On toeplitz approximation to empirical correlation matrix of financial asset returns

We present a Toeplitz approximation to symmetric empirical correlation matrix of asset returns by auto-regressive order one, AR(1), signal source modeling. AR(1) approximation provides an analytical framework where the corresponding eigenvalues and eigenvectors are defined in closed forms. Furthermore, we show discrete cosine transform (DCT) offers comparable performance to Karhunen-Loeve transform (KLT) for decomposition of empirical correlation matrix of a given portfolio where the first is significantly more efficient to implement. It is concluded that the proposed framework has a potential use for noise filtering and risk management in quantitative finance.