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Home  >  Volume 28. No.2 (Nov. 2014)

34.On Statistical Analysis and Modeling of Rare Events with Autoregressive Integrated Moving Average (Arima) Model- T.O. Olatayo, Mayor Andrew, O.O. Alabi and R.B. Afolayan Volume28, No. 2, (November, 2014), pp 235 – 244
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The study was carried out to analyse and model a rare event and forecast future occurrences. Rare events are those event that follows a Poisson distribution and are mostly non stationary in nature.

The Box-Jenkins approach for Autoregressive Integrated Moving Average (ARIMA) modeling and the Adaptive Response Rate Single Exponential Smoothing (ARRSES) method were employed in comparison for forecasting. The parameters estimated were Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC) and Mean

Square Error (MSE) respectively.

The results was obtained for three models, ARIMA (1,1,1), ARIMA (0,1,3) and ARIMA (2,0,0) and it showed that ARIMA (1,1,1) is the best fit. We compared ARIMA (1,1,1) with the Adaptive Response Rate Single Exponential Smoothing (ARRSES) method, which showed that forecast made by ARIMA models are more accurate and a reliable model to be fitted with minimum AIC, BIC and MSE.

In conclusion, this research provides a framework for the investigation of other rare events in future. The best model to be fitted for a rare event that follow Poisson process and are normally and independently distributed with a non stationary nature is ARIMA (1,1,1).

Keywords: Rare event, ARIMA, ARRSES,MSE, Poisson Distribution.