Forecasting hierarchical and grouped time series

Host institution: RMIT University

Seminar Abstract:

Time series can often be naturally disaggregated in a hierarchical or grouped structure. For example, a manufacturing company can disaggregate total demand for their products by country of sale, retail outlet, product type, package size, and so on. As a result, there can be thousands (or even millions) of individual time series to forecast at the most disaggregated level, plus additional series to forecast at higher levels of aggregation. The disaggregated forecasts need to add up to the forecasts of the aggregated data. This is known as reconciliation.

I will show that the optimal reconciliation method involves fitting an ill-conditioned linear regression model where the design matrix has one column for each of the series at the most disaggregated level. For problems involving huge numbers of series, the model is impossible to estimate using standard regression algorithms.

For strictly hierarchical time series, it is possible to construct an algorithm where the computations can be handled efficiently by exploiting the structure of the associated design matrix. This algorithm allows the reconciliation of forecasts with hierarchies of unlimited size, making forecast reconciliation feasible in business applications involving very large numbers of time series. I will demonstrate this algorithm in real time on problems involving a few hundred thousand time series.

Seminar Convenor: Stelios Georgiou