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

arXiv: https://arxiv.org/abs/2212.13706 · HTML: https://mlsanity.com/paper/2212.13706/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 30 references that are in the map.
- First posted on arXiv 28 Dec 2022.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [FIRM: An Intelligent Fine-Grained Resource Management Framework for SLO-Oriented Microservices](https://mlsanity.com/paper/2008.08509/) (2020)
- [A Meta Reinforcement Learning Approach for Predictive Autoscaling in the Cloud](https://mlsanity.com/paper/2205.15795/) (2022)
- [Reconciliation of probabilistic forecasts with an application to wind power](https://mlsanity.com/paper/1808.02635/) (2018)

## Built on by (most cited first, 4 of 4)

- [Time-MoE: Billion-Scale Time Series Foundation Models with Mixture of Experts](https://mlsanity.com/paper/2409.16040/) (2024)
- [TimeMixer++: A General Time Series Pattern Machine for Universal Predictive Analysis](https://mlsanity.com/paper/2410.16032/) (2024)
- [Multiscale Representation Enhanced Temporal Flow Fusion Model for Long-Term Workload Forecasting](https://mlsanity.com/paper/2407.19697/) (2024)
- [Cross-Temporal Forecast Reconciliation at Digital Platforms with Machine Learning](https://mlsanity.com/paper/2402.09033/) (2024)

## Abstract (arXiv)

Multivariate time series forecasting with hierarchical structure is pervasive in real-world applications, demanding not only predicting each level of the hierarchy, but also reconciling 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 Alipay's data center) and the preliminary results demonstrate efficacy of our proposed method.