American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: Editor-in-chief: Mohamed Seddeek
Open Access
Journal Browser
American Journal of Applied Mathematics and Statistics. 2014, 2(3), 172-178
DOI: 10.12691/ajams-2-3-14
Open AccessArticle

Forecast Performance of Multiplicative Seasonal Arima Model: an Application to Naira/Us Dollar Exchange Rate


1Department of Statistics, University of Ibadan, Nigeria

Pub. Date: June 11, 2014

Cite this paper:
ONASANYA OLANREWAJU. K, OLUSEGUN ALFRED OLAKUNLE and ADENIJI OYEBIMPE EMMANUEL. Forecast Performance of Multiplicative Seasonal Arima Model: an Application to Naira/Us Dollar Exchange Rate. American Journal of Applied Mathematics and Statistics. 2014; 2(3):172-178. doi: 10.12691/ajams-2-3-14


Seasonality accounts majorly for quarterly and monthly movements in macro-economics and time series and in modelling such patterns to have a forecasting robustness, precision and reliability have been steadily increased in recent years but no consensus has been reached as to which model yields the appropriate description. However, this research seeks to address the robustness and accuracy of seasonal ARIMA model of Naira/Dollar exchange rate using a monthly data for the period of Jan 1994 to July 2013. The series was subjected to a time plot revealing seasonal patterns and upward trend. Both behaviours were taken into account by moving average and seasonal moving average, where little or fewer months of data were used to estimate the local level and trend and also few seasons of data were averaged over to estimate the seasonal patterns. The proposed model shows predictive power, robustness and precision which was revealed by the normality of data and residual analysis. The estimated forecast values from our proposed model are more realistic and closely reflect in the current economic reality in two countries as indicated by the forecast measurement criteria.

autocorrelation function partial autocorrelation function time plot exchange rate LM test Non – seasonal components seasonal components mean squared error mean absolute percentage error

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit


[1]  Box, G.E.P and Jenkins, G.M. (1976). Time series Analysis: Forecasting and Control, Revised Edition, Holden-Day.
[2]  Brockwell, P.J. and Davis, R. (2002). A. Introduction to Time series and Forecasting. Springer-Verlag, New York.
[3]  Brillinger, M. et. al (2008). Time series data Analysis and Theory Expanded Edition, Mc-Graw-Hill Inc. New York.
[4]  Chatfield, C. (2003). The Analysis of Time series: An introduction. Chapman and Hall, London.
[5]  Damodar N.G. & Dawn C.P (2006). Basic Econometrics. M.C. Graw Hill.
[6]  Dickey, D.A and Fuller, W.A. (1979). Distribution of the estimators for Autoregressive time series with a unit root. Journal of the American Statistical Association. 74: 427-431.
[7]  Ghysels, E. and Osborn, D.R. The Econometric Analysis of Seasonal Time series. Cambridge, U.K: Cambridge University.
[8]  E Ghysels, Osborn, D.R, Rodrigues, P. (2006). Forecasting Seasonal Time series, in Handbook of Economic Forecasting. Vol. 1, ed. Elliot, G., Granger, C. and Timmermann, A. pp: 659-711. Elsevier.
[9]  Hamilton, J. (1994). Time series Analysis. Princeton, New Jersey: Princeton University Press.
[10]  Hooper, P and J. Martins (1982): Fluctuations in the dollar: A model of nominal and real exchange rate determination”. Journal of International Money and Finance. 1: 39-56.
[11]  Ljung, G.M and G.E.P Box (1978). On a Measure of lack of fit in time series models. Biometrika. 65: 297-303.
[12]  Mills, T.C (1999). The Econometric Modeling of Financial Time series. Cambridge University Press.
[13]  Pfaff, B (2004). Urca “Unit root and Cointegration test for time series” R Package, version 0, 6-1.
[14]  Theil, H. (1966). Applied Economic Forecasting. North-Holland, Amsterdam.