[01] Ette Harrison Etuk, Department of Mathematics and Computer Science, Rivers State University of Science and Technology, Port Harcourt, Nigeria. [02] Bazinzi Natamba, Department of Accounting, Faculty of Commerce, Makerere University Business School, Kampala, Uganda.

A brief history of the exchange rates between the Uganda shilling and the United States dollars is given. Moreover, this work involves modeling of their monthly exchange rates by seasonal Box-Jenkins methods. Clearly with time more shillings are exchanged for the dollar, an evidence of relative depreciation of the shilling. An inspection of a realization of the time series which covers from July 1990 to November 2014 reveals a 12-monthly seasonality. A 12-monthly seasonal differencing and then a non-seasonal differencing of the seasonal differences is enough to rid the series of non-stationarity. The autocorrelation structure of the resultant series suggests two seasonal autoregressive integrated moving average (SARIMA) models of orders: (0, 1, 1)x(0, 1, 1)12 and (0, 1, 1)x(1, 1, 1)12. Diagnostic checking shows that the former is the more adequate on all counts. It is therefore recommended that forecasting of the series be based on it.

Uganda Shilling, Us Dollar, Foreign Exchange Rates, Sarima Models, Seasonal Models

[01] Abdul-Aziz, A. R., Anokye, M., Kwame, A., Munyakazi, L. and Nsowah-Nuamah, N. N. N. (2013). Modeling and Forecasting Rainfall Pattern in Ghana as a Seasonal Arima Process: The Case of Ashanti Region. International Journal of humanities and Social Science, 3(3): 224 – 233. [02] Akaike, H. (1977). On Entropy Maximazation Principle. Proceedings of the Symposium on Applied Statistics. (P. R. Krishnaiah, ed.) Amsterdam, North-Holland. [03] Asamoah-Boaheng, M. (2014). Using SARIMA to forecast Monthly Mean Surface Air Temperature in the Ashanti Region of Ghana. International Journal of Statistics and Applications, 4(6): 292 – 298. [04] Bank of Uganda (2009). Quarterly Economic Report, September, Kampala: BOU. [05] Barungi, B. M. (1997). Exchange rate policy and inflation: The case of Uganda. AERC Research Paper 59, African Research Consortium, Nairobi, March. [06] Box, G. E. P. and Jenkins, G. M. (1976). Time Series Analysis, Forecasting and Control, Holden-Day, San Francisco. [07] Dureval, D., Leoning, J. L., and Birru, Y. A. (2012). Inflation Dynamics and Food prices in Ethiopia. Mimieo. [08] Etuk, E. H. (2014). An additive SARIMA Model for Daily Exchange Rates of the Malaysian Ringgit (MYR) and Nigerian Naira (NGN). International Journal of Empirical Finance, 2(4): 193 – 201. [09] Etuk, E. H. and Igbudu, R. C. (2015). Appropriate Marketing Information System tools for citrus plantation in Lattakia, Syria: a revisitation. Journal of Multidisciplinary Engineering Science and Technology, 2(1): 180 – 184. [10] Etuk, E. H. and Mohamed, M. (2014). Time Series Analysis of Monthly Rainfall data for the Gadaref rainfall station, Sudan, by Sarima Methods. International Journal of Scientific Research in Knowledge, 2(7): 320 – 327. [11] Gikungu, S. W., Waititu, A. G. and Kihoro, J. M. (2015). Forecastiing inflation rate in Kenya using SARIMA model. American Journal of the Theoritical and Applied Statistics, 4(1): 15 – 18. [12] Hannan, E. J. and Quinn, B. G. (1979). The Determination of the Order of an Autoregression. Journal of the Royal Statistical Society, Series B, 41, 190 – 195. [13] Jagathnath, K. K. M., Nithujanathan, V. S., Giriyappa, K. and Chandramouli, D. (2013). Identification of SARIMA as a model for forecasting Indian Leather Export. International Journal of Research in Management, 3(6): 18 – 30. [14] Mahsin, M., Akhter, Y. and Begun, M. (2012). Modeling Rainfall in Dhaka Division of Bangladesh Using Time Series Analysis. Journal of Mathematical Modelling and Application, 1(5): 67 – 73. [15] Meshran, D. T., Gorantiwar, S. D., Singh, N. V. and Pal, R. K. (2014). SARIMA for generation and forecasting of pomegranate (Punica granatum L.) evapotranspiration of Solapur district of Maharashtra, India. 2nd International Conference on Agricultural & Horticultural Sciences, Radisson Biu Plaza Hotel, Hyderabad, India, February 03 – 05, 2014. www.amicsgroup.org/journals/2168-9881/2168-9881-51.007-082.pdf. [16] Otu, A. O., Osuji, G. A., Opara, J., Mbachu, H. I. and Iheagwara, A. I. (2014). Application of Sarima Models in Modelling and Forecasting Nigeria’s Inflation Rates, American Journal of Applied Mathematics and Statistics, 2(1): 16 – 28. [17] Pattranurakyothin, T. and Kumnungkit, K. (2012). Forecasting Model for Para Rubber’s Export sales. KMITL Sci. Tech. J., 12(2): 198 – 202. [18] Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6, 461 – 464. [19] Smolen, H. J. (2014). Development of an Influenza Outbreak Forecasting Model Using Time Series Analysis methods, presented at the Pharmacoeconomics and Outcomes Research (ISPOR), 17th Annual European Congress, 8 – 12 November 2014. www.ispor.org/research_pdfs/48/pdffiles/PRM102.pdf [20] Suleman, N. and Sarpong, S. (2011). Modeling the Pattern of Reserve Money Growth in Ghana. Current Research Journal of Economic Theory, 4(2): 39 – 42.