Abstract
In this paper, the Box-Jenkins modelling procedure is used to determine an ARIMA model and go further to forecasting. We consider data of Malaria cases from Ministry of Health (Kabwe District)-Zambia for the period, 2009 to 2013 for age 1 to under 5 years. The model-building process involves three steps: tentative identification of a model from the ARIMA class, estimation of parameters in the identified model, and diagnostic checks. Results show that an appropriate model is simply an ARIMA (1, 0, 0) due to the fact that, the ACF has an exponential decay and the PACF has a spike at lag 1 which is an indication of the said model. The forecasted Malaria cases for January and February, 2014 are 220 and 265, respectively.
Highlights
IntroductionWe discuss the Box-Jenkins modeling procedure to determine an Autoregressive Integrated Moving Average (ARIMA) model and forecast
Malaria remains one of the most causes of human morbidity and mortality with a high rate in Africa and Asia.Reference [1] states that, “the vast majority of cases (81%) were in the African region followed by South-EastAsia (13%) and Eastern Mediterranean Region (6%)”
The autocorrelation function (ACF) and partial autocorrelation function (PACF) show that the ACF decays exponentially and the PACF has a single spike at lag 1 indicating that the series is generated by an Autoregressive Integrated Moving Average (ARIMA) (1, 0, 0) process, X t =μ + φ ( X t −1 − μ ) + et
Summary
We discuss the Box-Jenkins modeling procedure to determine an ARIMA model and forecast. Box-Jenkins forecasting is of greatest use when the underlying factors causing demand for products, services, revenue, and, in this case, disease burden is believed to behave in the future in much the same manner as it did in the past [5]. Tentative identification of model—at this stage we use two graphical devices which are the estimated autocorrelation function (ACF) and an estimated partial autocorrelation function (PACF) as guides to choosing one or more Autoregressive Integrated Moving Average (ARIMA) models that are appropriate. If the tentatively identified model passes the diagnostic tests, the model is ready to be used for forecasting If it does not, the diagnostic tests should indicate how the model ought to be modified, and a new cycle of identification, estimation and diagnosis is performed.
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