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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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  • Chirok Han & Jin Seo Cho & Peter C.B. Phillips, 2009. "Infinite Density at the Median and the Typical Shape of Stock Return Distributions," Cowles Foundation Discussion Papers 1701, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1701
    Note: CFP 1338.
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    1. Cho, Jin Seo & Han, Chirok & Phillips, Peter C.B., 2010. "Lad Asymptotics Under Conditional Heteroskedasticity With Possibly Infinite Error Densities," Econometric Theory, Cambridge University Press, vol. 26(3), pages 953-962, June.
    2. Cho, Jin Seo & Kim, Tae-hwan & Shin, Yongcheol, 2015. "Quantile cointegration in the autoregressive distributed-lag modeling framework," Journal of Econometrics, Elsevier, vol. 188(1), pages 281-300.
    3. Byung-hill Jun & Hosin Song, 2019. "Tests for Detecting Probability Mass Points," Korean Economic Review, Korean Economic Association, vol. 35, pages 205-248.

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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