Using the Bootstrap method to determine uncertainty bounds for change point utility bill energy models

Statistical inverse modeling of energy use in buildings and of HVAC&R equipment and systems has been widely researched, and are fairly well ingrained in the profession. However, there are still a few nagging issues; one of them is related to the accuracy in estimating model prediction uncertainty bands at a pre-specified confidence level. This issue is important since it bears directly on the risk associated with the identified energy savings. While several papers have been published dealing with uncertainty in statistical models, the non-heteroscedascity and the non-gaussian behavior of the residuals are problematic to handle using classical statistical equations of model prediction uncertainty. This paper proposes and illustrates the use of the Bootstrap method as a robust and flexible alternative approach to determining uncertainty bands for change point model predictions identified from utility bills. In essence, the bootstrap method works by taking a data set and resampling it with replacement. In the case of utility bill analysis, one starts with 12 data points representing energy use for each month of the year. Such samples are repeatedly generated to produce a large (say, m) number of synthetic data sets from which m different change point models can be identified. These m models are used to make predictions at any pre-specified outdoor temperature, and the 95% (or any other) prediction interval bands can be determined non-parametrically from the m data predictions. This paper fully describes and illustrates this approach along with a case study example.