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To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.jeconom.2005.06.023 Byline: Hiroyuki Kawakatsu Abstract: I propose a new multivariate GARCH specification that maintains positive definiteness of the conditional covariance matrix. The idea is to specify the dynamics in the matrix logarithm of the conditional covariance. Because the matrix exponential transformation ensures positive definiteness, the dynamics can be specified without the positive definiteness constraint. This affords a variety of specifications and, in particular, we can specify element-by-element the dynamics of the matrix logarithm. I discuss specifications with leverage effects, estimation with multivariate Gaussian and t-distributions, and diagnostics that evaluate the appropriateness of the matrix exponential specification. Author Affiliation: School of Management and Economics, 25 University Square, Queen's University, Belfast, Belfast BT7 1NN, Northern Ireland

I propose a new multivariate GARCH specification that maintains positive definiteness of the conditional covariance matrix. The idea is to specify the dynamics in the matrix logarithm of the conditional covariance. Because the matrix exponential transformation ensures positive definiteness, the dynamics can be specified without the positive definiteness constraint. This affords a variety of specifications and, in particular, we can specify element-by-element the dynamics of the matrix logarithm. I discuss specifications with leverage effects, estimation with multivariate Gaussian and t-distributions, and diagnostics that evaluate the appropriateness of the matrix exponential specification. JEL classification: C32; C51 Keywords: Multivarate GARCH; Matrix exponential; Non-nested tests

Byline: Hiroyuki Kawakatsu (1) Keywords: characteristic function; numerical transform inversion; tail probability Abstract: The paper considers the problem of computing p-values of non-standard distributions for which the characteristic function is available in closed form. When the characteristic function is a multivalued complex function, the standard numerical inversion method needs to be used with care as the integrand may become discontinous due to branch cuts. An alternative inversion method based on the Gaver-Wynn-Rho algorithm is shown to be a general and effective solution to the discontinuity problem as it works with real-valued functions. The method is illustrated with two well-known time series tests with non-standard distributions. Author Affiliation: (1) School of Management and Economics, Queen's University, Belfast, 25 University Square, Belfast, BT7 1NN, Northern Ireland Article History: Registration Date: 06/12/2005 Received Date: 25/02/2005 Accepted Date: 04/12/2005 Online Date: 07/03/2006 Article note: JEL classification: C40 C12