ARIMA and ARIMAX Stochastic Models for Fertility in Nigeria
Journal Title: International Journal of Mathematics and Computer Applications Research (IJMCAR) - Year 2017, Vol 7, Issue 5
Abstract
The aim of this study to compare forecasting abilities of two time series models: Univariate autoregressive integrated moving average (ARIMA) and autoregressive integrated moving average with exogenous variable, (ARIMAX). A stochastic time series model for live births series in Nigeria was built, starting from an identified univariate ARIMA model. The first step in formulating the ARIMAX model for the series was to identify a suitable ARIMA model for such series. ARIMAX time series model is a healthy marriage between regression and ARIMA model. A univariate ARIMA (1, 1, 0) model was developed for the disaggregated live births series, and was found adequate in modelling the series, as confirmed by the results of the diagnostic checks conducted on the model. One of the demographic factors that could have influence on livebirths is the population of women-of-childbearing-age, which was the exogenous variable in the ARIMAX model. The cross-correlation function (ccf) of the bivariate process of the livebirths series and women-of-child-bearing-age series gave an indication that, live births were related to the current and previous lagged values of the predictor variable. Inclusion of the exogenous variable into the identified ARIMA model yielded ARIMAX (1,1,0,1) model. The results of the measures of model adequacy and forecast accuracy suggested that both the ARIMA and the ARIMAX models have satisfactory predictive ability for the live births series. The ARIMAX model was considered to be a more suitable model due to its slightly smaller AIC with better MAPE compared with the ARIMA model. It may be true that live births are also influenced by factors other than women-ofchildbearing- age, but the inclusion of this exogenous variable in the identified ARIMA model captured the major variations in live births in Nigeria. Forecast of future live births in Nigeria will aid in determining forecast demands of this demographic phenomenon on the various systems in the country.
Authors and Affiliations
Adekanmbi Damilola Bolanle, Akinyemi Oluwadare
Keywords
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