Use the data in VOLAT.RAW for this exercise.
(i) Confirm that Isp500 = log(sp500) and lip = log(ip) appear to contain unit roots. Use Dickey-Fuller tests with four lagged changes and do the tests with and without a linear time trend.
(ii) Run a simple regression of lsp500 on lip. Comment on the sizes of the I statistic and R-squared.
(iii) Use the residuals from part (ii) to test whether Isp500 and lip are co integrated. Use the standard Dickey-Fuller test and the ADF test with two lags. What do you conclude?
(iv) Add a linear time trend to the regression from part (ii) and now test for co integration using the same tests from part (iii).
(v) Does it appear that stock prices and real economic activity have a long-run equilibrium relationship?