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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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  • Markku Lanne & Pentti Saikkonen, 2005. "Non-linear GARCH models for highly persistent volatility," Econometrics Journal, Royal Economic Society, vol. 8(2), pages 251-276, July.
    • Handle: RePEc:ect:emjrnl:v:8:y:2005:i:2:p:251-276
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    1. Nagapetyan, Artur, 2019. "Precondition stock and stock indices volatility modeling based on market diversification potential: Evidence from Russian market," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 56, pages 45-61.
    2. Emmanuel Afuecheta & Idika E. Okorie & Saralees Nadarajah & Geraldine E. Nzeribe, 2024. "Forecasting Value at Risk and Expected Shortfall of Foreign Exchange Rate Volatility of Major African Currencies via GARCH and Dynamic Conditional Correlation Analysis," Computational Economics, Springer;Society for Computational Economics, vol. 63(1), pages 271-304, January.
    3. Levine, Michael & Li, Jinguang (Tony), 2012. "A simple additivity test for conditionally heteroscedastic nonlinear autoregression," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2421-2429.
    4. Léo Parent, 2022. "The EWMA Heston model," Post-Print hal-04431111, HAL.
    5. repec:ntu:ntugeo:vol2-iss1-14-042 is not listed on IDEAS
    6. 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).
    7. Ngozi G. Emenogu & Monday Osagie Adenomon & Nwaze Obini Nweze, 2020. "On the volatility of daily stock returns of Total Nigeria Plc: evidence from GARCH models, value-at-risk and backtesting," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-25, December.
    8. Day Yang Liu & Ming Chen Chun & Yi Kai Su, 2021. "The impacts of Covid-19 pandemic on the smooth transition dynamics of stock market index volatilities for the Four Asian Tigers and Japan," International Journal of Research in Business and Social Science (2147-4478), Center for the Strategic Studies in Business and Finance, vol. 10(4), pages 183-194, June.
    9. Vito Polito, 2020. "Nonlinear Business Cycle and Optimal Policy: A VSTAR Perspective," CESifo Working Paper Series 8060, CESifo.
    10. Day-Yang Liu & Chun-Ming Chen & Yi-Kai Su, 2020. "The Impact of COVID-19 Pandemic on the Smooth Transition Dynamics of Broad-based Indices Volatilities in Taiwan," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 10(5), pages 1-14.
    11. Subbotin, Alexandre, 2009. "Volatility Models: from Conditional Heteroscedasticity to Cascades at Multiple Horizons," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 15(3), pages 94-138.
    12. Dueker Michael J. & Psaradakis Zacharias & Sola Martin & Spagnolo Fabio, 2011. "Contemporaneous-Threshold Smooth Transition GARCH Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(2), pages 1-25, March.
    13. Philippe Charlot & Vêlayoudom Marimoutou, 2008. "Hierarchical hidden Markov structure for dynamic correlations: the hierarchical RSDC model," Working Papers halshs-00285866, HAL.
    14. Monday Osagie Adenomon & Richard Adekola Idowu, 2022. "Modelling the Impact of the COVID-19 Pandemic on Some Nigerian Sectorial Stocks: Evidence from GARCH Models with Structural Breaks," FinTech, MDPI, vol. 2(1), pages 1-20, December.
    15. Tobias A. Möller & Maria Eduarda Silva & Christian H. Weiß & Manuel G. Scotto & Isabel Pereira, 2016. "Self-exciting threshold binomial autoregressive processes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(4), pages 369-400, October.
    16. Teräsvirta, Timo, 2006. "An introduction to univariate GARCH models," SSE/EFI Working Paper Series in Economics and Finance 646, Stockholm School of Economics.
    17. Stein, Michael & Islami, Mevlud & Lindemann, Jens, 2012. "Identifying time variability in stock and interest rate dependence," Discussion Papers 24/2012, Deutsche Bundesbank.
    18. Hsiang-Hsi Liu & Chun-Chou Wu & Yi Kai Su, 2012. "The influence of direct cross-straits shipping on the smooth transition dynamics of stock volatilities of shipping companies," Applied Financial Economics, Taylor & Francis Journals, vol. 22(16), pages 1331-1342, August.
    19. 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.
    20. Annastiina Silvennoinen & Timo Ter�svirta, 2015. "Modeling Conditional Correlations of Asset Returns: A Smooth Transition Approach," Econometric Reviews, Taylor & Francis Journals, vol. 34(1-2), pages 174-197, February.
    21. 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.
    22. Hubner, Stefan, 2016. "Topics in nonparametric identification and estimation," Other publications TiSEM 08fce56b-3193-46e0-871b-0, Tilburg University, School of Economics and Management.
    23. Malmsten, Hans, 2004. "Evaluating exponential GARCH models," SSE/EFI Working Paper Series in Economics and Finance 564, Stockholm School of Economics, revised 03 Sep 2004.
    24. Hurn Stan & Johnson Nicholas & Silvennoinen Annastiina & Teräsvirta Timo, 2022. "Transition from the Taylor rule to the zero lower bound," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 26(5), pages 635-647, December.
    25. Adrian Cantemir Calin & Tiberiu Diaconescu & Oana – Cristina Popovici, 2014. "Nonlinear Models for Economic Forecasting Applications: An Evolutionary Discussion," Computational Methods in Social Sciences (CMSS), "Nicolae Titulescu" University of Bucharest, Faculty of Economic Sciences, vol. 2(1), pages 42-47, June.

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