摘要
There has been a moderate increase in newly diagnosed HIV-infected Minna populace, which calls for serious attention.<span style="font-family:;" "=""> </span><span style="font-family:Verdana;">This study</span><span style="font-family:;" "=""> </span><span style="font-family:Verdana;">used time series data based on monthly HIV cases from January 2007 to December 2018 taken from the statistical data document on HIV prevalence recorded in General Hospital Minna, Niger State.</span><span style="font-family:;" "=""> </span><span style="font-family:Verdana;">The methodology employed to analyze the data is base</span><span style="font-family:Verdana;">d</span><span style="font-family:;" "=""><span style="font-family:Verdana;"> on mathematical models of ARMA, ARIMA and SARIMA which were computed and diagnosed. From the results of parameter estimation of </span><span style="font-family:Verdana;">the models, ARMA(2, 1) model was the best model among the other ARMA models using information criteria (AIC). Diagnostic test was run on the ARMA(2, 1) model where the results show that the model was adequate and normally distributed using Box-Lung test and Q</span></span><span style="font-family:Verdana;">-</span><span style="font-family:Verdana;">Q plot respectively. Fur</span><span style="font-family:Verdana;">thermore, ARIMA of first and second differences w</span><span style="font-family:Verdana;">as</span><span style="font-family:Verdana;"> estimated and ARIMA(1,</span><span style="font-family:;" "=""> </span><span style="font-family:Verdana;">0,</span><span style="font-family:;" "=""> </span><span style="font-family:Verdana;">1) was the best model from the result of the AIC and diagnostic test carried out which revealed that the model was adequate and normally distributed using Box-Lung and Q-Q plot respectively. Furthermore, the results obtained in the ARMA and ARIMA models were used to arrive at a combined model given as ARIMA(1, 0, 1) </span><span style="font-family:;" "=""><span style="font-family:Verdana;">×</span><span><span style="font-family:Verdana;"> SARIMA(1, 0, 1)</span><sub><span style="font-family:Verdana;">12</span></sub></span></span><span style="font-family:;" "=""> </span><span style="font-family:Verdana;">which was subsequently estimated and found to be adequate from the result of the Box-Lung and Q-Q plot respectively. Post forecasting estimation and performance evolution were evaluated using the RMSE and MAE. The results showed that, ARIMA(1, 0, 1) </span><span style="font-family:;" "=""><span style="font-family:Verdana;">×</span><span><span style="font-family:Verdana;"> SARIMA(1, 0, 1)</span><sub><span style="font-family:Verdana;">12</span></sub><span style="font-family:Verdana;"> is the best forecasting model followed by ARIMA(1, 0, 2) on monthly HIV prevalence in Minna, Niger state.</span></span></span>
There has been a moderate increase in newly diagnosed HIV-infected Minna populace, which calls for serious attention.<span style="font-family:;" "=""> </span><span style="font-family:Verdana;">This study</span><span style="font-family:;" "=""> </span><span style="font-family:Verdana;">used time series data based on monthly HIV cases from January 2007 to December 2018 taken from the statistical data document on HIV prevalence recorded in General Hospital Minna, Niger State.</span><span style="font-family:;" "=""> </span><span style="font-family:Verdana;">The methodology employed to analyze the data is base</span><span style="font-family:Verdana;">d</span><span style="font-family:;" "=""><span style="font-family:Verdana;"> on mathematical models of ARMA, ARIMA and SARIMA which were computed and diagnosed. From the results of parameter estimation of </span><span style="font-family:Verdana;">the models, ARMA(2, 1) model was the best model among the other ARMA models using information criteria (AIC). Diagnostic test was run on the ARMA(2, 1) model where the results show that the model was adequate and normally distributed using Box-Lung test and Q</span></span><span style="font-family:Verdana;">-</span><span style="font-family:Verdana;">Q plot respectively. Fur</span><span style="font-family:Verdana;">thermore, ARIMA of first and second differences w</span><span style="font-family:Verdana;">as</span><span style="font-family:Verdana;"> estimated and ARIMA(1,</span><span style="font-family:;" "=""> </span><span style="font-family:Verdana;">0,</span><span style="font-family:;" "=""> </span><span style="font-family:Verdana;">1) was the best model from the result of the AIC and diagnostic test carried out which revealed that the model was adequate and normally distributed using Box-Lung and Q-Q plot respectively. Furthermore, the results obtained in the ARMA and ARIMA models were used to arrive at a combined model given as ARIMA(1, 0, 1) </span><span style="font-family:;" "=""><span style="font-family:Verdana;">×</span><span><span style="font-family:Verdana;"> SARIMA(1, 0, 1)</span><sub><span style="font-family:Verdana;">12</span></sub></span></span><span style="font-family:;" "=""> </span><span style="font-family:Verdana;">which was subsequently estimated and found to be adequate from the result of the Box-Lung and Q-Q plot respectively. Post forecasting estimation and performance evolution were evaluated using the RMSE and MAE. The results showed that, ARIMA(1, 0, 1) </span><span style="font-family:;" "=""><span style="font-family:Verdana;">×</span><span><span style="font-family:Verdana;"> SARIMA(1, 0, 1)</span><sub><span style="font-family:Verdana;">12</span></sub><span style="font-family:Verdana;"> is the best forecasting model followed by ARIMA(1, 0, 2) on monthly HIV prevalence in Minna, Niger state.</span></span></span>
