Autoregressive Conditional Skewness

TLDR

The study introduces a maximum‑likelihood framework to model and estimate time‑varying variance and skewness in time‑series data using a non‑central conditional t distribution. They parameterize conditional variance and skewness in an autoregressive GARCH‑style model, estimate parameters via a conditional non‑central t likelihood with time‑varying degrees of freedom and noncentrality, and apply it to daily and monthly equity returns from the U.S., Germany, and Japan. The model reveals significant conditional skewness in the equity return series.

Abstract

We present a framework for modeling and estimating dynamics of variance and skewness from time-series data using a maximum likelihood approach assuming that the errors from the mean have a non-central conditional t distribution. We parameterize conditional variance and conditional skewness in an autoregressive framework similar to that of GARCH models and estimate the parameters in a conditional noncentral t distribution. The likelihood function has two time-varying parameters, the degrees of freedom and the noncentrality parameter. We apply this methodology to daily and monthly equity returns data from the U.S., Germany and Japan, concurrently estimating conditional mean, variance and skewness. We find that there is significant conditional skewness.