a. Estimate the following model, C_{t} _{ }= β_{0} + β_{1} * DI_{t} + ε_{t}
Where
C_{t} = Aggregate Consumption Expenditure in Australia, quarterly data for the period 1985:1 - 2005:2
DI_{t} = Disposable Income in Australia, quarterly data for the period 1985:1 - 2005:2 and write down your results in full reporting mode.
b. Since you are using time-series data, you want to check for the existence of Serial Correlation. Use the estimated residuals to calculate the Durbin-Watson d-statistic and make an assessment about the existence of serial correlation on the basis of it.
c. Plot a scatter graph of the residuals from your equation in (a) above against time to visually verify the existence of serial correlation.
d. Assuming that you have proof of positive serial correlation, calculate the estimated rho directly from the DW d-statistic.
e. Use the Cochrane-Orcutt method to estimate rho and write your results in reporting mode.
f. Apply the rho you have estimated in (c) above to correct your data and run a Generalized Least Squares Regression. Show the formulation of the model and write down your results.
g. Calculate the residuals from (e) above and re-estimate the DW d-statistic. Report your conclusions.
h. Compare the equation from (a) or (e) above. Which of the two models do you prefer? Explain.