Testing Conditional Dynamics in Asymmetry. A Residual-Based Approach

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