Identification of Robust Garch Models with Symmetric and Asymmetric Process with the use of Beta Volatility Coefficient and Model Accuracy Measure
Biu, Emmanuel Oyinebifun
Department of Mathematics and Statistics, University of Port Harcourt, Choba, Rivers State, Nigeria.
Orumie Ukamaka Cynthia
*
Department of Mathematics and Statistics, University of Port Harcourt, Choba, Rivers State, Nigeria.
Ockiya, Atto Kennedy
Department of Mathematics and Statistics, Ignatius Ajuru University of Education, Rivers State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The goal of this study was to identify a reliable GARCH model for modeling and forecasting each economic variable in Nigeria, including the price of crude oil, the consumer price index, the exchange rate, and the inflation rate. Monthly secondary data and simulated data sets were the data sets that were used. Between January 2004 and December 2020, the secondary data are covered. Beta Volatility Coefficient (BVC) model was proposed for detecting volatility in research data. Using a proposed method called Beta Volatility Coefficient (BVC) and Model Accuracy Measure (MAM) for the different sample sizes: 50, 100, 150, and 200, robust models for each variable were found. Leverage impact was there, according to the Asymmetric models' results. All the variables have a statistically significant value for the value. Inflation rate series is 11% more volatile than the Crude Oil Price and Exchange rate series, and when the sample size is large, the Consumer Price Index is 55% more volatile than the Crude Oil Price and Exchange rate, according to the results of the BVC of the Symmetric and Asymmetric models at the various sample sizes (200). The asymmetric "E-GARCH (1, 1) Model," the symmetric "GARCH-M (1, 1) Model," the symmetric "GARCH (1, 1) Model," and the symmetric "E-GARCH (1, 1) Model" are the identified robust models for the prediction of the Crude Oil Price series, the Inflation Rate series, the Exchange Rate series, and the Consumer Price Index series, respectively. In general, the Asymmetric GARCH model outperformed the Symmetric GARCH model for Exchange rate and Consumer Price Index, which is an improvement over earlier research. The Symmetric GARCH model outperformed the Asymmetric GARCH model for Crude Oil Price and Inflation Rate. For each variable, the found reliable models were utilized to create predictions between January 2022 and December 2024. The expected ranges for the price of crude oil are $31.82 ±1.08, the inflation rate is N14.65 ±0.03, the exchange rate is N/$756.76 ±53.84, and the consumer price index is N2.26 ±0.11.
Keywords: Univariate GARCH (M-GARCH) models, Information Criteria, Symmetric and Asymmetric process, Univariate Economic Variables, Leverage Effect, Beta Volatility Coefficient (BVC) and Model Accuracy Measure (MAM). ±