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

Obinna D. Adubisi; Ahmed Abdulkadir; Chidi. E. Adubisi; Obinna D. Adubisi; Ahmed Abdulkadir; Chidi. E. Adubisi

doi:10.3934/DSFE.2022003

Data Science in Finance and Economics

2022, Volume 2, Issue 2: 54-79. doi: 10.3934/DSFE.2022003

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Research article

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

1.
Department of Mathematics and Statistics, Federal University, Wukari, Nigeria
2.
Department of Mathematical Sciences, Abubakar Tafawa Balewa University, Bauchi, Nigeria
3.
Department of Physics, University of Ilorin, Ilorin, Nigeria

Received: 11 March 2022 Revised: 30 April 2022 Accepted: 05 May 2022 Published: 12 May 2022
JEL Codes: C15, C13, C40, C46, G17

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 EHL_ST 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 EHL_ST 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 EHL_ST innovation density relative to ten commonly used innovation densities validates the superiority of the GARCH (1, 1) and GJRGARCH (1, 1) models with EHL_ST innovation density in both in-sample and out-samples performance over other models.
- Maximum Likelihood,
- Cramer-Von Mises,
- inflation rates,
- hybrid distribution,
- simulation,
- GARCH volatility model
Citation: Obinna D. Adubisi, Ahmed Abdulkadir, Chidi. E. Adubisi. A new hybrid form of the skew-t distribution: estimation methods comparison via Monte Carlo simulation and GARCH model application[J]. Data Science in Finance and Economics, 2022, 2(2): 54-79. doi: 10.3934/DSFE.2022003

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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 EHL_ST 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 EHL_ST 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 EHL_ST innovation density relative to ten commonly used innovation densities validates the superiority of the GARCH (1, 1) and GJRGARCH (1, 1) models with EHL_ST innovation density in both in-sample and out-samples performance over other models.

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