The Score of Conditionally Heteroskedastic Dynamic Regression Models with Student T Innovations, and an Lm Test for Multivariate Normality

CEMFI Working Paper No. 0007

Posted: 17 Jan 2001

See all articles by Enrique Sentana

Enrique Sentana

Centro de Estudios Monetarios y Financieros (CEMFI); Financial Markets Group; Centre for Economic Policy Research (CEPR)

Gabriele Fiorentini

Universita di Firenze - Dipartimento di Statistica

Giorgio Calzolari

Universita di Firenze - Dipartimento di Statistica

Date Written: July 2000

Abstract

We provide numerically reliable analytical expressions for the score of conditionally heteroskedastic dynamic regression models when the conditional distribution is multivariate t. We also derive one-sided and two-sided LM tests for multivariate normality versus multivariate t based on the first two moments of the (squared) norm of the standardised innovations evaluated at the Gaussian quasi-ML estimators of the conditional mean and variance parameters. We reinterpret them as specification tests for multivariate excess kurtosis, and show that they have power against leptokurtic alternatives. Finally, we analyse UK stock returns, and confirm that their conditional distribution has fat tails.

Keywords: Kurtosis, Inequality Constraints, ARCH, Financial Returns.

JEL Classification: C51, C52

Suggested Citation

Sentana, Enrique and Fiorentini, Gabriele and Calzolari, Giorgio, The Score of Conditionally Heteroskedastic Dynamic Regression Models with Student T Innovations, and an Lm Test for Multivariate Normality (July 2000). CEMFI Working Paper No. 0007. Available at SSRN: https://ssrn.com/abstract=256129

Enrique Sentana (Contact Author)

Centro de Estudios Monetarios y Financieros (CEMFI) ( email )

Casado del Alisal 5
28014 Madrid
Spain
+34 91 429 0551 (Phone)
+34 91 429 1056 (Fax)

HOME PAGE: http://www.cemfi.es/~sentana/

Financial Markets Group

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London School of Economics & Political Science (LSE)
London WC2A 2AE
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+44 20 7852 3580 (Fax)

Centre for Economic Policy Research (CEPR)

London
United Kingdom

Gabriele Fiorentini

Universita di Firenze - Dipartimento di Statistica ( email )

Viale Morgagni, 59
50134 Firenze
Italy
+39 055 4237 274 (Phone)
+39 055 4223 560 (Fax)

Giorgio Calzolari

Universita di Firenze - Dipartimento di Statistica ( email )

Viale Morgagni, 59
50134 Firenze
Italy
+39 055 4237 217 (Phone)
+39 055 4223 560 (Fax)

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