Monthly Nigerian Interbank Call Rates Modeling by Seasonal Box-Jenkins Approach

Abstract

The realization of the monthly Nigerian interbank call rates herein referred to as IBCR and analyzed span from January 2006 to August 2013. The time plot of IBCR in Figure 1 shows an overall horizontal secular trend.  There are two peaks: one between 2008 and 2009 and the other between 2011 and 2013. The two peaks are separated by a trough in 2010. Augmented Dickey Fuller (ADF) Test shows that IBCR is non-stationary. Seasonal (i.e. 12-point) differencing of IBCR yields a series called SDIBCR with basically a similar structure as IBCR, a trough between 2009 and 2010 separating two peaks (See Figure 2). The ADF seasonality test adjudges SDIBCR as still non-stationary. A non-seasonal differencing of SDIBCR yields DSDIBCR which has a horizontal trend and no discernible seasonality. It is adjudged to be stationary by the same test procedure. The correlogram of DSDIBCR in Figure 4 shows significant negative spikes at lag 12 for both the autocorrelations and partial autocorrelations. This indicates 12-monthly seasonality and the involvement of a seasonal moving average component of order one and a seasonal autoregressive component, also of order one, respectively. Based on this autocorrelation structure, four SARIMA models: (1, 1, 1)x(1, 1, 1)₁₂, (1, 1, 2)x(1, 1, 1)₁₂, (2, 1, 1)x(1, 1, 1)₁₂ and (2, 1, 2)x(1, 1, 1)₁₂ are proposed and fitted. In the Akaike’s Information Criterion (AIC) sense, the SARIMA(2, 1, 1)x(1, 1, 1)₁₂ model is adjudged the most adequate.