A new hybrid form of the skew-t distribution: estimation methods comparison via Monte Carlo simulation and GARCH model application

Abstract

In this work, estimating the exponentiated half logistic skew-t model parameters using some classical estimation procedures is considered. The finite sample performance of the EHLST parameter estimates is examined through extensive Monte Carlo simulations. The ordering performance of the six criterions was based on the partial and overall ranks of the estimation procedures for all parameter combinations. The criterions performance ordering from finest to poorest, using the overall ranks is maximum likelihood, maximum product of spacing, Anderson-Darling, Cramer-von Mises, least squares and weighted least squares estimators for all the parameter combinations. The simulation results confirm the dominance of the maximum likelihood estimation method over other methods with the least overall rank but shows that the maximum product of spacing is most advantageous when the sample size is 200. More so, the EHLST model efficacy is demonstrated through its application on Nigeria inflation rates dataset using the maximum likelihood and maximum product of spacing estimation procedures. Furthermore, the volatility modeling of the Nigeria inflation log-returns using the GARCH-type models with the EHLST innovation density relative to ten commonly used innovation densities validates the superiority of the GARCH (1, 1) and GJRGARCH (1, 1) models with EHLST innovation density in both in-sample and out-samples performance over other models.

Keywords

• maximum likelihood
• cramer-von mises
• inflation rates
• hybrid distribution
• simulation
• garch volatility model