Seasonal Arima Modelling of Nigerian Monthly Crude Oil Prices

The time plot of the series NCOP reveals a peak in 2008 and a depression in early 2009. The overall trend is horizontal and no seasonality is obvious. Twelve-month differencing yields SDNCOP exhibiting still a peak in 2008 and a trough in 2009, the overall trend being slightly positive and seasonality not easily discernible. Nonseasonal differencing of SDNCOP yields DSDNCOP with an overall horizontal trend and no obvious seasonality. However its correlogram reveals an autocorrelation structure of a seasonal model of order 12. Moreover it suggests the product of two moving average components both of order one, one non-seasonal and the other 12-month seasonal. The partial autocorrelation function suggests the involvement of a seasonal (i.e. 12-month) autoregressive component of order one. A (0, 1, 1)x(1, 1, 1)12 autoregressive integrated moving average model was therefore proposed and fitted. It has been shown to be adequate.