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.
Bibliographical noteFunding 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.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Social Sciences (miscellaneous)
- Economics and Econometrics
- Statistics, Probability and Uncertainty