The research delved into analysing the stochastic characteristics of Nigeria's Real GDP, the exchange rate of the Naira to US Dollar, and the inflation rate employing Autoregressive fractionally integrated moving average (ARFIMA) and the Autoregressive Fractionally Integrated Moving Average Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity (FIGARCH) modelling approach. The ability of the hybrid formation of ARFIMA-FIGARCH model with Nigeria macroeconomic variables in modeling the periodicity of long memory volatilities was examined. ARIMA GARCH method of modeling was also employed in analyzing the volatilities of Nigeria selected macroeconomic variables to enrich the study. The efficiency of ARFIMA, ARFIMA FIGARCH and ARIMA GARCH models were evaluated with the forecast evaluation measurements. Results revealed that ARFIMA FIGARCH and ARIMA GARCH models are more adequate in modeling the Inflation rate and the exchange rate while ARFIMA present more adequacies in modeling the RGDP. This result revealed evidence of high volatilities in Nigeria Inflation and the exchange rate of Naira to US dollar