Arma Type Modeling of Certain Non-stationary Time Series in Calabar

Abstract

Divergently different time series are considered in this article. The monthly passengers traffic at Cross lines limited, Calabar from 1990 to 2015 and monthly incidence of tuberculosis diseases at University of Calabar Teaching Hospital based from 1990-2015. The research adopted the statistical models based on time series analysis by Box and Jenkins methodology via the autocorrelation and the partial autocorrelation functions which showed that the two series are not stationary. Logarithm transformation was used to stabilize the variances of the two series and the residual autocorrelation and the partial autocorrelation functions is made stationary. Both regular and seasonal differencing was applied to the two-transformed set of data to obtain stationary series. The study employed ARIMA model on the classes of the two series, and the parameters of the identified model were estimated by the use of SPSS. The two models so chosen were ARMA (2,1,0) x (1,1,1)12 for passengers’ traffic and ARMA (1,0,1) x (1,1,2)12 for tuberculosis cases and forecasts was done for 12 months for the two series. The adequacy of the model was achieved and model fit for passengers traffic yields R-square, RMSE and MAPE of 0.876, 9.137, and 27.479 respectively and for tuberculosis cases yields R-square, RMSE and MAPE of 0.614, 6.785 and 26.522 respectively, recommendation and conclusion was made for the area of study.