The computational efficiency of outlier estimates for different generating process

Abstract

The performances of non-seasonal time series models assumed on outlier free series in describing the generating mechanism of an outlier is discussed. The contribution of the magnitude of outliers and bias introduced into these models are investigated. Analytically we have shown that the magnitude of outlier depends on the respective weight of their generating mechanism, although it was found that for an additive outlier model the estimates of outliers gave an unbiased estimate of the actual values observed. For a given innovative model, the first observation, if certified as outlier, has the same magnitude as the actual observed value. The efficiency of the estimates of the outliers varies according to the weights of their generating mechanisms. Analytically, additive model is more efficient for all the generating mechanism if the weights ${\mathit{\pi }}_{\mathit{i}}$ ’s lie within the unit circle. An empirical comparison of the analytical study is considered using three simulated series.