Modified Volatility Conditional Heteroscedastic Models using Binary Variable

Abstract

This study modified some of the existing conditional heteroscedastic models by introducing binary variable to sort out categorical data into mutually exclusive categories and compared the existing conditional heteroscedastic models with the modified conditional heteroscedastic models. Jarque-Bera statistic was used for normality test, Augmented dickey-fuller (ADF) test was used to test the stationarity of the return series, Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) was used for model selection, and root mean square error was for model fitness. The parameters of these models were estimated using the Marquardt’s numerical optimization algorithm in the Econometric view software.  Time series behaviour of daily closing stocks returns of seven oil companies listed in the Nigerian stocks market from 4th January, 2017 to 30th June, 2023 was considered. ARCH (1), ARCH (2), GARCH (1,1), GARCH (2,1), EGARCH (1,1), EGARCH (2,1), GJRGARCH (1,1) and GJRGARCH (2,1) with generalized error distribution were used for the analysis. Results revealed that all the oil stocks returns were all stationary and not normally distributed. These shows the evidence of volatility clustering, negative skewness, leptokurtic and leverage effect which are usually observed in financial time series. Also, the modified GJRGARCH (1,1) outperformed better than other models for forecast evaluation and fitness performance respectively.