Like the outlier and transfer function models, intervention models belong to the univariate time series models with which the occurrence of conspicuous observation values can be modeled. The intervention model assumes that the time t at which the abnormal observation value occurs is known. A distinction can be made between interventions, which
- unique ,
- for an indefinite period or
- for a certain duration
This is modeled with the help of an indicator function I. In addition, the strength or duration of the effect must be modeled. This is done with a lag operator polynomial , which is also referred to as the impulse response function . It determines whether the effect of the intervention wears off over time, is intensified, or is constant. A possible formal notation would be:
A time series can also be affected by several interventions of different types occurring at different times . This is known as the multiple intervention model. The estimate of the entire model can be estimated using the maximum likelihood method . The noise model as well as the impulse-response function must be identified beforehand. In doing so, one must fall back on expert knowledge of the observed time series . If there are several possible models to choose from, the suitable model can be selected using a selection criterion.