Sparse and Smooth Adjustments for Coherent Forecasts in Temporal Aggregation of Time Series

Independent forecasts obtained from different temporal aggregates of a given time series may not be mutually consistent. State-of-the art forecasting methods usually apply adjustments on the individual level forecasts to satisfy the aggregation constraints. These adjustments require the estimation of the covariance between the individual forecast errors at all aggregation levels. In order to keep a maximum number of individual forecasts unaffected by estimation errors, we propose a new forecasting algorithm that provides sparse and smooth adjustments while still preserving the aggregation constraints. The algorithm computes the revised forecasts by solving a generalized lasso problem. It is shown that it not only provides accurate forecasts, but also applies a significantly smaller number of adjustments to the base forecasts in a large-scale smart meter dataset.