Improved parameter estimators for the flexible extended skew-t model with extensive simulations, applications and volatility modeling

Abstract

This study introduces a new conditional innovation density called the generalized odd generalized exponentiated skew-t (GOGEST) distribution for the generalized autoregressive conditional heteroscedasticity (GARCH) volatility models. Structural properties of the GOGEST distribution such as the density and cumulative functions, failure rate and quantile functions are presented in explicit forms. The simulation study indicates that the best estimator for estimating the GOGEST parameters is the maximum likelihood procedure. Applications to two real skewed datasets established that the GOGEST distribution provides the best fit compared with existing distributions. Moreso, new GARCH-type models with GOGEST distributed innovations for time series showing asymmetric volatility is proposed. An empirical application to a real dataset concerning the First bank Nigeria (FBN) daily shock return is considered to demonstrate the superiority of the proposed GARCH-type models specified with GOGEST density relative to the skew-normal, skew-t, skew generalized error, generalized hyperbolic, Johnson reparametrized, normal, Student-t, generalized error, generalized hyperbolic skew Student-t and Normal inverse Gaussian. Overall, the empirical findings validate that the Glosten-Jagannathan-Runkle GARCH (GJRGARCH)-GOGEST model provides better in-and out-of-sample predictive performance compared with other models. Therefore, the GOGEST density should be an extensively useful conditional innovation density in GARCH-type specifications for modeling volatility.

Keywords

• Conditional innovation density
• Generalized odd generalized exponentiated family of distributions
• GARCH-volatility models
• Simulation
• Skew-t distribution