Income Ratio

QUESTION 1
(a) Plot c t and y t over time on the same graph and describe both variables’ main feature(s).
(b) Based on a maximum lag of eight, use VARselect (as in tutorial 10) to choose an appropriate lag length for a VAR model for c t and y t . Report the chosen lag length.
(c) (*) Write out in equation form your chosen estimated equation for c t from (b) above.
(d) Does the residual correlogram (autocorrelation function) suggest that your chosen equation for c t constitutes a valid forecasting model, and why (or why not)?
(e) Use your estimated equation for c t to forecast log consumption two periods ahead. Report these forecasts.
QUESTION 2
(a) Generate the new variable, r t = c t − y t , which is the log of the consumption to income ratio. Plot r t over time and describe its main feature(s).
(b) Using a maximum lag of eight, test for a unit root in each of c t , y t , r t , ∆c t , ∆y t and ∆r t. For each variable, report the p-value for the unit root test and draw an appropriate conclusion.
(c) Based on the results obtained in (b) above, which variables are stationary, and which are nonstationary, and why?
(d) (*) Based on the CADFtest input and ADF test output for r t , estimate the regression used to test r t for a unit root directly (i.e., using dynlm), and write out your results in equation form.
(e) Based on all the results from this question, explain the difficulty of specifying an appropriate bivariate time series model for c t and y t .