The TESLA Model consists of two parts: a highly parameterized non-linear regression model and a time series filter for forecast adjustment based on recent experience. Combined, they offer significant accuracy advantages. Energy demand is determined by a very large number of independent decisions made by a very large number of people. To attempt to model that kind of system, the TESLA Model takes an information-intensive approach to the problem.
Basic Model Structure
At the simplest level, the model is specified as a stratified nonlinear regression model. We stratify the sample first between the summer and winter “seasons” delineated on the Fall and Spring clock change days and then again into three groups for each season: weekdays, Saturdays, and Sundays.
The TESLA Model makes extensive use of two econometric techniques: variable parameters and piecewise linearization. Variable parameter models are used when the explanatory variables are normally significant in both the operational and the statistical sense, but the response of the dependent variable to changes in them is not constant. For example, in an energy model, the response of energy demand to changes in temperature is not at all the same across the hours of the day, or across the days of the week.
Piecewise linearization of the model recognizes that the response of energy demand to the relevant variables is not linear. Rather, the response is complexly nonlinear in a way that cannot be modeled by imposing a simple nonlinear functional form.
Variables such as economic and population growth do not vary quickly enough to be usefully included in a linear model of hourly or sub-hourly energy demand, but they do impact that demand. The TESLA Model includes a single non-linear latent trend parameter designed to capture the collective effects of these slower moving independent variables.
Error Correction Filter
Each TESLA Model uses available observed and forecast weather inputs to solve the model described above for the week preceding the current day plus the forecast period. It then compares real-time observed demand data with the demand backcast over the preceding week to identify error patterns using a dynamically stable time series filter method. Once identified, those error patterns are used to make slight adjustments to the short-range demand forecast.