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Large Scale Conditional Covariance Matrix Modeling, Estimation and Testing

18 Pages Posted: 7 Nov 2008  

Zhuanxin Ding

Russell Investments

Robert F. Engle

New York University - Leonard N. Stern School of Business - Department of Economics; New York University (NYU) - Department of Finance; National Bureau of Economic Research (NBER)

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Date Written: May 2001

Abstract

A new representation of the diagonal Vech model is given using the Hadamard product. Sufficient conditions on parameter matrices are provided to ensure the positive definiteness of covariance matrices from the new representation. Based on this, some new and simple models are discussed. A set of diagnostic tests for multivariate ARCH models is proposed. The tests are able to detect various model misspecifications by examing the orthogonality of the squared normalized residuals. A small Monte-Carlo study is carried out to check the small sample performance of the test. An empirical example is also given as guidance for model estimation and selection in the multivariate framework. For the specific data set considered, it is found that the simple one and two parameter models and the constant conditional correlation model perform fairly well.

Keywords: conditional covariance, Multivariate ARCH, Hadamard product, M-test

Suggested Citation

Ding, Zhuanxin and Engle, Robert F., Large Scale Conditional Covariance Matrix Modeling, Estimation and Testing (May 2001). NYU Working Paper No. S-DRP-01-07. Available at SSRN: https://ssrn.com/abstract=1296437

Zhuanxin Ding

Russell Investments

909 A Street
Tacoma, WA 98402
United States

Robert F. Engle

New York University - Leonard N. Stern School of Business - Department of Economics ( email )

269 Mercer Street
New York, NY 10003
United States

New York University (NYU) - Department of Finance

Stern School of Business
44 West 4th Street
New York, NY 10012-1126
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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