Toeplitz approximation to empirical correlation matrix of asset returns: A signal processing perspective

Document Type

Article

Publication Date

7-27-2012

Abstract

Empirical correlation matrix of asset returns has its intrinsic noise component. Eigen decomposition, also called Karhunen-Loeve Transform (KLT), is employed for noise filtering where an identified subset of eigenvalues replaced by zero. The filtered correlation matrix is utilized for calculation of portfolio risk and rebalancing. We introduce Toeplitz approximation to symmetric empirical correlation matrix by using auto-regressive order one, AR(1), signal model. It leads us to an analytical framework where the corresponding eigenvalues and eigenvectors are defined in closed forms. Moreover, we show that discrete cosine transform (DCT) with implementation advantages provides comparable performance as a good approximation to KLT for processing the empirical correlation matrix of a portfolio with highly correlated assets. The energy packing of both transforms degrade for lower values of correlation coefficient. The theoretical reasoning for such a performance is presented. It is concluded that the proposed framework has a potential use for quantitative finance applications. © 2012 IEEE.

Identifier

84864153015 (Scopus)

Publication Title

IEEE Journal on Selected Topics in Signal Processing

External Full Text Location

https://doi.org/10.1109/JSTSP.2012.2204724

ISSN

19324553

First Page

319

Last Page

326

Issue

4

Volume

6

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