Intervention model

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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:


It is the ARMA part or the noise model , is the indicator function , and the impulse response function . The impulse-response function

has the polynomial in the denominator , which models the permanent effect of the intervention . The polynomial in the numerator represents the expected initial effect.

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.