Infinite density at the median and the typical shape of stock return distributions

Chirok Han, Jin Seo Cho, Peter C.B. Phillips

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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 nonparametric 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.

Original languageEnglish
Pages (from-to)282-294
Number of pages13
JournalJournal of Business and Economic Statistics
Issue number2
Publication statusPublished - 2011 Apr

Bibliographical note

Funding Information:
The authors thank the joint editor, associate editor, and three referees for helpful comments on the original version of the article. The authors also benefited from discussions with Jiti Gao, Isao Ishida, Leigh Roberts, Peter Thomson, and other participants at the New Zealand Econometrics Study Group Meeting held at Christchurch in March, 2005. Han acknowledges research support from Korea University under grant K0823571 and Phillips acknowledges research support from a Kelly fellowship and the NSF under grant SES 06-47086.


  • Asymptotic leptokurtosis
  • Infinite density at the median
  • Kernel density estimation
  • Least absolute deviations
  • Stylized facts

ASJC Scopus subject areas

  • Statistics and Probability
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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