3t and it is I(0). (i) Suppose the researcher estimates the following regression by OLS: st=0+1jt+ut and finds that the autocorrelation function of the estimated residuals has the value of 0.5 at lag one and thereafter declines towards zero. How would you describe the movement of st and jt over time relative to one another? Explain your answer fully. (1 mark). Would you recommend the researcher estimate the regression st=0+1jt+ut as well? Justify your answer. (1 mark) (ii) Suppose the researcher estimates the following regression by OLS: kt=0+1jt+ut and finds that the autocorrelation function of the estimated residuals is indistinguishable from one at all lags. How would you describe the movement of kt and jt over time relative to one another? Explain your answer fully. (1 mark). Would you recommend the researcher estimate the regression kt=0+1jt+ut as well? Justify your answer. (1 mark) (iii) Suppose the researcher estimates the following regression by OLS: jt=0+1y3t+ut and finds the autocorrelation function of the estimated residuals. What pattern (if any) would you expect to see in the autocorrelation function of the estimated residuals? Justify your answer. (1 mark)
