a) Test for stationarity of each series, determine its order of integration and whether drift is present or not.
b) Test for cointegration of the variables in the model using the Engle and Granger (1987) approach.
c) Based on your cointegration and stationarity test results, is the bivariate model above still applicable to estimates the long-run relationship between the two variables? Justify, If the answer NO. if the answer is yes, give a justification and estimate the long run relationship and give a full interpretation of your results.
d) Based on your stationarity and cointegration results, is ECM applicable to assess both the short-run and long-term relationship between the two variables above. Justify if your answer is NO. If you answer is YES, estimate the appropriate ECM model and provide a comprehensive interpretation of your results.
e) Test for the model specification using the examination of residuals approach, Durbin-Watson d-statistic and Ramsey RESET test approach.
f) Assuming you were asked to add the exogenous-squared variable to the long-run model (model 1) above the reason being that the first model was under-fitted since the explanatory variable has a curve-linear (non-linear) effect on the dependent variable. Test for the exclusion of a crucial variable using the Lagrange Multiplier (LM) test.
g) Test for heteroscedasticity using:
i) Park test
ii) Koenker-Bassett (KB) test
iii) Breusch-Pagan-Godfrey (BPG) test
iv) Goldfeld-Quandt test
v) Spearman’s Rank Correlation test
vi) Glejser test
vii) White’s test
1) AR(1) process
2) Breusch-Goldfrey test
3) Runs test
4) Durbin-Watson d-test
i) Assuming the AR(1) process in h1) show that there is autocorrelation, apply the generalised least squares method to the estimated model using the from the AR(1) and correct the problem based on the results.