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

**Authors:** Tomokaze Shiratori, Ken Kobayashi, Yuichi Takano  
**arXiv:** [2007.15159](https://arxiv.org/abs/2007.15159)  
**Date:** 2020-07-30  
**Summary page:** https://www.summarizepaper.com/en/paper/2007.15159v1/

## Abstract

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.