Parameter Estimation and Change Detection in Linear Regression Models Using Mixed Integer Linear Programming

We present a method for detecting changes and estimating parameters in AR(X) models. The method is based on the assumption of piecewise constant parameters resulting in a sparse structure of their derivative. To illustrate the algorithm and its performance, we apply it to the change in the mean model and compare it with four other change detection algorithms. Two applications, fuel monitoring and airbag control are treated with good results. The AR(X) change model shows good performance of the method in two illustrative examples.