User menu

Accès à distance ? S'identifier sur le proxy UCLouvain

On Asymptotic Theory for ARCH (∞) Models

Primary tabs

Hafner, Christian [UCL] Preminger, Arie [CORE, UCLouvain]

Autogressive conditional heteroskedasticity (ARCH)(∞) models nest a wide range of ARCH and generalized ARCH models including models with long memory in volatility. Existing work assumes the existence of second moments. However, the fractionally integrated generalized ARCH model, one version of a long memory in volatility model, does not have finite second moments and rarely satisfies the moment conditions of the existing literature. This article weakens the moment assumptions of a general ARCH(∞) class of models and develops the theory for consistency and asymptotic normality of the quasi-maximum likelihood estimator.

Document type Article de périodique (Journal article)
Access type Accès restreint
Publication date 2017
Language Anglais
Journal information "Journal of Time Series Analysis" - Vol. 38, p. 865-879 (2017)
Peer reviewed yes
Publisher Wiley-Blackwell
issn 0143-9782
Publication status Publié
Affiliations UCL - SSH/LIDAM/ISBA - Institut de Statistique, Biostatistique et Sciences Actuarielles
UCL - SSH/LIDAM/CORE - Center for operations research and econometrics
Links
  1. Baillie Richard T., Bollerslev Tim, Mikkelsen Hans Ole, Fractionally integrated generalized autoregressive conditional heteroskedasticity, 10.1016/s0304-4076(95)01749-6
  2. Bardet Jean-Marc, Wintenberger Olivier, Asymptotic normality of the quasi-maximum likelihood estimator for multidimensional causal processes, 10.1214/08-aos674
  3. Berkes Istv\'an, Horv\'ath Lajos, Kokoszka Piotr, GARCH processes: structure and estimation, 10.3150/bj/1068128975
  4. Billingsley, Convergence of Probability Measures (1968)
  5. Billingsley, Probability and Measure (1995)
  6. Bollerslev Tim, Generalized autoregressive conditional heteroskedasticity, 10.1016/0304-4076(86)90063-1
  7. Conrad C., Inequality Constraints in the Fractionally Integrated GARCH Model, 10.1093/jjfinec/nbj015
  8. Davidson James, Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, and a New Model, 10.1198/073500103288619359
  9. Ding Zhuanxin, Granger Clive W.J., Modeling volatility persistence of speculative returns: A new approach, 10.1016/0304-4076(95)01737-2
  10. Douc Randal, Roueff François, Soulier Philippe, On the existence of some ARCH(∞) processes, 10.1016/j.spa.2007.06.002
  11. Drost Feike C., Klaassen Chris A.J., Efficient estimation in semiparametric GARCH models, 10.1016/s0304-4076(97)00042-0
  12. Engle Robert F., Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation, 10.2307/1912773
  13. Giraitis Liudas, Leipus Remigijus, Surgailis Donatas, ARCH(∞) Models and Long Memory Properties, Handbook of Financial Time Series (2009) ISBN:9783540712961 p.71-84, 10.1007/978-3-540-71297-8_3
  14. Kazakevi??ius Vytautas, Leipus Remigijus, ON STATIONARITY IN THE ARCH(???) MODEL, 10.1017/s0266466602181011
  15. Kazakevičius Vytautas, Leipus Remigijus, A new theorem on the existence of invariant distributions with applications to ARCH processes, 10.1017/s0021900200022312
  16. Loeve, Probability Theory 1 (1977)
  17. Robinson P.M., Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression, 10.1016/0304-4076(91)90078-r
  18. Robinson Peter M., Zaffaroni Paolo, Pseudo-maximum likelihood estimation of ARCH(∞) models, 10.1214/009053606000000245
  19. Shinki Kazuhiko, Zhang Zhengjun, Asymptotic theory for fractionally integrated asymmetric power ARCH models, 10.1016/j.jspi.2012.04.004
  20. Straumann, Estimation in Conditionally Heteroscedastic Time Series Models (2005)
  21. Tayefi Maryam, Ramanathan T.V., An Overview of FIGARCH and Related Time Series Models, 10.17713/ajs.v41i3.172
  22. White, Asymptotic Theory for Econometricians (1994)
Bibliographic reference Hafner, Christian ; Preminger, Arie. On Asymptotic Theory for ARCH (∞) Models. In: Journal of Time Series Analysis, Vol. 38, p. 865-879 (2017)
Permanent URL http://hdl.handle.net/2078.1/190444