Time Series Analysis Intervals and Energy Economics Forecast[Analyse des séries temporelles intervalles et prévision en économie de l'énergie]

This working paper presents the methods for estimating the parameters of a regression model when the variables are observed in an interval format. It illustrates this estimation procedure on electricity consumption data in France, in order to make a comparison between the forecast values ​​from the interval data and the confidence interval of the forecast from the point data. First, we show that the use of single values ​​to characterize an economic variable leads to a loss of information. In a second step, these estimation methods were applied to interval electricity consumption data in France for forecasting purposes. Examining the evolution of our data via tests allowed us to detect a seasonal effect, but not an extra-seasonal one. Thus, the estimation procedures are implemented on seasonally adjusted data by the Census X12 method, and the forecast will take into account the seasonal coefficients obtained after seasonal adjustment. To measure the value of analysis on interval data, we compared the forecast on interval data to the confidence interval of the forecast on point data. In the last section, the observation of the profile of the forecast confidence intervals and that of the forecasts on the interval data revealed the inclusion of the confidence interval of the forecast on the classical data, in the bounds predicted by the interval data. This inclusion persists with the increase in the level of confidence in the forecast confidence interval. We therefore concluded on the impossibility of conventional data to cover the range of the true value of the variable studied.