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

  • Peter C.B.Phillips

    (Yale University, University of Auckland,University of York & Singapore Management University)

  • Jin Seo Cho

    (Korea University)

  • Chirok Han

    (Korea University)

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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Paper provided by Sim Kee Boon Institute for Financial Economics in its series Working Papers with number CoFie-03-2009.

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Length: 32 Pages
Date of creation: Apr 2009
Date of revision:
Publication status: Published in SMU-SKBI CoFie Working Paper
Handle: RePEc:skb:wpaper:cofie-03-2009
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