IDEAS home Printed from
   My bibliography  Save this paper

Statistical Modeling of Stock Returns: Explanatory or Descriptive? A Historical Survey with Some Methodological Reflections


  • Phoebe Koundouri
  • Nikolaos Kourogenis

    () (Department of Banking and Financial Management, University of Piraeus.)

  • Nikitas Pittis

    () (University of Piraeus, Greece)


The purpose of this paper is twofold: first, to survey the statistical models of stock returns that have been suggested in the finance literature since the middle of the twentieth century; second, to examine under the prism of the contemporary philosophy of science, which of the aforementioned models can be classified as explanatory and which as descriptive. Special emphasis is paid on tracing the interactions between the motivation for the birth of statistical models of stock returns in any given historical period and the concurrent changes of the theoretical paradigm in financial economics, as well as those of probability theory.

Suggested Citation

  • Phoebe Koundouri & Nikolaos Kourogenis & Nikitas Pittis, 2014. "Statistical Modeling of Stock Returns: Explanatory or Descriptive? A Historical Survey with Some Methodological Reflections," DEOS Working Papers 1410, Athens University of Economics and Business.
  • Handle: RePEc:aue:wpaper:1410

    Download full text from publisher

    File URL:
    File Function: First version
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    1. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    2. Fama, Eugene F & French, Kenneth R, 1992. " The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-465, June.
    3. Kon, Stanley J, 1984. " Models of Stock Returns-A Comparison," Journal of Finance, American Finance Association, vol. 39(1), pages 147-165, March.
    4. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
    5. Chan, Louis K C & Hamao, Yasushi & Lakonishok, Josef, 1991. " Fundamentals and Stock Returns in Japan," Journal of Finance, American Finance Association, vol. 46(5), pages 1739-1764, December.
    6. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    7. Phoebe Koundouri & Nikolaos Kourogenis, 2011. "On the Distribution of Crop Yields: Does the Central Limit Theorem Apply?," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 93(5), pages 1341-1357.
    8. Nikolaos Kourogenis & Nikitas Pittis, 2008. "Testing for a unit root under errors with just barely infinite variance," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(6), pages 1066-1087, November.
    9. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
    10. F. W. Taussig, 1921. "Is Market Price Determinate?," The Quarterly Journal of Economics, Oxford University Press, vol. 35(3), pages 394-411.
    11. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
    12. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420-420.
    13. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-1304, September.
    14. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    15. Praetz, Peter D, 1972. "The Distribution of Share Price Changes," The Journal of Business, University of Chicago Press, vol. 45(1), pages 49-55, January.
    16. Chen, Nai-Fu & Roll, Richard & Ross, Stephen A, 1986. "Economic Forces and the Stock Market," The Journal of Business, University of Chicago Press, vol. 59(3), pages 383-403, July.
    17. 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.
    18. Eugene F. Fama, 1965. "Portfolio Analysis in a Stable Paretian Market," Management Science, INFORMS, vol. 11(3), pages 404-419, January.
    19. Larson, Arnold B., 1960. "Measurement of a Random Process in Futures Prices," Food Research Institute Studies, Stanford University, Food Research Institute, issue 03.
    20. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, vol. 47(2), pages 244-280, April.
    21. Roll, Richard & Ross, Stephen A, 1980. " An Empirical Investigation of the Arbitrage Pricing Theory," Journal of Finance, American Finance Association, vol. 35(5), pages 1073-1103, December.
    22. Connor, Gregory & Korajczyk, Robert A., 1986. "Performance measurement with the arbitrage pricing theory : A new framework for analysis," Journal of Financial Economics, Elsevier, vol. 15(3), pages 373-394, March.
    23. Harry V. Roberts, 1959. "Stock‐Market “Patterns” And Financial Analysis: Methodological Suggestions," Journal of Finance, American Finance Association, vol. 14(1), pages 1-10, March.
    24. 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.
    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. Jan F. Kiviet & Zhenxi Chen, 2016. "A critical appraisal of studies analyzing co-movement of international stock markets with a focus on East-Asian indices," Economic Growth Centre Working Paper Series 1606, Nanyang Technological University, School of Social Sciences, Economic Growth Centre.
    2. Kiviet Jan F., 2017. "Discriminating between (in)valid External Instruments and (in)valid Exclusion Restrictions," Journal of Econometric Methods, De Gruyter, vol. 6(1), pages 1-9, January.

    More about this item


    Stock Returns; Statistical Model; Explanatory Model; Scientific Explanation; Market Efficiency; Brownian Motion.;

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

    NEP fields

    This paper has been announced in the following NEP Reports:


    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:aue:wpaper:1410. 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: (Ekaterini Glynou). 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 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.

    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.