Box-Jenkins Method Based Additive Simulating Model for Daily Ugx-Ngn Exchange Rates

A 177-point realization of daily exchange rates of the Uganda shilling (UGX) – Nigerian naira (NGN) from 22nd September, 2015 to 16th March, 2016, is analyzed by Box-Jenkins methods. The original series being non-stationary is differenced seasonally i.e. on a seven-day basis. A further non-seasonal differencing is done to ensure seasonality. These differences of the seasonal differences of the series are modeled by seasonal autoregressive integrated moving average (SARIMA) approach. The first 170 values are used for the modeling process and the remaining 7 are used for out-of-sample forecast goodness-of-fit test. By a new fitting algorithm, it is concluded that the time series follows the additive SARIMA (1,1,0)x(1,1,0)7 model. Forecasts obtained for the daily rates from March 10 to March 16, 2016 agree so closely with the observed values that the calculated goodness-of-fit chi-square test statistic is far from being statistically significant with a p-value of more than 99%. Daily exchange rates between the two currencies may be simulated or forecasted by the model.