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Long memory and nonlinearity in conditional variances: A smooth transition FIGARCH model

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  • KIlIç, Rehim

Abstract

This paper introduces the Smooth Transition version of FIGARCH model which is designed to account for both long memory and nonlinear dynamics in the conditional variance. Nonlinearity is introduced via a logistic transition function. The model can capture smooth changes in the volatility across different regimes as well as asymmetric response to negative and positive shocks and allows for nonzero thresholds. Simulations find that the Smooth Transition FIGARCH model outperforms the standard FIGARCH model when nonlinearity is present, and ignoring nonlinearity in the data may induce considerable costs in terms of bias and efficiency. Applications to exchange rate and stock market data show that the proposed model performs well both in-sample fit as well as in forecasting one-day ahead volatility.

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  • KIlIç, Rehim, 2011. "Long memory and nonlinearity in conditional variances: A smooth transition FIGARCH model," Journal of Empirical Finance, Elsevier, vol. 18(2), pages 368-378, March.
    • Handle: RePEc:eee:empfin:v:18:y:2011:i:2:p:368-378
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    3. Chkili, Walid & Aloui, Chaker & Nguyen, Duc Khuong, 2012. "Asymmetric effects and long memory in dynamic volatility relationships between stock returns and exchange rates," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 22(4), pages 738-757.
    4. Juan Benjamín Duarte Duarte & Juan Manuel Mascare?nas P�rez-I�igo, 2014. "Comprobación de la eficiencia débil en los principales mercados financieros latinoamericanos," Estudios Gerenciales, Universidad Icesi.
    5. Koubaa, Yosra & Slim, Skander, 2019. "The relationship between trading activity and stock market volatility: Does the volume threshold matter?," Economic Modelling, Elsevier, vol. 82(C), pages 168-184.
    6. Anna Perekhodko & Robert 'Slepaczuk, 2025. "Stochastic Volatility Modelling with LSTM Networks: A Hybrid Approach for S&P 500 Index Volatility Forecasting," Papers 2512.12250, arXiv.org.
    7. Markus Vogl, 2022. "Quantitative modelling frontiers: a literature review on the evolution in financial and risk modelling after the financial crisis (2008–2019)," SN Business & Economics, Springer, vol. 2(12), pages 1-69, December.
    8. Juan Benjamín Duarte Duarte & Juan Manuel Mascare�as P�rez-I�igo, 2014. "¿Han sido los mercados bursátiles eficientes informacionalmente?," Apuntes del Cenes, Universidad Pedagógica y Tecnológica de Colombia.
    9. Díaz-Hernández, Adán & Constantinou, Nick, 2019. "A multiple regime extension to the Heston–Nandi GARCH(1,1) model," Journal of Empirical Finance, Elsevier, vol. 53(C), pages 162-180.
    10. Pengfei Zhao & Haoren Zhu & Wilfred Siu Hung NG & Dik Lun Lee, 2024. "From GARCH to Neural Network for Volatility Forecast," Papers 2402.06642, arXiv.org.

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