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Statistical Modeling of Stock Returns: A Historical Survey with Methodological Reflections

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  • Phoebe Koundouri

    (Dept. of International and European Economic Studies, Athens University of Economics and Business)

  • Nikolaos Kourogenis

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

  • Nikitas Pittis

    ()
    (University of Piraeus, Greece)

Abstract

This paper aims at identifying the motivating forces that gave birth to the statistical models of asset returns since the beginning of the twentieth century. The major question addressed is: Where do statistical models of asset returns come from?" This central question encompasses a number of secondary ones: What do these models do? Do they explain or simply describe the empirical regularities of asset returns, identified at different historical periods? If explanation provides `something', over and above description, then how can it be defined? Moreover, how is this reflected on explanatory versus descriptive models of asset returns? In the context of the models identified as explanatory, do these models offer an actual explanation for the regularities of interest or merely a potential explanation? Related to the last question, does the realism of the assumptions underlying the explanatory models matter? Has the literature adopted a realist or an instrumentalist attitude towards the explanatory models of asset returns? Our answers to these questions are being informed by our attempts to draw some analogies between the main issues concerning the statistical modelling of asset prices and those concerning the theoretical modelling of the Brownian motion in Physics.

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Bibliographic Info

Paper provided by Athens University of Economics and Business in its series DEOS Working Papers with number 1226.

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Handle: RePEc:aue:wpaper:1226

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  1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  2. Drost, F.C. & Nijman, T.E., 1993. "Temporal aggregation of GARCH processes," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153273, Tilburg University.
  3. 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.
  4. 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, 09.
  5. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420.
  6. Larson, Arnold B., 1960. "Measurement of a Random Process in Futures Prices," Food Research Institute Studies, Stanford University, Food Research Institute, issue 03.
  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. Francq, Christian & Zako an, Jean-Michel, 2006. "Mixing Properties Of A General Class Of Garch(1,1) Models Without Moment Assumptions On The Observed Process," Econometric Theory, Cambridge University Press, vol. 22(05), pages 815-834, October.
  9. 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.
  10. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February.
  11. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January.
  12. Antonios Antypas & Phoebe Koundouri & Nikolaos Kourogenis, 2010. "Aggregational Gaussianity And Barely Infinite Variance In Crop Prices," DEOS Working Papers 1001, Athens University of Economics and Business.
  13. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
  14. 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.
  15. 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 244-80, April.
  16. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
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