Autoregressive Modeling and Forecasts of Degema Monthly Allocation: Buy’s-Ballot and Bartlett’s Transformation
Herbert, AfeyaIbibo
Department of Mathematics/ Statistics, Faculty of Natural and Applied Science, Ignatius Ajuru University of Education, Port Harcourt, Rivers State, Nigeria.
Biu, Oyinebifun Emmanuel
Department of Mathematics and Statistics, Faculty of Science, University of Port Harcourt, Nigeria.
Enegesele, Dennis *
Department of Mathematics and Computing Sciences, Kola Daisi University, Ibadan, Nigeria.
Wokoma, Dagogo Samuel Allen
Department of Mathematics and Statistics, Captain Elechi Amadi Polytechnic, Rumuola, Port Harcourt, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The paper focused on Autoregressive modeling and forecasts of Degema Local Government Council Monthly Allocation (DLGCMA) in River State, Nigeria. The Buys-Ballot table and Bartlett’s Transformation method were adopted to identify the trend pattern and to determine the best transformation for the series. The logarithmic transformation was adjudged to be the best and was applied to stabilize the variance. Identification of the trend and stationary for the data set was done and the DLGCMA series showed a linear trend that was non-stationary. The stationarity of the DLGCMA series was obtained after the first difference. The ARIMA models were fitted to the series base on the behaviour of autocorrelation function (ACF) and partial autocorrelation function (PACF). Finally, the model selection criteria called Akaike information criterion was used to determine the best model among the predicted models. The AR(3,1,0) model ( Xt = 0.56Xt-1 + 0.17Xt-2 + 0.64Xt-3 - 0.37Xt-4 + et) was considered to be the best model because it has the least value of the Akaike information criterion (AIC). Hence, the forecasts for the next allocation of twenty-four (24) months ahead were determined.
Keywords: Autoregressive modeling, forecasts, buys-ballot table, bartlett’s transformation method, Akaike Information Criterion (AIC).