Autoregressive gamma processes

May 25, 2017 | Autor: Joann Jasiak | Categoria: Econometrics, Forecasting, STOCK EXCHANGE

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Autoregressive Gamma Process Article in Journal of Forecasting · March 2006 DOI: 10.2139/ssrn.757358 · Source: RePEc

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2 authors: Christian Gourieroux

Joann Jasiak

University of Toronto

York University

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Les Cahiers du CREF

ISSN: 1707-410X

Autoregressive Gamma Processes Christian Gouriéroux Joann Jasiak CREF 05-03 April 2005

Copyright © 2005. Christian Gouriéroux, Joann Jasiak Tous droits réservés pour tous les pays. Toute traduction et toute reproduction sous quelque forme que ce soit sont interdites. Les textes publiés dans la série «Les Cahiers du CREF» de HEC Montréal n'engagent que la responsabilité de leurs auteurs. La publication de cette série de rapports de recherche bénéficie d'une subvention du programme de l'Initiative de la nouvelle économie (INE) du Conseil de recherches en sciences humaines du Canada (CRSH).

Autoregressive Gamma Processes Christian Gouriéroux Professor CREF, CREST, CEPREMAP and University of Toronto 15, boulevard Gabriel Péri 92245 Malakoff France E-Mail: [email protected]

Joann Jasiak Professor CREF and York University Department of Economics 4700 Keele Street Toronto, Ontario M3J 1P3 Canada E-Mail: [email protected]

April 2005

Les Cahiers du CREF CREF 05-03

Les Cahiers du CREF

CREF 05-03

Autoregressive Gamma Processes Abstract We introduce a class of autoregressive gamma processes with conditional distributions from the family of noncentered gamma (up to a scale factor). The paper provides the stationarity and ergodicity conditions for ARG processes of any autoregressive order p, including long memory, and closed-form expressions of conditional moments. The nonlinear state space representation of an ARG process is used to derive the filtering, smoothing and forecasting algorithms. The paper also presents estimation and inference methods, illustrated by an application to interquote durations data on an infrequently traded stock listed on the Toronto Stock Exchange (TSX). Keywords: Frequency

Intertrade Durations, Autoregressive Gamma, CIR, High

JEL Classification : C51

Processus gamma autorégressifs Résumé Nous présentons une classe de processus gamma autorégressifs dont la distribution conditionnelle appartient à la famille de gamma décentrées. L’article fournit les conditions de stationnarité et d’ergodicité de ces processus autorégressifs de tous ordre p, incluant ceux à mémoire longue, et des expressions fermées des moments conditionnels. La représentation non linéaire de l’espace d’état d’un processus gamma autorégressif est utilisée pour dériver des algorithmes de filtrage, de lissage et de prévision. L’article présente également des méthodes d’estimation et d’inférence, illustrées par une application aux données de durée inter-cotations d’une action du Toronto Stock Exchange transigée peu fréquemment. Mots clés : Durées inter-transactions, Gamma autorégressifs, CIR, Haute fréquence

___________________________ Acknowledgments: The authors gratefully acknowledge financial support of the Natural Sciences and Engineering Research Council of Canada.

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Autoregressive gamma processes

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