The Box-Jenkins method or the Box-Jenkins program goes to G. E. P. Box and G. M. Jenkins and her book of 1970 Time Series Analysis - Forecasting and Control back. It marked a new epoch in the time series analysis. In contrast to the previously prevailing trend model, which assumed a deterministic process, Box and Jenkins are based on a stochastic process, with whose assistance is the modeling of a time series. An important consequence of this approach is that (random) shocks can have a lasting effect on subsequent time series values . This is mainly for economic time series a more realistic assumption.
An important dogma of the Box-Jenkins method is the so-called law of parsimony. This calls for an economical parameterization of the model in terms of the smallest possible number of parameters.