A starting point for the concept of ITSA is Shadish, Cooke, & Campbell (2002) and a starting palce for the mathematical procedures for ITSA is Glass, Wilson, & Gottman (1975).
Some researchers may recommend a dummy code moderator in a multiple regression, where 0 represents no intervention and 1 represents intervention:
This is a simple solution and may work if you do not care about autocorrelation.
However, the interrupted time series (ITSA) allows you to include autoregressive and moving average components:
where $z_t$ is the observed value of teh DV at time point $t$, $AR$ is the order of autoregression of the series, $I$ is the order of differencing required to create a stationary series, $MA$ is the order of moving average of the series, and $a_t$ is the error.
Alternatively, and more precisely, an ARIMA (p, d, q) process may be modeled by:
where $ϕ$ is the autocorrelation coefficient, $θ$ is the moving average coefficient, and $Δzt=zt−zt−d$ when $d>0$. When $d=0$, $Δzt=zt−1$ or simply $Δzt$ is ignored, depending on the order of p and q.
You can identify $ϕ$, $θ$, and $Δ$ using software, such as Rob Hyndman's
auto.arima in R. The models are all different given the order of the coefficients and I do not know of any comprehensive source for all possible ITSA or a generalization thereof. Generally, though, there is a level at baseline, $L$, and a change from that level in the treatment phase, $\delta$, where the level of the treatment phase is $L+\delta$. This is similar to the dummy coding solution, but now you are incorporating the ARIMA model. You may need to derive the model yourself, as I did for an ARIMA(1,1,0) in a submitted manuscript where most of this information comes from (Raadt, in-press).
Glass, G. V., Willson, V. L., Gottman, J. M. (1975). Design and analysis of time-series experiments. Boulder, CO: Colorado Associated University Press.
Shadish, W. R., Cook, T. D., & Campbell, D. T. (2002). Experimental and quasi-experimental designs for generalized causal inference. Boston, MA, US: Houghton, Mifflin and Company.