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This research compares the symmetric and asymmetric effects of generalized autoregressive conditional heteroscedasticity (GARCH)-type models to investigate the volatility of the autoregressive fractionally integrated moving average (ARFIMA) model using the monthly Brent crude oil price series for the period of January 1979–July 2019. The best model of volatility is determined by comparing 13 hybrid models of GARCH (sGARCH, fGARCH, EGARCH, TGARCH, IGARCH, AVGARCH, NGARCH, NAGARCH, APARCH, apARCH, GJRGARCH, gjrGARCH, and csGARCH) in terms of symmetric and asymmetric effects at the level of (1,1). R/S analysis is used to achieve this target. The aggregated variance method, the Higuchi method, and the structural break test are performed to determine the presence of long memory in the dataset. Furthermore, the Hurst exponent method and the Geweke and Porter–Hudak method are used to estimate the fractional difference values. The ARFIMA(2,0.3589648,2)–IGARCH(1,1) model under normal distribution is selected as the best model based on the Akaike information criterion, Schwartz Bayesian information criterion, and by the smallest value for root-mean-squared error, in which this model can be used to predict more accurately than other models.

communications in statistics - simulation and computation

Comparing the performances of symmetric and asymmetric generalized autoregressive conditionally heteroscedasticity models based on long-memory models under different distributions