Intervention Analysis Evaluating the Transient Response

Traditionally, if a time series was subjected to a known intervention occurring at a specific time, its effect in changing the mean level of the time series was evaluated using a two-sample t-test (Liu and Hudak 2004). However, the t-test is not appropriate in the case of serially correlated data (Box and Tiao 1965). Further, this test may not be appropriate where the intervention is a pulse lasting some t time periods. 

Box and Tiao (1975) subsequently developed a procedure for analysis of a time series in the presence of known external interventions. In their approach, there are two types of interventions - pulses and steps. A pulse is an intervention with a finite duration (typically one time period), while a step involves a permanent change or intervention (e.g., the introduction of a new governmental regulation or the permanent loss of a supplier). Intervention analysis is a statistical procedure that enables the researcher to evalnate the impact on a time series, as represented by an ARIMA (Autoregressive Integrated Moving Average) process. 

There are several components in an intervention model a deterministic component describing the intervention(s), the associated response of the system to the intervention, and a stochastic disturbance term. The overall modeling strategy is to obtain reasonable initial representations for these components and to iterate to a final model based on intermediate estimates, diagnostic checks, and model interpretations (Liu and Hudak 2004). 

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