Regularized regression for hierarchical forecasting without unbiasedness conditions

Forecasting a large set of time series with hierarchical aggregation constraints is a central problem for many organizations. However, it is particularly challenging to forecast these hierarchical structures. In fact, it requires not only good forecast accuracy at each level of the hierarchy, but also the coherency between dierent levels, i.e. the forecasts should satisfy the hierarchical aggregation constraints. Given some incoherent base forecasts, the state-of-the-art methods compute revised forecasts based on forecast combination which ensures that the aggregation constraints are satised. However, these methods assume the base forecasts are unbiased and constrain the revised forecasts to be also unbiased. We propose a new forecasting method which relaxes these unbiasedness conditions, and seeks the revised forecasts with the best tradeo between bias and forecast variance. We also present a regularization method which allows us to deal with high-dimensional hierarchies, and provide its theoretical justication. Finally, we compare the proposed method with the state-of-the-art methods both theoretically and empirically. The results on both simulated and real-world data indicate that our methods provide competitive results compared to the state-of-the-art methods.