Consider the monthly log stock returns, in percentages and including dividends, of Merck & Company, Johnson & Johnson, General Electric, General Motors, Ford Motor Company, and value-weighted index from January 1960 to December 2008; see the file m-mrk2vw.txt.

(a) Compute the sample mean, covariance matrix, and correlation matrix of the data.

(b) Test the hypothesis \(H_{0}: ho_{1}=\cdots=ho_{6}=\mathbf{0}\), where \(\boldsymbol{ho}_{i}\) is the lag- \(i\) crosscorrelation matrix of the data. Draw conclusions based on the \(5 \%\) significance level.

(c) Is there any lead-lag relationship among the six return series?