End-to-End Modeling of Hierarchical Time Series Using Autoregressive Transformer and Conditional Normalizing Flow-based Reconciliation

Multivariate time series forecasting with hierarchi-cal structure is pervasive in real-world applications, demanding not only predicting each level of the hierarchy, but also recon-ciling all forecasts to ensure coherency, i.e., the forecasts should satisfy the hierarchical aggregation constraints. Moreover, the disparities of statistical characteristics between levels can be huge, worsened by non-Gaussian distributions and non-linear correlations. To this extent, we propose a novel end-to-end hierarchical time series forecasting model, based on conditioned normalizing flow-based autoregressive transformer reconciliation, to represent complex data distribution while simultaneously reconciling the forecasts to ensure coherency. Unlike other state-of-the-art methods, we achieve the forecasting and reconciliation simultaneously without requiring any explicit post-processing step. In addition, by harnessing the power of deep model, we do not rely on any assumption such as unbiased estimates or Gaussian distribution. Our evaluation experiments are conducted on four real-world hierarchical datasets from different industrial domains (three public ones and a dataset from the application servers of Alipay11Alipay is the world's leading company in payment technology. https:/len.wikipedia.org/wiki/Alipay) and the preliminary results demonstrate efficacy of our proposed method.