Abrupt Temporary Impact

In Time Series , the abrupt temporary impact pattern implies an initial abrupt increase or decrease due to the intervention which then slowly decays, without permanently changing the mean of the series. This type of intervention can be summarized by the expressions:
Prior to intervention: Impactt = 0
At time of intervention: Impactt=
After intervention: Impactt = *Impactt-1
Note that this impact pattern is again defined by the two parameters (delta) and (omega). As long as the parameter is greater than 0 and less than 1 (the bounds of system stability), the initial abrupt impact will gradually decay. If is near 0 (zero) than the decay will be very quick, and the impact will have entirely disappeared after only a few observations. If is close to 1 then the decay will be slow, and the intervention will affect the series over many observations. Note that, when evaluating a fitted model, it is again important that both parameters are statistically significant; otherwise one could reach paradoxical conclusions. For example, suppose the parameter is not statistically significant from 0 (zero) but the parameter is; this would mean that an intervention did not cause an initial abrupt change, which then showed significant decay.