A major objective of this thesis is to study the statistical inference problem for GARCH-type models, including fractionally-integrated (FI) GARCH, fractional (F) GARCH, long-memory (LM) GARCH, and non-stationary GARCH models. / Among various types of generalizations to the ARCH models, fractionally-integrated (FI) GARCH model proposed in Baillie et al. (1996) and Bollerslev and Mikkelson (1996) is one of the most interesting ones as it offered many challenging theretical problems. / Parameters in the ARCH-type models are commonly estimated using the quasi-maximum likelihood estimator (QMLE). To establish consistency and asymptotic normality of the QMLE, one usually has to impose stringent assumptions, see Robinson and Zaffaroni (2006) and Straumann (2005). They have to assume that a stationary solution to the true model exists and this solution has some finite moments. These two assumptions are too restrictive to be applied to FIGARCH models. Formal results of the asymptotic properties of the QMLE of the FIGARCH models are still not available. Progresses on asymptotic theory of QMLE have only been made on certain models that resemble the FIGARCH model, including the FGARCH model of Ding and Granger (1996) and Robinson and Zaffaroni (2006), the LM-GARCH model of Robinson and Zaffaroni (1997) and the non-stationary ARCH model, but not the FIGARCH model itself. / This study attempts to solve the FIGARCH problem and extend the current findings on FGARCH, LM-GARCH and non-stationary GARCH models. We show that if the fractional parameter d is known, the QMLE for the parameters are strongly consistent and asymptotically normal. The results of LM-GARCH (0, d, 0) model in Konlikov (2003a,b) will be generalized to encompass the LM-GARCH(p, d, q) models. We also furnish a general result for non-stationary GARCH (p, q) models, extending the results of Jensen and Rahbek (2004) on weak consistency and asymptotic normality of the QMLE of the non-stationary GARCH (1, 1) models. / Ng, Chi Tim. / "June 2007." / Adviser: Chan Ngai Hang. / Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0398. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_343988 |
| Date | January 2007 |
| Contributors | Ng, Chi Tim., Chinese University of Hong Kong Graduate School. Division of Statistics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, theses |
| Format | electronic resource, microform, microfiche, 1 online resource (188 p.) |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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