On toeplitz approximation to empirical correlation matrix of financial asset returns

Ali N. Akansu; Mustafa U. Torun

doi:10.1109/CISS.2012.6310806

On toeplitz approximation to empirical correlation matrix of financial asset returns

Ali N. Akansu, Mustafa U. Torun

Electrical and Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

3 Scopus citations

Abstract

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.

Original language	English (US)
Title of host publication	2012 46th Annual Conference on Information Sciences and Systems, CISS 2012
DOIs	https://doi.org/10.1109/CISS.2012.6310806
State	Published - 2012
Event	2012 46th Annual Conference on Information Sciences and Systems, CISS 2012 - Princeton, NJ, United States Duration: Mar 21 2012 → Mar 23 2012

Publication series

Name	2012 46th Annual Conference on Information Sciences and Systems, CISS 2012

Other

Other	2012 46th Annual Conference on Information Sciences and Systems, CISS 2012
Country/Territory	United States
City	Princeton, NJ
Period	3/21/12 → 3/23/12

All Science Journal Classification (ASJC) codes

Information Systems

Keywords

AR(1) model
Discrete cosine transform
Empirical correlation matrix
Karhunen-Loeve transform
Risk management

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10.1109/CISS.2012.6310806

Cite this

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title = "On toeplitz approximation to empirical correlation matrix of financial asset returns",

abstract = "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.",

keywords = "AR(1) model, Discrete cosine transform, Empirical correlation matrix, Karhunen-Loeve transform, Risk management",

author = "Akansu, {Ali N.} and Torun, {Mustafa U.}",

year = "2012",

doi = "10.1109/CISS.2012.6310806",

language = "English (US)",

isbn = "9781467331401",

series = "2012 46th Annual Conference on Information Sciences and Systems, CISS 2012",

booktitle = "2012 46th Annual Conference on Information Sciences and Systems, CISS 2012",

note = "2012 46th Annual Conference on Information Sciences and Systems, CISS 2012 ; Conference date: 21-03-2012 Through 23-03-2012",

}

Akansu, AN & Torun, MU 2012, On toeplitz approximation to empirical correlation matrix of financial asset returns. in 2012 46th Annual Conference on Information Sciences and Systems, CISS 2012., 6310806, 2012 46th Annual Conference on Information Sciences and Systems, CISS 2012, 2012 46th Annual Conference on Information Sciences and Systems, CISS 2012, Princeton, NJ, United States, 3/21/12. https://doi.org/10.1109/CISS.2012.6310806

On toeplitz approximation to empirical correlation matrix of financial asset returns. / Akansu, Ali N.; Torun, Mustafa U.
2012 46th Annual Conference on Information Sciences and Systems, CISS 2012. 2012. 6310806 (2012 46th Annual Conference on Information Sciences and Systems, CISS 2012).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - On toeplitz approximation to empirical correlation matrix of financial asset returns

AU - Akansu, Ali N.

AU - Torun, Mustafa U.

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - AR(1) model

KW - Discrete cosine transform

KW - Empirical correlation matrix

KW - Karhunen-Loeve transform

KW - Risk management

UR - http://www.scopus.com/inward/record.url?scp=84868517240&partnerID=8YFLogxK

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U2 - 10.1109/CISS.2012.6310806

DO - 10.1109/CISS.2012.6310806

M3 - Conference contribution

AN - SCOPUS:84868517240

SN - 9781467331401

T3 - 2012 46th Annual Conference on Information Sciences and Systems, CISS 2012

BT - 2012 46th Annual Conference on Information Sciences and Systems, CISS 2012

T2 - 2012 46th Annual Conference on Information Sciences and Systems, CISS 2012

Y2 - 21 March 2012 through 23 March 2012

ER -

On toeplitz approximation to empirical correlation matrix of financial asset returns

Abstract

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All Science Journal Classification (ASJC) codes

Keywords

Access to Document

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