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

Ali N. Akansu, Mustafa U. Torun

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


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.

Original languageEnglish (US)
Article number6218750
Pages (from-to)319-326
Number of pages8
JournalIEEE Journal on Selected Topics in Signal Processing
Issue number4
StatePublished - 2012

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Electrical and Electronic Engineering


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


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