The file "m-spibmge.dat" contains the monthly log returns in percentages of S\&P 500 index, IBM stock, and General Electric stock from January 1926 to December 1999. The returns include dividends.

(a) Compute the sample mean, sample covariance matrix, and sample correlation matrix of the three return series.

(b) Compute the lag-1 and lag-2 cross-correlation matrixes of the three series. Draw inference concerning the linear relationships between the three series. Is there any lead-lag relation?

(c) Use the multivariate Ljung-Box statistics to test the null hypothesis that \(H_{0}\) : \(ho_{1}=\cdots=ho_{4}=\mathbf{0}\) at the \(5 \%\) significance level. Draw your conclusion.