Time series analysis of enrolment of pupils in public second cycle schools in Assin South District

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Education plays an important role in a developing country like Ghana. Education is needed to improve productivity as a result of harnessing human resources effectively. After the basic education, the pupils are enrolled in the second cycle schools through the Basic Education Certificate Examination (BECE). The study analyses the mean number of pupils enrolled in the public second cycle schools in Assin South District in the Central Region of Ghana (from 1991 to 2012). It also uses the Box-Jenkins modeling to fit a model to the enrolment of pupils in the four (4) public second cycle schools, which can be used to predict future enrolment in the district. The secondary data obtained from the four (4) public second cycle schools in the district was made up of twenty-two (22) consecutive years of number of pupils enrolled from 1991 to 2012. The Box-Jenkins ARIMA modeling was used to model the data. The appropriate ARIMA models; ARIMA (2, 2, 1), ARIMA (2, 2, 2) and ARIMA (2, 2, 3) were chosen based on the autocorrelation and partial autocorrelation functions. The estimation of the model parameters was carried out using the maximum likelihood estimation method with the R statistical software package. The ARIMA (2, 2, 1) model was selected as the best model since its AIC and BIC values were far lower than the other competing models. The T-test revealed that the MA part of the ARIMA (2, 2, 1) was statistically not significant and the final ARIMA model for forecasting was ARIMA (2,2,0). It was observed that enrolment of pupils in the public second cycle schools in the district had been increasing and it may also increase in 2013, 2014 and 2015.
A thesis submitted to the Department of Mathematics in partial fulfillment of the requirements for the award of the degree of Master of Science (Industrial Mathematics), 2014