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Multivariate time series forecasting with hierarchical structure is pervasivein real-world applications, demanding not only predicting each level of thehierarchy, but also reconciling all forecasts to ensure coherency, i.e., theforecasts 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 thisextent, we propose a novel end-to-end hierarchical time series forecastingmodel, based on conditioned normalizing flow-based autoregressive transformerreconciliation, to represent complex data distribution while simultaneouslyreconciling the forecasts to ensure coherency. Unlike other state-of-the-artmethods, we achieve the forecasting and reconciliation simultaneously withoutrequiring any explicit post-processing step. In addition, by harnessing thepower of deep model, we do not rely on any assumption such as unbiasedestimates or Gaussian distribution. Our evaluation experiments are conducted onfour real-world hierarchical datasets from different industrial domains (threepublic ones and a dataset from the application servers of Alipay's data center)and the preliminary results demonstrate efficacy of our proposed method.

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