Skip Navigation


Journal of Financial Econometrics Advance Access originally published online on June 8, 2006
Journal of Financial Econometrics 2006 4(3):413-449; doi:10.1093/jjfinec/nbj015
This Article
Right arrow Full Text
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
4/3/413    most recent
nbj015v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Conrad, C.
Right arrow Articles by Haag, B. R.
Right arrow Search for Related Content
Related Collections
Right arrow C22 - Time-Series Models
Right arrow F31 - Foreign Exchange
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author 2006. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Inequality Constraints in the Fractionally Integrated GARCH Model

Christian Conrad
     University of Mannheim

Berthold R. Haag
     University of Mannheim

Address correspondence to Christian Conrad, Universität Mannheim, Fakultät für Rechtswissenschaft und Volkswirtschaftslehre, Lehrstuhl für Statistik, L7 3–5, 68131 Mannheim, Germany, or e-mail: cconrad{at}rumms.uni-mannheim.de.

In this article we derive necessary and sufficient conditions for the nonnegativity of the conditional variance in the fractionally integrated generalized autoregressive conditional heteroskedastic (p, d, q) (FIGARCH) model of the order p ≤ 2 and sufficient conditions for the general model. These conditions can be seen as being analogous to those derived by Nelson and Cao (1992, Journal of Business & Economic Statistics 10, 229–235) for the GARCH(p, q) model. However, the inequality constraints which we derive for the FIGARCH model illustrate two remarkable properties of the FIGARCH model which are in contrast to the GARCH model: (i) even if all parameters are nonnegative, the conditional variance can become negative and (ii) even if all parameters are negative (apart from d), the conditional variance can be nonnegative almost surely. In particular, the conditions for the (1, d, 1) model substantially enlarge the sufficient parameter set provided by Bollerslev and Mikkelsen (1996, Journal of Econometrics 73, 151–184). The importance of the result is illustrated in an empirical application of the FIGARCH(1, d, 1) model to Japanese yen versus U.S. dollar exchange rate data.

KEYWORDS: inequality constraints, long-memory and fractionally integrated GARCH processes

Received June 15, 2005; revised April 11, 2006; accepted April 25, 2006


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.