IDEAS home Printed from https://ideas.repec.org/p/ulp/sbbeta/2019-06.html
   My bibliography  Save this paper

Testing Nonlinearity through a Logistic Smooth Transition AR Model with Logistic Smooth Transition GARCH Errors

Author

Listed:
  • Mohamed Chikhi
  • Claude Diebolt

Abstract

This paper analyzes the cyclical behavior of CAC 40 by testing the existence of nonlinearity through a logistic smooth transition AR model with logistic smooth transition GARCH errors. We study the daily returns of CAC 40 from 1990 to 2018. We estimate several models using nonparametric maximum likelihood, where the innovation distribution is replaced by a nonparametric estimate for the density function. We find that the rate of transition and the threshold value in both the conditional mean and conditional variance are highly significant. The forecasting results show that the informational shocks have transitory effects on returns and volatility and confirm nonlinearity.

Suggested Citation

  • Mohamed Chikhi & Claude Diebolt, 2019. "Testing Nonlinearity through a Logistic Smooth Transition AR Model with Logistic Smooth Transition GARCH Errors," Working Papers of BETA 2019-06, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    • Handle: RePEc:ulp:sbbeta:2019-06
    as

    Download full text from publisher

    File URL: http://beta.u-strasbg.fr/WP/2019/2019-06.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Stefan Reitz & Frank Westerhoff, 2007. "Commodity price cycles and heterogeneous speculators: a STAR–GARCH model," Empirical Economics, Springer, vol. 33(2), pages 231-244, September.
    2. 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.
    3. Terasvirta, T & Anderson, H M, 1992. "Characterizing Nonlinearities in Business Cycles Using Smooth Transition Autoregressive Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages 119-136, Suppl. De.
    4. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    5. Junsoo Lee & Mark C. Strazicich, 2013. "Minimum LM unit root test with one structural break," Economics Bulletin, AccessEcon, vol. 33(4), pages 2483-2492.
    6. Eitrheim, Oyvind & Terasvirta, Timo, 1996. "Testing the adequacy of smooth transition autoregressive models," Journal of Econometrics, Elsevier, vol. 74(1), pages 59-75, September.
    7. Lundbergh, Stefan & Teräsvirta, Timo, 2000. "Forecasting with smooth transition autoregressive models," SSE/EFI Working Paper Series in Economics and Finance 390, Stockholm School of Economics.
    8. Robinson, P.M. & Henry, M., 1999. "Long And Short Memory Conditional Heteroskedasticity In Estimating The Memory Parameter Of Levels," Econometric Theory, Cambridge University Press, vol. 15(3), pages 299-336, June.
    9. Medeiros, Marcelo C. & Veiga, Alvaro, 2009. "Modeling Multiple Regimes In Financial Volatility With A Flexible Coefficient Garch(1,1) Model," Econometric Theory, Cambridge University Press, vol. 25(1), pages 117-161, February.
    10. Jianing Di & Ashis Gangopadhyay, 2014. "One-step Semiparametric Estimation of the GARCH Model," Journal of Financial Econometrics, Oxford University Press, vol. 12(2), pages 382-407.
    11. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    12. Chan, Felix & Theoharakis, Billy, 2011. "Estimating m-regimes STAR-GARCH model using QMLE with parameter transformation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(7), pages 1385-1396.
    13. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    14. Felix Chan & Michael McAleer, 2003. "Estimating smooth transition autoregressive models with GARCH errors in the presence of extreme observations and outliers," Applied Financial Economics, Taylor & Francis Journals, vol. 13(8), pages 581-592.
    15. Pavlidis Efthymios G & Paya Ivan & Peel David A, 2010. "Specifying Smooth Transition Regression Models in the Presence of Conditional Heteroskedasticity of Unknown Form," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(3), pages 1-40, May.
    16. Enders, Walter & Granger, Clive W J, 1998. "Unit-Root Tests and Asymmetric Adjustment with an Example Using the Term Structure of Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 304-311, July.
    17. Barnett,William A. & Geweke,John & Shell,Karl (ed.), 1989. "Economic Complexity: Chaos, Sunspots, Bubbles, and Nonlinearity," Cambridge Books, Cambridge University Press, number 9780521355636, October.
    18. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    19. John Geweke & Susan Porter‐Hudak, 1983. "The Estimation And Application Of Long Memory Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(4), pages 221-238, July.
    20. Donald W. K. Andrews & Patrik Guggenberger, 2003. "A Bias--Reduced Log--Periodogram Regression Estimator for the Long--Memory Parameter," Econometrica, Econometric Society, vol. 71(2), pages 675-712, March.
    21. Mohamed Chikhi & Claude Diebolt, 2009. "Transitory exogenous shocks in a non-linear framework: application to the cyclical behaviour of the German aggregate wage earnings," Historical Social Research (Section 'Cliometrics'), Association Française de Cliométrie (AFC), vol. 34(1), pages 354-366.
    22. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, October.
    23. 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.
    24. Mohamed Chikhi & Ali Bendob, 2018. "Nonparametric NAR-ARCH Modelling of Stock Prices by the Kernel Methodology," Journal of Economics and Financial Analysis, Tripal Publishing House, vol. 2(2), pages 105-120.
    25. Teräsvirta, Timo, 1996. "Smooth Transition Models," SSE/EFI Working Paper Series in Economics and Finance 132, Stockholm School of Economics.
    26. Sarantis, Nicholas, 1999. "Modeling non-linearities in real effective exchange rates," Journal of International Money and Finance, Elsevier, vol. 18(1), pages 27-45, January.
    27. Granger, Clive W. J. & Terasvirta, Timo, 1993. "Modelling Non-Linear Economic Relationships," OUP Catalogue, Oxford University Press, number 9780198773207.
    28. Franses, Ph.H.B.F. & Neele, J. & van Dijk, D.J.C., 1998. "Forecasting volatility with switching persistence GARCH models," Econometric Institute Research Papers EI 9819, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    29. Breitung, Jorg, 2002. "Nonparametric tests for unit roots and cointegration," Journal of Econometrics, Elsevier, vol. 108(2), pages 343-363, June.
    Full references (including those not matched with items on IDEAS)

    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. Mohamed CHIKHI & Claude DIEBOLT, 2022. "Testing the weak form efficiency of the French ETF market with the LSTAR-ANLSTGARCH approach using a semiparametric estimation," Eastern Journal of European Studies, Centre for European Studies, Alexandru Ioan Cuza University, vol. 13, pages 228-253, June.
    2. Scharth, Marcel & Medeiros, Marcelo C., 2009. "Asymmetric effects and long memory in the volatility of Dow Jones stocks," International Journal of Forecasting, Elsevier, vol. 25(2), pages 304-327.
    3. Wang, Rudan & Morley, Bruce & Stamatogiannis, Michalis P., 2019. "Forecasting the exchange rate using nonlinear Taylor rule based models," International Journal of Forecasting, Elsevier, vol. 35(2), pages 429-442.
    4. Param Silvapulle & Titi Kanti Lestari & Jae Kim, 2004. "Nonlinear Modelling of Purchasing Power Parity in Indonesia," Econometric Society 2004 Australasian Meetings 316, Econometric Society.
    5. Mohamed CHIKHI & Claude DIEBOLT & Tapas MISHRA, 2019. "Memory that Drives! New Insights into Forecasting Performance of Stock Prices from SEMIFARMA-AEGAS Model," Working Papers 07-19, Association Française de Cliométrie (AFC).
    6. Sandberg, Rickard, 2016. "Trends, unit roots, structural changes, and time-varying asymmetries in U.S. macroeconomic data: the Stock and Watson data re-examined," Economic Modelling, Elsevier, vol. 52(PB), pages 699-713.
    7. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521779654, September.
    8. Mohamed CHIKHI & Claude DIEBOLT & Tapas MISHRA, 2019. "Does Predictive Ability of an Asset Price Rest in 'Memory'? Insights from a New Approach," Working Papers of BETA 2019-43, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    9. Mohamed Chikhi & Claude Diebolt & Tapas Mishra, 2019. "Measuring Success: Does Predictive Ability of an Asset Price Rest in 'Memory'? Insights from a New Approach," Working Papers 11-19, Association Française de Cliométrie (AFC).
    10. Rodriguez, Gabriel & Sloboda, Michael J., 2005. "Modeling nonlinearities and asymmetries in quarterly revenues of the US telecommunications industry," Structural Change and Economic Dynamics, Elsevier, vol. 16(1), pages 137-158, March.
    11. Terasvirta, Timo, 2006. "Forecasting economic variables with nonlinear models," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 8, pages 413-457, Elsevier.
    12. Singh, Tarlok, 2014. "On the regime-switching and asymmetric dynamics of economic growth in the OECD countries," Research in Economics, Elsevier, vol. 68(2), pages 169-192.
    13. Jieye Qin & Christopher J. Green & Kavita Sirichand, 2019. "Determinants of Nikkei futures mispricing in international markets: Dividend clustering, currency risk, and transaction costs," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(10), pages 1269-1300, October.
    14. Franses,Philip Hans & Dijk,Dick van & Opschoor,Anne, 2014. "Time Series Models for Business and Economic Forecasting," Cambridge Books, Cambridge University Press, number 9780521520911, October.
    15. 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.
    16. Mehmet Balcilar & Rangan Gupta & Stephen M. Miller, 2015. "The out-of-sample forecasting performance of nonlinear models of regional housing prices in the US," Applied Economics, Taylor & Francis Journals, vol. 47(22), pages 2259-2277, May.
    17. Milas Costas & Legrenzi Gabriella, 2006. "Non-linear Real Exchange Rate Effects in the UK Labour Market," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(1), pages 1-34, March.
    18. Mohamed Chikhi & Anne Péguin-Feissolle & Michel Terraza, 2013. "SEMIFARMA-HYGARCH Modeling of Dow Jones Return Persistence," Computational Economics, Springer;Society for Computational Economics, vol. 41(2), pages 249-265, February.
    19. Ellington, Michael & Milas, Costas, 2019. "Global liquidity, money growth and UK inflation," Journal of Financial Stability, Elsevier, vol. 42(C), pages 67-74.
    20. Hany Fahmy, 2014. "Modelling nonlinearities in commodity prices using smooth transition regression models with exogenous transition variables," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(4), pages 577-600, November.

    More about this item

    Keywords

    LSTAR model; LSTGARCH model; nonparametric maximum likelihood; nonlinearity; informational shocks; time series analysis.;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:ulp:sbbeta:2019-06. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/bestrfr.html .

    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.