FRT: Flow-based Reconcile Transformer for Hierarchical Time Series

Many real-world applications contain data in the form of multivariate time series (TS) with the hierarchical structure, where classic methods forecasting each TS independently are inadequate for coherency (i.e., satisfying the hierarchical aggregation constraints).Furthermore, the discrepancies between statistical properties of different levels can be huge, exacerbated by non-Gaussian distributions and non-linear correlations.In this paper, we propose a novel end-to-end hierarchical TS forecasting model, i.e., a Flow-based Reconcile Transformer (FRT).FRT employs a conditional normalizing flow-based autoregressive transformer, to represent complex data distribution, while simultaneously reconciling the forecasts to ensure coherency.Go beyond other state-of-the-art methods, FRT accomplishes forecasting and reconciliation simultaneously, while avoiding any post-processing steps.Moreover, FRT is a deep model that does not rely on any strong assumptions such as unbiased estimates or Gaussian distribution.Our experiments are conducted on four real-world hierarchical datasets from different industrial domains (three public ones and a dataset from the application servers of our company's data center) and the results demonstrate the efficacy of our proposed method.Our method has been implemented extensively within the production environments of a prominent global payment company.It has emerged as a cornerstone for workload forecasting within their data center and plays a critical role in the optimization of cloud computing resource allocation across