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Holighi, Khalil Shafie

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The asymmetric loss function is used in a situation where a positive error may be more serious than a negative error of the same magnitude or vice versa. One of the most commonly used asymmetric loss functions is the linex loss. The linex unbiased predictor has been developed and applied to real world applications. This study investigated how the linex unbiased prediction behaves when time series processes, AR(p), MA(q) and ARMA (p,q), parameters are unknown and being estimated, with different levels of variance, forecast step, shape parameter and series length. It started with deriving the predictor for each time series process, computing this predictor, and then discussing its properties. Empirical studies of the behavior of this predictor were investigated by using the Monte Carlo simulation. The results of this study showed that, a simpler time series model produced values that were closer to the condition of linex unbiasedness than a complex model. The condition of linex unbiasedness was affected by the variance but not the sign of the linex loss function shape parameter. For any time series model and any condition, as series length increased, the condition of linex unbiasedness values approached zero. When the time series parameters are unknown, the prediction is asymptotically linex unbiased.


Autoregressive moving average, Linex loss, Unbiased prediction


238 pages

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