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Stationary Arch Models: Dependence Structure And Central Limit Theorem

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Author Info
Giraitis, Liudas
Kokoszka, Piotr
Leipus, Remigijus
Abstract

This paper studies a broad class of nonnegative ARCH( ) models. Sufficient conditions for the existence of a stationary solution are established and an explicit representation of the solution as a Volterra type series is found. Under our assumptions, the covariance function can decay slowly like a power function, falling just short of the long memory structure. A moving average representation in martingale differences is established, and the central limit theorem is proved.

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File URL: http://journals.cambridge.org/abstract_S0266466600161018
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Publisher Info
Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 16 (2000)
Issue (Month): 01 (February)
Pages: 3-22
Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Handle: RePEc:cup:etheor:v:16:y:2000:i:01:p:3-22_16

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  1. Nour Meddahi & Éric Renault, 2000. "Temporal Aggregation of Volatility Models," CIRANO Working Papers 2000s-22, CIRANO. [Downloadable!]
  2. Liudas Giraitis & Remigijus Leipus & Peter M Robinson & Donatas Surgailis, 2003. "LARCH, Leverage and Long Memory," STICERD - Econometrics Paper Series /2003/460, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  3. Arup Bose, 2006. "Bootstrapping a linear estimator of the ARCH parameters," University of Cincinnati, Economics Working Papers Series 2006-03, University of Cincinnati, Department of Economics. [Downloadable!]
  4. Eric Ghysels & Pedro Santa-Clara & Rossen Valkanov, 2004. "Predicting Volatility: Getting the Most out of Return Data Sampled at Different Frequencies," CIRANO Working Papers 2004s-19, CIRANO. [Downloadable!]
    Other versions:
  5. Liudas Giraitis & Peter M Robinson, 2001. "Parametric Estimation under Long-Range Dependence," STICERD - Econometrics Paper Series /2001/416, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  6. Elena Andreou & Eric Ghysels, 2004. "Monitoring for Disruptions in Financial Markets," CIRANO Working Papers 2004s-26, CIRANO. [Downloadable!]
  7. Teräsvirta, Timo, 2006. "An introduction to univariate GARCH models," Working Paper Series in Economics and Finance 646, Stockholm School of Economics. [Downloadable!]
  8. Peter M Robinson & Paolo Zaffaroni, 2005. "Pseudo-Maximum Likelihood Estimation of ARCH(8) Models," STICERD - Econometrics Paper Series /2005/495, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  9. Dominique Guegan, 2005. "How can we define the concept of long memory ? An econometric survey," Post-Print halshs-00179343_v1, HAL. [Downloadable!]
    Other versions:
  10. Nour Meddahi, 2001. "An Eigenfunction Approach for Volatility Modeling," CIRANO Working Papers 2001s-70, CIRANO. [Downloadable!]
  11. Wolfgang Härdle & Julius Mungo, 2008. "Value-at-Risk and Expected Shortfall when there is long range dependence," SFB 649 Discussion Papers SFB649DP2008-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  12. Abdou Kâ Diongue & Dominique Guegan, 2007. "The Stationary Seasonal Hyperbolic Asymmetric Power ARCH model," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00179275_v1, HAL. [Downloadable!]
    Other versions:
  13. Trino-Manuel Ñíguez, 2008. "Volatility and VaR forecasting in the Madrid Stock Exchange," Spanish Economic Review, Springer, vol. 10(3), pages 169-196, September. [Downloadable!] (restricted)
  14. Marc Henry & Paolo Zaffaroni, 2002. "The long range dependence paradigm for macroeconomics and finance," Discussion Papers 0102-19, Columbia University, Department of Economics. [Downloadable!]
  15. Wolfgang Härdle & Julius Mungo, 2007. "Long Memory Persistence in the Factor of Implied Volatility Dynamics," SFB 649 Discussion Papers SFB649DP2007-027, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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