Toeplitz Approximation to Empirical Correlation Matrix of Asset Returns: A Signal Processing Perspective

IEEE Journal of Selected Topics in Signal Processing, Vol. 6, Number 4, pp. 319-326, August 2012

8 Pages Posted: 22 Jul 2012 Last revised: 1 Dec 2015

See all articles by Ali Akansu

Ali Akansu

New Jersey Institute of Technology

Mustafa Torun

New Jersey Institute of Technology

Date Written: 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.

Keywords: Karhunen-Loeve transform, discrete cosine transform, AR(1) model, empirical correlation matrix, portfolio management, risk management

Suggested Citation

Akansu, Ali and Torun, Mustafa, Toeplitz Approximation to Empirical Correlation Matrix of Asset Returns: A Signal Processing Perspective (2012). IEEE Journal of Selected Topics in Signal Processing, Vol. 6, Number 4, pp. 319-326, August 2012, Available at SSRN: https://ssrn.com/abstract=2114835

Ali Akansu (Contact Author)

New Jersey Institute of Technology ( email )

University Heights
Newark, NJ 07102
United States

Mustafa Torun

New Jersey Institute of Technology ( email )

University Heights
Newark, NJ 07102
United States

HOME PAGE: http://web.njit.edu/~umt2

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