Robust short-term load forecasting using projection statistics

It has been observed that the French electric load series possesses outliers and breaks. Outliers are deviant data points while breaks are lasting abrupt changes in the stochastic pattern of the series. It turns out that outliers and breaks significantly degrade the reliability and accuracy of conventional day-ahead estimation and forecasting methods. Robust methods are needed for this application. In this paper, we propose to use a robust diagnostic approach for which the identification of outliers and breaks is carried out via a robust multivariate estimation of location and covariance based on projection statistics (PS). The developed procedure consists of the following steps: (i) estimate the parameters and the order of a high order autoregressive AR(p*) by means of the PS, (ii) execute a robust filter cleaner to identify and reject the outliers, and (iii) apply a maximum-likelihood estimator defined at the Gaussian distribution that handles missing values. The performance of this method has been evaluated on the French electric demand in terms of execution time and forecasting accuracy. This approach improves the load forecasting quality for "normal days" and presents several interesting properties such as fast execution, good robustness, simplicity and easy on-line implementation. A novel multivariate approach is also proposed in order to deal with heteroscedasticity.