IDEAS home Printed from
   My bibliography  Save this article

Nonparametric NAR-ARCH Modelling of Stock Prices by the Kernel Methodology


  • Mohamed Chikhi

    (University of Ouargla)

  • Ali Bendob

    (University of Ain-Temouchent)


This paper analyses cyclical behaviour of Orange stock price listed in French stock exchange over 01/03/2000 to 02/02/2017 by testing the nonlinearities through a class of conditional heteroscedastic nonparametric models. The linearity and Gaussianity assumptions are rejected for Orange Stock returns and informational shocks have transitory effects on returns and volatility. The forecasting results show that Orange stock prices are short-term predictable and nonparametric NAR-ARCH model has better performance over parametric MA-APARCH model for short horizons. Plus, the estimates of this model are also better comparing to the predictions of the random walk model. This finding provides evidence for weak form of inefficiency in Paris stock market with limited rationality, thus it emerges arbitrage opportunities.

Suggested Citation

  • 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.
  • Handle: RePEc:trp:01jefa:jefa0020

    Download full text from publisher

    File URL:
    Download Restriction: no

    File URL:
    Download Restriction: no

    File URL:
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item

    References listed on IDEAS

    1. James J. Kung, 2016. "A nonparametric kernel regression approach for pricing options on stock market index," Applied Economics, Taylor & Francis Journals, vol. 48(10), pages 902-913, February.
    2. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    3. Yang, Lijian & Tschernig, Rolf, 2002. "Non- And Semiparametric Identification Of Seasonal Nonlinear Autoregression Models," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1408-1448, December.
    4. 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.
    5. Rolf Tschernig & Lijian Yang, 2000. "Nonparametric Lag Selection for Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(4), pages 457-487, July.
    6. Mohamed Chikhi & Claude Diebolt, 2010. "Nonparametric analysis of financial time series by the Kernel methodology," Quality & Quantity: International Journal of Methodology, Springer, vol. 44(5), pages 865-880, August.
    7. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
    8. P. M. Robinson, 1983. "Nonparametric Estimators For Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 185-207, May.
    9. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    10. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    11. Barnett,William A. & Geweke,John & Shell,Karl (ed.), 1989. "Economic Complexity: Chaos, Sunspots, Bubbles, and Nonlinearity," Cambridge Books, Cambridge University Press, number 9780521355636, December.
    12. Kristensen, Dennis, 2010. "Nonparametric Filtering Of The Realized Spot Volatility: A Kernel-Based Approach," Econometric Theory, Cambridge University Press, vol. 26(1), pages 60-93, February.
    13. Hou, Aijun & Suardi, Sandy, 2012. "A nonparametric GARCH model of crude oil price return volatility," Energy Economics, Elsevier, vol. 34(2), pages 618-626.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    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. Mitra Lal Devkota, 2018. "The Dynamic Causality Between Stock Prices And Macroeconomic Variables: Evidence From Nepal," Annals - Economy Series, Constantin Brancusi University, Faculty of Economics, vol. 6, pages 5-14, December.
    3. 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.

    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. CHIKHI, Mohamed, 2017. "Chocs exogènes et non linéarités dans les séries boursières: Application à la modélisation non paramétrique du cours de l'action Orange [Exogenous Shocks and nonlinearity in the stock exchange seri," MPRA Paper 76691, University Library of Munich, Germany, revised 2017.
    2. Sin-Yu Ho & N.M. Odhiambo, 2018. "Analysing the macroeconomic drivers of stock market development in the Philippines," Cogent Economics & Finance, Taylor & Francis Journals, vol. 6(1), pages 1451265-145, January.
    3. Carmen López-Martín & Sonia Benito Muela & Raquel Arguedas, 2021. "Efficiency in cryptocurrency markets: new evidence," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 11(3), pages 403-431, September.
    4. Jian Guo & Saizhuo Wang & Lionel M. Ni & Heung-Yeung Shum, 2022. "Quant 4.0: Engineering Quantitative Investment with Automated, Explainable and Knowledge-driven Artificial Intelligence," Papers 2301.04020,
    5. Bas Peeters & Cees L. Dert & André Lucas, 2003. "Black Scholes for Portfolios of Options in Discrete Time: the Price is Right, the Hedge is wrong," Tinbergen Institute Discussion Papers 03-090/2, Tinbergen Institute.
    6. Lütkepohl,Helmut & Krätzig,Markus (ed.), 2004. "Applied Time Series Econometrics," Cambridge Books, Cambridge University Press, number 9780521547871, December.
    7. David Daewhan Cho, 2004. "Uncertainty in Second Moments: Implications for Portfolio Allocation," Econometric Society 2004 Far Eastern Meetings 433, Econometric Society.
    8. Stafylas, Dimitrios & Anderson, Keith & Uddin, Moshfique, 2017. "Recent advances in explaining hedge fund returns: Implicit factors and exposures," Global Finance Journal, Elsevier, vol. 33(C), pages 69-87.
    9. Jack S. K. Chang & Jean C. H. Loo & Carolyn C. Wu Chang, 1990. "The Pricing Of Futures Contracts And The Arbitrage Pricing Theory," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 13(4), pages 297-306, December.
    10. Ferreira, Eva & Gil-Bazo, Javier & Orbe, Susan, 2008. "Nonparametric estimation of conditional beta pricing models," DEE - Working Papers. Business Economics. WB wb082403, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    11. Tim Bollerslev & Ray Y. Chou & Narayanan Jayaraman & Kenneth F. Kroner - L, 1991. "es modéles ARCH en finance : un point sur la théorie et les résultats empiriques," Annals of Economics and Statistics, GENES, issue 24, pages 1-59.
    12. Singh, Manish K. & Gómez-Puig, Marta & Sosvilla-Rivero, Simón, 2021. "Quantifying sovereign risk in the euro area," Economic Modelling, Elsevier, vol. 95(C), pages 76-96.
    13. Ion STANCU & Laura OBREJABRAŞOVEANU & Anamaria CIOBANU & Andrei Tudor STANCU, 2017. "Are Company Valuation Models the Same? – A Comparative Analysis between the Discounted Cash Flows (DCF), the Adjusted Net Asset, Value and Price Multiples, the Market Value Added (MVA) and the Residua," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 51(3), pages 5-20.
    14. Peter Carr & Dilip Madan, 2012. "Factor Models for Option Pricing," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 19(4), pages 319-329, November.
    15. repec:adr:anecst:y:1991:i:24:p:01 is not listed on IDEAS
    16. repec:dau:papers:123456789/5374 is not listed on IDEAS
    17. Merton, Robert, 1990. "Capital market theory and the pricing of financial securities," Handbook of Monetary Economics, in: B. M. Friedman & F. H. Hahn (ed.), Handbook of Monetary Economics, edition 1, volume 1, chapter 11, pages 497-581, Elsevier.
    18. Keith A. Lewis, 2019. "A Simple Proof of the Fundamental Theorem of Asset Pricing," Papers 1912.01091,
    19. Aloy Soppe, 2010. "Book Review," Journal of Business Ethics, Springer, vol. 91(3), pages 451-456, February.
    20. Ferreira, Eva & Gil-Bazo, Javier & Orbe, Susan, 2011. "Conditional beta pricing models: A nonparametric approach," Journal of Banking & Finance, Elsevier, vol. 35(12), pages 3362-3382.
    21. Eckhard Platen, 2005. "On The Role Of The Growth Optimal Portfolio In Finance," Australian Economic Papers, Wiley Blackwell, vol. 44(4), pages 365-388, December.

    More about this item


    Final Prediction Error; Kernel; Bandwidth; Conditional Heteroscedastic Functional Autoregressive Process; Orange Stock Price; Forecasts.;
    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


    Access and download statistics


    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:trp:01jefa:jefa0020. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: .

    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: David Simon Hall (email available below). General contact details of provider: .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.