Testing conditional asymmetry: A residual-based approach

We propose three residual-based tests for conditional asymmetry. The distribution is assumed to fall into the class of skewed distributions of Fernandez and Steel (1998). In this class, asymmetry is measured by the ratio between the probabilities of being larger and smaller than the mode. Estimation is performed under the null hypothesis of constant asymmetry of the innovations and, in a second step, tests for conditional asymmetry are performed on generalized residuals through parametric and non-parametric methods. We derive the asymptotic distribution of the tests that incorporates the uncertainty of the estimated parameters. A Monte Carlo study shows that neglecting this uncertainty severely biases the tests. An empirical application on a basket of daily returns reveals that financial data often present dynamics in the conditional skewness.