Abstract:
In this study, an autoregressive fractionally integrated moving average (ARFIMA) model of orders
p, d and q were formulated for Nigeria’s crude oil price over a period of 10 years, spanning (from
15/06/2009 to 21/06/2019). The time plot shows that there was kind of persistence in the crude oil
price for long period of time. Tsay test shows the crude oil price follows some autoregressive
process at 5% level of significance while McLeod-Li test shows that the crude oil price does not
follow some ARIMA process at 5% level of significance. The test for stationarity was carried out
using Augmented Dickey Fuller (ADF) test, the test showed that the crude oil price was
nonstationary. It was observed that the crude oil price exhibits long memory or long term
dependence because there is a significant autocorrelation, slowly decaying. The fractionally
differenced operator was employed to crude oil price. The crude oil price became stationary at d
= 0.21. At d = 0.21, ARFIMA (p, 0.21, q) model was fitted to the crude oil price for some values
of p and q. Akaike information criterion (AIC) and root mean square error(RMSE) were employed
for model selection. The optimal model was identified as the one with the least AIC or least RMSE.
The ARFIMA (2,0.21,1) model was found to be optimal model for the crude prices. The
parameters of the model were estimated and the result show that all the parameters for the crude
oil price are significantly different from zero. The Ljung –Box test showed that residuals of the
optimal model are random, indicating that the optimal ARFIMA (2,0.21,1) model is adequate for
analysing Nigeria’s
crude oil price.
