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

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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 L_1 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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File URL: http://cowles.econ.yale.edu/P/cd/d17a/d1701.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1701.

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Length: 32 pages
Date of creation: Jun 2009
Date of revision:
Publication status: Published in Journal of Business and Economic Statistics (April 2011), 29(2): 282-294
Handle: RePEc:cwl:cwldpp:1701

Note: CFP 1338.
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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
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Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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

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Cited by:
  1. Peter C.B.Phillips & Jin Seo Cho & Chirok Han, 2009. "LAD Asymptotics under Conditional Heteroskedasticity with Possibly Infinite Error Densities," Working Papers CoFie-02-2009, Sim Kee Boon Institute for Financial Economics.

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