Event Details

Dr Anastasios Panagiotelis from University of Sydney Business School will present a seminar to the Management Science Department.

Abstract: Collections of time series where some series are aggregates of one another, are known as hierarchical time series. When forecasting hierarchical time series, the linear constraints due to this aggregation structure may not hold. Forecast reconciliation allows for the adjustment of such forecasts ex post, to ensure that aggregation constraints are satisfied, i.e. forecasts are coherent. In the probabilistic setting, this implies that regions of points that do not satisfy the constraints are assigned zero probability, or alternatively, that a sample from the predictive distribution only contains coherent points. In this work, an algorithm for forecast reconciliation is proposed targeting optimality with respect to a given quantile level. This framework builds upon the score optimisation framework introduced by Panagiotelis et al (2023) but uses the pinball loss as the objective function. Due to the fact that the reconciled quantiles are themselves the solution to an optimisation involving pinball loss, the problem become one of bilevel optimisation. While we show that the problem can be solved by mixed integer linear programming, this proves to be slow to compute even with modern solvers and moderately sized hierarchies. Therefore we propose an approximate technique based on a smooth version of the pinball loss function. By exploiting a lemma that allows gradients to be found in bilevel optimisation problems, we show that the problem can be tackled using gradient based methods such as stochastic gradient descent. The proposed method will be demonstrated with an application to Australian tourism data.

Bio: Anastasios Panagiotelis is an Associate Professor and Deputy Head of Business Analytics at the University of Sydney Business School. He is also a Director of the International Institute of Forecasters and Associate Editor of the International Journal of Forecasting. His work lies in the intersection of business analytics, statistics and econometrics. He has published in a diverse range of top-tier journals including the Journal of the American Statistical Association, Journal of Econometrics and the European Journal of Operational Research and he led the Australian Research Council Discovery Project “ Macroeconomic Forecasting in a Big Data World ”. Anastasios received his PhD from the University of Sydney and was previously a member of Faculty at Monash University and an Alexander von Humboldt Postdoctoral Researcher in the Faculty of Mathematics at the Technical University of Munich.