Correlation Matrices of yields and Total Positivity
AbstractIt has been empirically observed that correlation matrices of forward interest rates have the first three eigenvalues which are simple and their corresponding eigenvectors, termed as shift, slope and curvature respectively, with elements presenting changes of sign in a regular way. These spectral properties are very similar to those exhibited by Strictly Totally Positive and Oscillatory matrices. In the present paper we investigate how these spectral properties are related with those characterizing the correlation matrices considered, i.e. the positivity and the monotonicity of their elements. On the basis of these relations we prove the simplicity of the first two eigenvalues and provide an estimate of the second one.
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Bibliographic InfoPaper provided by SEMEQ Department - Faculty of Economics - University of Eastern Piedmont in its series Working Papers with number 109.
Date of creation: Nov 2005
Date of revision:
Forward rates; Correlation matrices; Principal Component Analysis; Total Positivity;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-12-09 (All new papers)
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