IDEAS home Printed from https://ideas.repec.org/a/eee/empfin/v18y2011i2p368-378.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0927-5398(10)00085-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dick van Dijk & Timo Terasvirta & Philip Hans Franses, 2002. "Smooth Transition Autoregressive Models — A Survey Of Recent Developments," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 1-47.
    2. Christian Conrad & Berthold R. Haag, 2006. "Inequality Constraints in the Fractionally Integrated GARCH Model," Journal of Financial Econometrics, Oxford University Press, vol. 4(3), pages 413-449.
    3. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    4. Baillie, Richard T. & Kapetanios, George, 2007. "Testing for Neglected Nonlinearity in Long-Memory Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 447-461, October.
    5. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    6. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    7. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
    8. Baillie, Richard T. & Morana, Claudio, 2009. "Modelling long memory and structural breaks in conditional variances: An adaptive FIGARCH approach," Journal of Economic Dynamics and Control, Elsevier, vol. 33(8), pages 1577-1592, August.
    9. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
    10. Pagan, Adrian R. & Schwert, G. William, 1990. "Alternative models for conditional stock volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 267-290.
    11. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    12. Meitz, Mika & Saikkonen, Pentti, 2011. "Parameter Estimation In Nonlinear Ar–Garch Models," Econometric Theory, Cambridge University Press, vol. 27(6), pages 1236-1278, December.
    13. Lundbergh, Stefan & Terasvirta, Timo, 2002. "Evaluating GARCH models," Journal of Econometrics, Elsevier, vol. 110(2), pages 417-435, October.
    14. Fornari, Fabio & Mele, Antonio, 1997. "Sign- and Volatility-Switching ARCH Models: Theory and Applications to International Stock Markets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(1), pages 49-65, Jan.-Feb..
    15. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    16. Davidson, James, 2004. "Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, and a New Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 16-29, January.
    17. Engle, Robert F & Ng, Victor K, 1993. "Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    18. Lee, Junsoo & Degennaro, Ramon P, 2000. "Smooth Transition ARCH Models: Estimation and Testing," Review of Quantitative Finance and Accounting, Springer, vol. 15(1), pages 5-20, July.
    19. Clark, Todd E. & West, Kenneth D., 2007. "Approximately normal tests for equal predictive accuracy in nested models," Journal of Econometrics, Elsevier, vol. 138(1), pages 291-311, May.
    20. Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus, 2000. "Stationary Arch Models: Dependence Structure And Central Limit Theorem," Econometric Theory, Cambridge University Press, vol. 16(1), pages 3-22, February.
    21. Li, C W & Li, W K, 1996. "On a Double-Threshold Autoregressive Heteroscedastic Time Series Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(3), pages 253-274, May-June.
    22. Dacorogna, Michael M. & Muller, Ulrich A. & Nagler, Robert J. & Olsen, Richard B. & Pictet, Olivier V., 1993. "A geographical model for the daily and weekly seasonal volatility in the foreign exchange market," Journal of International Money and Finance, Elsevier, vol. 12(4), pages 413-438, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Stavros Degiannakis & Pamela Dent & Christos Floros, 2014. "A Monte Carlo Simulation Approach to Forecasting Multi-period Value-at-Risk and Expected Shortfall Using the FIGARCH-skT Specification," Manchester School, University of Manchester, vol. 82(1), pages 71-102, January.
    2. Ngene, Geoffrey & Tah, Kenneth A. & Darrat, Ali F., 2017. "Long memory or structural breaks: Some evidence for African stock markets," Review of Financial Economics, Elsevier, vol. 34(C), pages 61-73.
    3. Juan Benjamín Duarte Duarte & Juan Manuel Mascare?nas Pérez-Iñigo, 2014. "Comprobación de la eficiencia débil en los principales mercados financieros latinoamericanos," Estudios Gerenciales, Universidad Icesi, November.
    4. 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.
    5. 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.
    6. 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.
    7. Juan Benjamín Duarte Duarte & Juan Manuel Mascareñas Pérez-Iñigo, 2014. "¿Han sido los mercados bursátiles eficientes informacionalmente?," Apuntes del Cenes, Universidad Pedagógica y Tecnológica de Colombia, June.
    8. 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.
    9. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521770415.
    2. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Volatility Forecasting," PIER Working Paper Archive 05-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    3. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    4. Nikolaos A. Kyriazis, 2021. "A Survey on Volatility Fluctuations in the Decentralized Cryptocurrency Financial Assets," JRFM, MDPI, vol. 14(7), pages 1-46, June.
    5. Trino-Manuel Ñíguez, 2008. "Volatility and VaR forecasting in the Madrid Stock Exchange," Spanish Economic Review, Springer;Spanish Economic Association, vol. 10(3), pages 169-196, September.
    6. repec:awi:wpaper:0472 is not listed on IDEAS
    7. LeBaron, Blake, 2003. "Non-Linear Time Series Models in Empirical Finance,: Philip Hans Franses and Dick van Dijk, Cambridge University Press, Cambridge, 2000, 296 pp., Paperback, ISBN 0-521-77965-0, $33, [UK pound]22.95, [," International Journal of Forecasting, Elsevier, vol. 19(4), pages 751-752.
    8. Degiannakis, Stavros & Xekalaki, Evdokia, 2004. "Autoregressive Conditional Heteroskedasticity (ARCH) Models: A Review," MPRA Paper 80487, University Library of Munich, Germany.
    9. Mehmet Sahiner, 2022. "Forecasting volatility in Asian financial markets: evidence from recursive and rolling window methods," SN Business & Economics, Springer, vol. 2(10), pages 1-74, October.
    10. Diongue, Abdou Kâ & Guégan, Dominique, 2007. "The stationary seasonal hyperbolic asymmetric power ARCH model," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1158-1164, June.
    11. Yanlin Shi & Yang Yang, 2018. "Modeling High Frequency Data with Long Memory and Structural Change: A-HYEGARCH Model," Risks, MDPI, vol. 6(2), pages 1-28, March.
    12. Adnen Ben Nasr & Ahdi Noomen Ajmi & Rangan Gupta, 2014. "Modelling the volatility of the Dow Jones Islamic Market World Index using a fractionally integrated time-varying GARCH (FITVGARCH) model," Applied Financial Economics, Taylor & Francis Journals, vol. 24(14), pages 993-1004, July.
    13. McAleer, Michael & Medeiros, Marcelo C., 2008. "A multiple regime smooth transition Heterogeneous Autoregressive model for long memory and asymmetries," Journal of Econometrics, Elsevier, vol. 147(1), pages 104-119, November.
    14. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2003. "Some Like it Smooth, and Some Like it Rough: Untangling Continuous and Jump Components in Measuring, Modeling, and Forecasting Asset Return Volatility," PIER Working Paper Archive 03-025, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Sep 2003.
    15. Giraitis, Liudas & Leipus, Remigijus & Robinson, Peter M. & Surgailis, Donatas, 2004. "LARCH, leverage, and long memory," LSE Research Online Documents on Economics 294, London School of Economics and Political Science, LSE Library.
    16. Christensen, Bent Jesper & Nielsen, Morten Ørregaard & Zhu, Jie, 2010. "Long memory in stock market volatility and the volatility-in-mean effect: The FIEGARCH-M Model," Journal of Empirical Finance, Elsevier, vol. 17(3), pages 460-470, June.
    17. John Cotter & Simon Stevenson, 2008. "Modeling Long Memory in REITs," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 36(3), pages 533-554, September.
    18. Nasr, Adnen Ben & Lux, Thomas & Ajmi, Ahdi Noomen & Gupta, Rangan, 2016. "Forecasting the volatility of the Dow Jones Islamic Stock Market Index: Long memory vs. regime switching," International Review of Economics & Finance, Elsevier, vol. 45(C), pages 559-571.
    19. Teräsvirta, Timo, 2006. "An introduction to univariate GARCH models," SSE/EFI Working Paper Series in Economics and Finance 646, Stockholm School of Economics.
    20. Liudas Giraitis & Remigijus Leipus & Peter M Robinson & Donatas Surgailis, 2003. "LARCH, Leverage and Long Memory," STICERD - Econometrics Paper Series 460, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    21. Halkos, George E. & Tsirivis, Apostolos S., 2019. "Effective energy commodity risk management: Econometric modeling of price volatility," Economic Analysis and Policy, Elsevier, vol. 63(C), pages 234-250.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:empfin:v:18:y:2011:i:2:p:368-378. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jempfin .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.