Abstract A 149-point realization of daily exchange rates of the Uganda shilling (UGX) – Nigerian naira (NGN) from 4th October, 2014 to 1st March, 2015, is analyzed by Box-Jenkins methods. By a new fitting algorithm, it is concluded that the time series follows the subset SARIMA (1,1,0)x(1,1,0)7 model. Daily exchange rates between the two currencies may be simulated or forecasted by the model.