Exercise Solution 9.8

  1. Using a spreadsheet, we calculate the determinant of as 0.000015.
  2. based upon the result of part (a), is conditionally multicollinear.
  3. We define ν as the matrix whose columns comprise the eigenvectors of  :




    where 1D is the eight-dimensional random vector of principal components of . It has mean 0 and diagonal covariance matrix whose diagonal elements are the eigenvalues of  :


    To construct our principal component remapping, we observe that the variances of the last two principal components of are small compared to the variances of the rest. We discard those two principal components, defining as the six-dimensional random vector comprising the first six principal components of . Then [s2] becomes


    where is a matrix comprising the first six columns of ν:


  4. The conditional mean vector and conditional covariance matrix of are obtained directly from the conditional mean vector and covariance matrix of 1D. Specifically, = 0, and


  5. With the addition of the principal component remapping, Schematic [9.54] becomes




Enter your address for insights that will transform your risk management.

Click the link in the email I just sent you to confirm your address and start your subscription.

Defining Risk

Enter your email address to receive your copy and subscribe to Glyn's Risk Management Newsletter.

Click the link in the email I just sent you to download your paper and start your subscription.