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Infinite Density at the Median and the Typical Shape of Stock Return Distributions

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Author Info
Chirok Han () (Korea University)
Jin Seo Cho () (Korea University)
Peter C. B. Phillips (Yale University, University of York, University of Auckland & Singapore Management University)

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Abstract

Statistics are developed to test for the presence of an asymptotic discontinuity (or infinite density or peakedness) in a probability density at the median. The approach makes use of work by Knight (1998) on L1 estimation asymptotics in conjunction with non-parametric kernel density estimation methods. The size and power of the tests are assessed, and conditions under which the tests have good performance are explored in simulations. The new methods are applied to stock returns of leading companies across major U.S. industry groups. The results confirm the presence of infinite density at the median as a new significant empirical evidence for stock return distributions.

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Publisher Info
Paper provided by Institute of Economic Research, Korea University in its series Discussion Paper Series with number 0914.

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Length: 32 pages
Date of creation: 2009
Date of revision:
Handle: RePEc:iek:wpaper:0914

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Related research
Keywords: Asymptotic leptokurtosis; Infinite density at the median; Least absolute deviations; Kernel density estimation; Stock returns; Stylized facts;

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Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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  7. Rogers, Alan J., 2001. "Least Absolute Deviations Regression Under Nonstandard Conditions," Econometric Theory, Cambridge University Press, vol. 17(04), pages 820-852, August. [Downloadable!]
  8. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 1(1), pages 41-66. [Downloadable!] (restricted)
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  9. Lo, Andrew W. & Craig MacKinlay, A., 1990. "An econometric analysis of nonsynchronous trading," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 181-211. [Downloadable!] (restricted)
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  10. Dimson, Elroy, 1979. "Risk measurement when shares are subject to infrequent trading," Journal of Financial Economics, Elsevier, vol. 7(2), pages 197-226, June. [Downloadable!] (restricted)
  11. Phillips, P.C.B., 1991. "A Shortcut to LAD Estimator Asymptotics," Econometric Theory, Cambridge University Press, vol. 7(04), pages 450-463, December. [Downloadable!]
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  12. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(02), pages 186-199, June. [Downloadable!]
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