ARX Modeling of Time Series

In this chapter we shall address the estimation of linear statistical models involving time, where the data of the inference problems are sequences of observations indexed by time. Due to errors and various causes of uncertainty these data are random and It is therefore reasonable to model them as trajectories of a stochastic process. The scope of the statistical exercise is to discover a stochastic mathematical model of the underlying physical or economic dynamical system for the purpose of prediction and control. We only concentrate on estimation of (stationary) ARX models since more general structures like ARMAX or ARIMAX lead to nonlinear estimation and unique convergence of the algorithms is not guaranteed. Moreover the analysis of these systems requires tools which we do not assume available to the students of this course.