Algorithm for explicit solution to the three parameter linear change-point regression model

Abstract

Linear change-point models (also known in the building industry as energy-signature models) are commonly used for the monitoring and verification of whole building energy consumption. They have proven to be useful in a variety of ways, from estimating building parameters to aiding in the calibration of simulations. Currently, there has been no agreed upon standard for the method used to fit these models. Current implementations for determining the coefficients of the regression model use various types of search routines with convergence criteria. The current article presents a method that returns the best estimates of the coefficients for three parameter linear change-point model with the sum of squared errors as the loss function. The method is robust, exact, and straightforward to program.