Temporal modelling of fire outbreaks case study: Ashanti region of Ghana

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November, 2015
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In spite of advances in technology, occurrence of Fire Outbreaks is growing at an increasing rate all over the world but particularly in developing countries like Ghana. It is thus worrying that not much work appears to have been done in Ghana regarding the formulation of statistical and other models for predicting Fire Outbreaks. Due to this, actuarial and insurance practitioners are unable to e ectively help manage the risk of Fire Outbreaks. A Fire Outbreaks is a sudden occurrence of re greater than would otherwise be expected at a particular time and place. Fire is a rare event often classi ed an 'Extremal event' and is characterized by relative rareness, huge impact, and statistical unexpectness. In this study, monthly time series data on Fire Outbreaks was obtained from Ghana's Ashanti Regional Fire Service database and was modelled using both SARIMA model and exponentially distributed survival model for monthly prediction of re occurrences and Fire Premium calculations respectively. The results revealed that ARIMA (4; 1; 1)(1; 1; 1)12 model was the best SARIMA model for the Fire Outbreaks. This model has the least AIC of 151.1116 and BIC of 176.9176. Diagnostic checks of this model with the Ljung- Box test and ARCH-LM test revealed that the model is free from higher-order serial correlation and conditional heteroscedasticity respectively. Moreover, the re premium calculation was based on the equivalence principle of calculating insurance premium approach based more on frequencies than on severity. A more complete risk portfolio model is suggested depending on the availability of data, which would capture both severity and frequency.
A Thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in partial fulfilment of the requirements for the award of the degree of Master of Philosophy in Acturial Science, 2015