A GMM Skewness and Kurtosis Ratio Test for Higher Moment Dependence

Abstract

Abstract This article extends the variance ratio test of Lo and MacKinlay (1988) to tests of skewness and kurtosis ratios using the generalized methods of moments. In particular, overlapping observations are used in which dependencies are explicitly modeled to make the tests more powerful and have better size properties. The proposed higher-order ratio tests can be useful in risk management where risk models are estimated using daily data but multiperiod forecasts of tail risks are required for the determination of risk capital. Application of the tests finds significant higher moment dependence in the U.S. stock market returns.