A Test for Asymmetry with Leptokurtic Financial Data
Gamini Premaratne and Anil K. Bera
University of Illinois at Urbana-Champaign
Department of Economics
484 Wohlers Hall
1206 South Sixth Street
Champaign, Illinois 61820
Abstract
Most of the tests for asymmetry are developed under the null hypothesis of normal distribution. As is well known, many financial data exhibits fat tail, and commonly used tests (such as the standard root-b1 test based on sample skewness) are not valid for leptokurtic financial data. Also, the root-b1 test uses the third moment, which may not be robust in the presence of gross outliers. In this paper, we propose a simple parametric test for symmetry based on the Pearson type IV family of distributions, which take account of leptokurtosis explicitly. Our test is based on a function that bounded over the real line, and we expect it to be more well behaved than the test based on sample skewness (third moment). Results from our Monte Carlo study reveal that the suggested test performs quite well in finite samples, and it is robust to excess kurtosis. We also apply the test to stock return data to illustrate its usefulness.
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updated March 19, 2002 by Linda Huff
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