Unfolded GARCH models

A new GARCH-type model for autoregressive conditional volatility, skewness, and kurtosis is proposed. The approach decomposes returns into their signs and absolute values, and specifies the joint distribution by combining a multiplicative error model for the absolute values, a dynamic binary choice model for the signs, and a copula function for their interaction. The conditional volatility and kurtosis are determined by innovations following a folded (or absolute) Student-t distribution with time-varying degrees of freedom, and separate time variation in conditional return skewness is achieved by allowing the copula parameter to be dynamic. Model estimation is performed with Bayesian methods using an adaptive Markov chain Monte Carlo algorithm. An empirical application to the returns on four major international stock market indices illustrates the statistical and economic significance of the new model for conditional higher moments.