A New Algorithm for Automated Box-Jenkins ARMA Time Series Modeling Using Residual Autocorrelation/Partial Autocorrelation Functions

Box-Jenkins time series modeling technique is a powerful tool. Yet, it requires a substantial amount of manual work and statistical skills for the user by inspecting the sample autocorrelation and partial autocorrelation function plots of a time series. This, in our opinion, prevents the technique from further applications in many areas. Therefore, it is highly desirable to automate the Box-Jenkins modeling technique. This paper has two major contributions. First, a new algorithm is proposed where by inspecting the sample autocorrelation function or the partial autocorrelation function of the model residuals, which is the key difference from Box-Jenkins', an ARMA( p, q) model can be automatically identified, estimated and diagnosed, without any manual interventions, for a stationary or invertible time series. And second, a new algorithm is proposed to identify the characteristics of correlograms, a fundamental step in the automated modeling processes.