Iterative Trace Minimization for the Reconciliation of Very Short Hierarchical Time Series

Abstract: Time series often appear in an additive hierarchical structure. In such cases, time series on higher levels are the sums of their subordinate time series. This hierarchical structure places a natural constraint on forecasts. However, univariate forecasting techniques are incapable of ensuring this forecast coherence. An obvious solution is to forecast only bottom time series and obtain higher level forecasts through aggregation. This approach is also known as the bottom-up approach. In their seminal paper, \citep{Wickramasuriya2019} propose an optimal reconciliation approach named MinT. It tries to minimize the trace of the underlying covariance matrix of all forecast errors. The MinT algorithm has demonstrated superior performance to the bottom-up and other approaches and enjoys great popularity. This paper provides a simulation study examining the performance of MinT for very short time series and larger hierarchical structures. This scenario makes the covariance estimation required by MinT difficult. A novel iterative approach is introduced which significantly reduces the number of estimated parameters. This approach is capable of improving forecast accuracy further. The application of MinTit is also demonstrated with a case study at the hand of a semiconductor dataset based on data provided by the World Semiconductor Trade Statistics (WSTS), a premier provider of semiconductor market data.