The data file shiller contains the stock market data in the book "Irrational Exuberance" by Robert Shiller. \({ }^{10}\) They comprise the monthly price and dividends of the S\&P Index (in logs) for the sample period 1871M1-2015M9. Finance theory suggests a long-run relationship between dividends and the stock price.

a. Plot each of the series. Do they appear to be moving together?

b. Carry out an empirical analysis to investigate whether there is evidence of a long-run relationship between the two series. Use a \(1 \%\) level of significance for all hypothesis tests.