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Non-linear GARCH models for highly persistent volatility

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  • Markku Lanne
  • Pentti Saikkonen

Abstract

In this paper we study a new class of nonlinear GARCH models. Special interest is devoted to models that are similar to previously introduced smooth transition GARCH models except for the novel feature that a lagged value of conditional variance is used as the transition variable. This choice of the transition variable is mainly motivated by the desire to find useful models for highly persistent volatility. The underlying idea is that high persistence in conditional variance is related to relatively infrequent changes in regime, which can be captured by a suitable specification of the new model. Using the theory of Markov chains, we provide sufficient conditions for the stationarity and existence of moments of various smooth transition GARCH models and even more general nonlinear GARCH models. An empirical application to an exchange rate return series demonstrates the differences between the new model and conventional GARCH models. Copyright 2005 Royal Economic Society

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Bibliographic Info

Article provided by Royal Economic Society in its journal The Econometrics Journal.

Volume (Year): 8 (2005)
Issue (Month): 2 (07)
Pages: 251-276

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Handle: RePEc:ect:emjrnl:v:8:y:2005:i:2:p:251-276

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Cited by:
  1. Annastiina Silvennoinen & Timo Teräsvirta, 2005. "Multivariate Autoregressive Conditional Heteroskedasticity with Smooth Transitions in Conditional Correlations," Research Paper Series 168, Quantitative Finance Research Centre, University of Technology, Sydney.
  2. Alexander Subbotin & Thierry Chauveau & Kateryna Shapovalova, 2009. "Volatility Models : from GARCH to Multi-Horizon Cascades," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00390636, HAL.
  3. Michael Dueker & Zacharias Psaradakis & Martin Sola & Fabio Spagnolo, 2009. "Contemporaneous-Threshold Smooth Transition GARCH Models," Department of Economics Working Papers 2009-06, Universidad Torcuato Di Tella.
  4. Teräsvirta, Timo, 2006. "An introduction to univariate GARCH models," Working Paper Series in Economics and Finance 646, Stockholm School of Economics.
  5. Malmsten, Hans, 2004. "Evaluating exponential GARCH models," Working Paper Series in Economics and Finance 564, Stockholm School of Economics, revised 03 Sep 2004.
  6. repec:ntu:ntugeo:vol2-iss1-14-042 is not listed on IDEAS
  7. Subbotin, Alexandre, 2009. "Volatility Models: from Conditional Heteroscedasticity to Cascades at Multiple Horizons," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 15(3), pages 94-138.
  8. Marcelo Cunha Medeiros & Alvaro Veiga, 2004. "Modelling multiple regimes in financial volatility with a flexible coefficient GARCH model," Textos para discussão 486, Department of Economics PUC-Rio (Brazil).

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