Homework 2

 

The data is available here in Matlab and as a text file. Save the data file into a directory, say C:\bus810. The commands to load the data are then:

>> cd c:\bus810

>> load usbondret.mat

If you want to do some analysis in Excel, just import the data using the text file.

 

There are five columns of 510 rows each. The data starts on January 8, 1990 and continues till October 11, 1999.

 

The Matlab file includes a variable “usbondretdates” which is the datenumber (utterly meaningless). You can find out the date using the command:

>> datestr(usbondretdates)

If you want the date in readable form for the 25th observation, type the command

>> datestr(usbondretdates(25))

 

The commands to compute:

The covariance matrix of the data from rows 100 to 205 is:

>> CovMat=cov(usbondret(100:205,:))

 

CovMat =

 

  1.0e-003 *

 

    0.0056    0.0115    0.0142    0.0160    0.0181

    0.0115    0.0254    0.0322    0.0371    0.0429

    0.0142    0.0322    0.0423    0.0502    0.0600

    0.0160    0.0371    0.0502    0.0624    0.0779

    0.0181    0.0429    0.0600    0.0779    0.1094

 

The eigenvalues and eigenvectors of this coviance matrix:

>> [EigMat,EigVec]=eig(CovMat)

 

EigMat =

 

    0.3802   -0.7259   -0.4810    0.2820    0.1329

   -0.6525    0.1971   -0.4332    0.5034    0.3072

    0.6143    0.4988    0.1037    0.4368    0.4151

   -0.2280   -0.4246    0.6915    0.1505    0.5167

    0.0190    0.0721   -0.3035   -0.6735    0.6699

 

 

EigVec =

 

  1.0e-003 *

 

    0.0001         0         0         0         0

         0    0.0003         0         0         0

         0         0    0.0014         0         0

         0         0         0    0.0134         0

         0         0         0         0    0.2300

 

If you want to use the princomp.m file, I have posted it online here (ssh!).