On Statistical Analysis and Modeling of Rare Events with Autoregressive integrated Moving Average (Arima) Model.
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Date
2014-11
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Publisher
Journal of the Nigerian Association of Mathematical Physics
Abstract
Forecasting methods to produced numerical estimates range from relative simple techniques to complex and sophisticated
techniques are discussed in this paper. Among forecasting methods were extrapolative or projective techniques i.e. moving averages and exponential smoothing. A moving average is a trend method wherein each point of a moving average of a time series is the arithmetic mean of a number of consecutive observations of the series. The number of observations in the moving average computation is chosen to minimize the effect of seasonality or other disturbances in the series [l-4]. Exponential smoothing is a flexible trend whereby past data observations arc given different weights in computing the forecast. It has the advantages of providing a simple up-to-date forecast where the new forecast is equal to the previous one plus some stated proportion of the previous periods of a forecasting error. Exponential smoothing methods are adaptable to adjustment to include trend and seasonal projections with adaptive types of optimum weighting procedures. Exponential smoothing methods are used to forecast large numbers of items. Time series decomposition methods are widely used to identify the systematic components of a time scries, trend cycle and seasonal pattern and the non systematic or random component. The seasonal Pattern is identified by first determining the seasonal indexes for each month or quarter of year and
in turn these patterns arc projected ahead. The cyclical forecast may be prepared by other systematic projection or by
economic judgment. Non systematic or irregular variation is usually assumed zero in a forecast but irregular adjustments may be needed for an anticipated stoppage in production or some other casual factors in the time period of the forecast. A highly analytical method for measuring seasonal fluctuations is called census I l or X-l l variant. In Regression models express the past relationships among the item being forecasted. These models are useful when adequate history of data are available on the major factors associated with variations in the item being forecasted [5,6].
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Keywords
Rare Event, ARIMA, MSE, Poisson Distribution, ARRSES