Question 1

Suppose that a researcher has data on the log stock price indices of Korea (kt), Japan (j t) and Singapore (st). Assume that kt, j t and st are non-stationary time

series.

1. (i)The researcher would like to test for cointegration between the Korean and
2. Japanese stock markets. Describe how the researcher would perform this test. Be sure to state the null and alternative hypothesis, and what you conclude if you reject the null hypothesis (For your information, the ADF 5% critical value is -2.891 and the Engle-Granger 5% critical value is -3.398). (3 marks)
3. (ii)Suppose the researcher estimated the following regression: K = P0 +M +ut
4. The autocorrelation function of the estimated residuals (ut) was approximately one for all lags. Can reliable inferences be drawn from this
5. regression? Explain your answer. (2 marks)

(b) You estimated the following AR(2) model for some time series: yt=.5+L3y-1-.4yt-2 +ut

1. (i)Is the AR(2) model stationary? Justify your answer. (2 marks)
2. (ii)Obtain an expression for the two-step ahead forecast for the series,
3. conditional on time t information i.e. find an expression for E(yt+21 Qt) where Qt is the information set at time t which includes observations on the y series
4. dated t and earlier. (2 marks)
5. (iii)Using the expression you derived in part (ii), what is the two-step ahead
6. forecast, given that yt = 0.5 and yt-1 = 1.0. (1 mark)