Likelihood-Based Estimation of Latent Generalised Arch Structures

CEMFI Working Paper No. 0204

Posted: 22 Nov 2002

See all articles by Gabriele Fiorentini

Gabriele Fiorentini

Universita di Firenze - Dipartimento di Statistica

Enrique Sentana

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

Neil Shephard

Harvard University

Date Written: September 2002

Abstract

GARCH models are commonly used as latent processes in econometrics, financial economics and macroeconomics. Yet no exact likelihood analysis of these models has been provided so far. In this paper we outline the issues and suggest a Markov chain Monte Carlo algorithm which allows the calculation of a classical estimator via the simulated EM algorithm or a Bayesian solution in O(T) computational operations, where T denotes the sample size. We assess the perfomance of our proposed algorithm in the context of both artificial examples and an empirical application to 26 UK sectorial stock returns, and compare it to existing approximate solutions.

Keywords: Bayesian inference, Dynamic heteroskedasticity, Factor models, Makov chain Monte Carlo, Simulated EM algorithm, Volatility

JEL Classification: C32, C51, G12

Suggested Citation

Fiorentini, Gabriele and Sentana, Enrique and Shephard, Neil, Likelihood-Based Estimation of Latent Generalised Arch Structures (September 2002). CEMFI Working Paper No. 0204. Available at SSRN: https://ssrn.com/abstract=336921

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)

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

Houghton Street
London School of Economics & Political Science (LSE)
London WC2A 2AE
United Kingdom
+44 20 7955 7002 (Phone)
+44 20 7852 3580 (Fax)

Centre for Economic Policy Research (CEPR)

London
United Kingdom

Neil Shephard

Harvard University ( email )

1875 Cambridge Street
Cambridge, MA 02138
United States

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