Correlation Matrices of yields and Total Positivity

Ernesto Salinelli () and Carlo Sgarra ()
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Carlo Sgarra: SEMEQ Department - Faculty of Economics - University of Eastern Piedmont

No 109, Working Papers from SEMEQ Department - Faculty of Economics - University of Eastern Piedmont

Abstract: It 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.

Keywords: Forward rates; Correlation matrices; Principal Component Analysis; Total Positivity (search for similar items in EconPapers)
Pages: 19
Date: 2005-11
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