A Test for Symmetry with Leptokurtic Financial Data

Most of the tests for symmetry are developed under the (implicitor explicit) null hypothesis of normal distribution. As is wellknown, many financial data exhibit fat tails, and thereforecommonly used tests for symmetry (such as the standard test based on sample skewness) are not valid fortesting the symmetry of leptokurtic financial data. In particular,the test uses third moment, which may not be robust in presence of gross outliers. In this article wepropose a simple test for symmetry based on the Pearson typeIV family of distributions, which take account of leptokurtosisexplicitly. Our test is based on a function that is boundedover the real line, and we expect it to be more well behavedthan the test based on sample skewness (third moment). Resultsfrom our Monte Carlo study reveal that the suggested test performsvery well in finite samples both in terms of size and power.Simulation results also support our conjecture of the teststo be well behaved and robust to excess kurtosis. We apply thetest to some selected individual stock return data to illustrateits usefulness.