A 180-point daily exchange rate series of the Uganda shilling (UGX) and the United States dollar (USD) covering from 25 August 2014 to 20 February 2015 is analyzed by seasonal Box-Jenkins methods. A time-plot of the series shows an upward trend indicating a relative depreciation of the UGX. A seven-day differencing of the series yield a series that is adjudged stationary by the Augmented Dickey Fuller (ADF) Test. However, its correlogram contradicts a stationarity hypothesis. A non-seasonal differencing of this series produces a series adjudged as stationary and having an autocorrelation function that suggests two models, namely: a SARIMA(0,1,1)x(0,1,1)7 and a SARIMA(0,1,1)x(1,1,1)7. Diagnostic checking methods used to compare the two models reveal that the former model is the more adequate model. Hence it is proposed that the exchange rates follow a SARIMA(0,1,1)x(0,1,1)7 model. Forecasting might therefore be based on this model.