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A Double-Threshold GARCH Model for the French Franc/Deutschmark Exchange Rate

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  • Brooks, Chris

Abstract

This paper combines and generalizes a number of recent time series models of daily exchange rate series by using a SETAR model which also allows the variance equation of a GARCH specification for the error terms to be drawn from more than one regime. An application of the model to the French Franc/Deutschmark exchange rate demonstrates that out-of-sample forecasts for the exchange rate volatility are also improved when the restriction that the data it is drawn from a single regime is removed. This result highlights the importance of considering both types of regime shift (i.e. thresholds in variance as well as in mean) when analysing financial time series. Copyright © 2001 by John Wiley & Sons, Ltd.

Suggested Citation

  • Brooks, Chris, 2001. "A Double-Threshold GARCH Model for the French Franc/Deutschmark Exchange Rate," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(2), pages 135-143, March.
  • Handle: RePEc:jof:jforec:v:20:y:2001:i:2:p:135-43
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    1. D'Andrade, Kendall, 1992. "The End of an Era," Business Ethics Quarterly, Cambridge University Press, vol. 2(03), pages 379-389, July.
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    Cited by:

    1. Antonio Rubia & Trino-Manuel Ñíguez, 2006. "Forecasting the conditional covariance matrix of a portfolio under long-run temporal dependence," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(6), pages 439-458.
    2. Funke, Michael & Shu, Chang & Cheng, Xiaoqiang & Eraslan, Sercan, 2015. "Assessing the CNH–CNY pricing differential: Role of fundamentals, contagion and policy," Journal of International Money and Finance, Elsevier, vol. 59(C), pages 245-262.
    3. Knight John & Satchell Stephen, 2011. "Some New Results for Threshold AR(1) Models," Journal of Time Series Econometrics, De Gruyter, vol. 3(2), pages 1-42, April.
    4. Gerlach, Richard & Chen, Cathy W.S. & Lin, Doris S.Y. & Huang, Ming-Hsiang, 2006. "Asymmetric responses of international stock markets to trading volume," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(2), pages 422-444.
    5. Ke Zhu & Wai Keung Li & Philip L. H. Yu, 2017. "Buffered Autoregressive Models With Conditional Heteroscedasticity: An Application to Exchange Rates," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(4), pages 528-542, October.
    6. Chen, Cathy W.S. & Gerlach, Richard H. & Tai, Amanda P.J., 2008. "Testing for nonlinearity in mean and volatility for heteroskedastic models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 489-499.
    7. Olmedo,E. & Velasco, F. & Valderas, J.M., 2007. "Caracterización no lineal y predicción no paramétrica en el IBEX35/Nonlinear Characterization and Predictions of IBEX 35," Estudios de Economía Aplicada, Estudios de Economía Aplicada, vol. 25, pages 815-842, Diciembre.
    8. Cathy W. S. Chen & Mike K. P. So & Ming-Tien Chen, 2005. "A Bayesian threshold nonlinearity test for financial time series," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 24(1), pages 61-75.
    9. Beg, A.B.M. Rabiul Alam & Anwar, Sajid, 2012. "Sources of volatility persistence: A case study of the U.K. pound/U.S. dollar exchange rate returns," The North American Journal of Economics and Finance, Elsevier, vol. 23(2), pages 165-184.
    10. W. K. Li & Shiqing Ling & Michael McAleer, 2001. "A Survey of Recent Theoretical Results for Time Series Models with GARCH Errors," ISER Discussion Paper 0545, Institute of Social and Economic Research, Osaka University.
    11. Shiyi Chen & Kiho Jeong & Wolfgang Härdle, 2008. "Support Vector Regression Based GARCH Model with Application to Forecasting Volatility of Financial Returns," SFB 649 Discussion Papers SFB649DP2008-014, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    12. Cathy Chen & Richard Gerlach, 2013. "Semi-parametric quantile estimation for double threshold autoregressive models with heteroskedasticity," Computational Statistics, Springer, vol. 28(3), pages 1103-1131, June.
    13. Yang, Yung-Lieh & Chang, Chia-Lin, 2008. "A double-threshold GARCH model of stock market and currency shocks on stock returns," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 458-474.
    14. Charles, Amélie, 2010. "The day-of-the-week effects on the volatility: The role of the asymmetry," European Journal of Operational Research, Elsevier, vol. 202(1), pages 143-152, April.
    15. Zhu, Junjun & Xie, Shiyu, 2010. "Bayesian Analysis of a Triple-Threshold GARCH Model with Application in Chinese Stock Market," MPRA Paper 28235, University Library of Munich, Germany.
    16. Dufrenot, Gilles & Guegan, Dominique & Peguin-Feissolle, Anne, 2005. "Modelling squared returns using a SETAR model with long-memory dynamics," Economics Letters, Elsevier, vol. 86(2), pages 237-243, February.
    17. Chen, Qian & Gerlach, Richard H., 2013. "The two-sided Weibull distribution and forecasting financial tail risk," International Journal of Forecasting, Elsevier, vol. 29(4), pages 527-540.
    18. Pedro Correia S. Bezerra & Pedro Henrique M. Albuquerque, 2017. "Volatility forecasting via SVR–GARCH with mixture of Gaussian kernels," Computational Management Science, Springer, vol. 14(2), pages 179-196, April.
    19. Toshio Utsunomiya, 2013. "A new approach to the effect of intervention frequency on the foreign exchange market: evidence from Japan," Applied Economics, Taylor & Francis Journals, vol. 45(26), pages 3742-3759, September.
    20. Sitzia, Bruno & Iovino, Doriana, 2008. "Nonlinearities in Exchange rates: Double EGARCH Threshold Models for Forecasting Volatility," MPRA Paper 8661, University Library of Munich, Germany.
    21. Chen, Cathy W.S. & Yang, Ming Jing & Gerlach, Richard & Jim Lo, H., 2006. "The asymmetric reactions of mean and volatility of stock returns to domestic and international information based on a four-regime double-threshold GARCH model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 401-418.
    22. Wu Xin-Yu & Zhou Hai-Lin, 2015. "A triple-threshold leverage stochastic volatility model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(4), pages 483-500, September.
    23. Cathy W. S. Chen & Mike K. P. So & Edward M. H. Lin, 2009. "Volatility forecasting with double Markov switching GARCH models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(8), pages 681-697.
    24. Suardi, Sandy, 2008. "Central bank intervention, threshold effects and asymmetric volatility: Evidence from the Japanese yen-US dollar foreign exchange market," Economic Modelling, Elsevier, vol. 25(4), pages 628-642, July.
    25. Kushal Banik Chowdhury & Nityananda Sarkar, 2015. "The Effect of Inflation on Inflation Uncertainty in the G7 Countries: A Double Threshold GARCH Model," International Econometric Review (IER), Econometric Research Association, vol. 7(1), pages 34-50, April.

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