The data file name is “RATES.xls”, which is uploaded to Canvas along with this file. The variables in the file are labelled TBILL, R3 and R7, respectively. Explain the concepts of non-stationarity and cointegration, and how they are connected. Illustrate how one can test for cointegration using the two-step Engle and Granger approach.

[15%]

a) Test the variables to show that the rates all behave as unit root processes.

[5%]

b) Test for the long-run relationship using the two-step Engle and Granger cointegration approach applied to the following regression:

c) After determining whether or not Equation (1) is a cointegrating relationship, estimate the respective Error Correction Model (ECM). Perform appropriate diagnostic tests on the estimated ECM. Comment on your results.

[15%]

Notes: (i) Conduct all your statistical tests for this question at the 5% significance level, (ii) Perform unit root and cointegration tests by using the maximum lag length of 8 lags, explaining your approach to selecting the appropriate lag order for each test, and (iii) Support your discussion for this question with appropriate mathematical equations and references in the relevant area(s) of