(a). Estimate the model to predict the exchange rate. How much of the variation in the exchange rate is explained by your model? Is this statistically significant?
(b). Test to see whether the intercept is required in your model.
(c). Obtain a graph of the residuals against the independent variable for part (b).
(d). Is there any evidence of problems? Test to see if the errors are autocorrelated. If autocorrelation is present, suggest possible reasons why. Try to correct it by including the appropriate number of autoregressive moving average (ARMA) terms.
(e). Test to see if the errors are heteroscedastic. If it is present, obtain an improved set of estimates for the t-statistics.
(f). Test to see if the errors are normally distributed. Based on the results of the three tests you have carried out, how reliable do you think the estimation and test statistics are?
(g). Now estimate a new Multiple Regression Model that uses all of the variables, as well as your original PREDICTOR variable. That is
(h). Identify the coefficients with large p-values. Eliminate the variable with the largest p-value, and re-estimate the new equation. Repeat this procedure until the only variables left in the model have coefficients for which the p-value is less than a = 0.05. Show the output for this final model (This is called the 'top-down' approach).
(i). Use the F-test for redundant variables to determine whether the joint impact of all the variables that you have excluded is significant.
(j). Based on the results of part (i), and any other tests you think are necessary, choose a model you think contains all the relevant variables.
(k). Obtain a set of (static) forecasts for the Australian dollar exchange rate. Asses the quality of your forecasts using the various error measures generated when you made your forecasts.
(l). Write a brief report discussing your results. You should comment on the reliability of your estimation and test procedures, the variables that are most important in explaining the exchange rate, and how well your model predicts the exchange rate.