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 1999; see the file "m-mrk2vw.dat," which has six columns in the order listed before.

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

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

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

(d) Perform a principal component analysis of the data using the sample covariance matrix.

(e) Perform a principal component analysis of the data using the sample correlation matrix.

(f) Perform a factor analysis on the data. Identify the number of common factors. Obtain estimates of factor loadings using both the principal component and maximum likelihood methods.