# Prediction of hierarchical time series using structured regularization and its application to artificial neural networks

arXiv: https://arxiv.org/abs/2007.15159 · HTML: https://mlsanity.com/paper/2007.15159/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jul 2020.

## Built on by (most cited first, 3 of 3)

- [A distribution-free mixed-integer optimization approach to hierarchical modelling of clustered and longitudinal data](https://mlsanity.com/paper/2302.03157/) (2023)
- [DC Algorithm for Estimation of Sparse Gaussian Graphical Models](https://mlsanity.com/paper/2408.04206/) (2024)
- [Hierarchical Time Series Forecasting with Robust Reconciliation](https://mlsanity.com/paper/2510.20383/) (2025)

## Abstract (arXiv)

This paper discusses the prediction of hierarchical time series, where each upper-level time series is calculated by summing appropriate lower-level time series. Forecasts for such hierarchical time series should be coherent, meaning that the forecast for an upper-level time series equals the sum of forecasts for corresponding lower-level time series. Previous methods for making coherent forecasts consist of two phases: first computing base (incoherent) forecasts and then reconciling those forecasts based on their inherent hierarchical structure. With the aim of improving time series predictions, we propose a structured regularization method for completing both phases simultaneously. The proposed method is based on a prediction model for bottom-level time series and uses a structured regularization term to incorporate upper-level forecasts into the prediction model. We also develop a backpropagation algorithm specialized for application of our method to artificial neural networks for time series prediction. Experimental results using synthetic and real-world datasets demonstrate the superiority of our method in terms of prediction accuracy and computational efficiency.