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. To improve 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 applying our method to artificial neural networks for time series prediction. Experimental results using synthetic and real-world datasets demonstrate that our method is comparable in terms of prediction accuracy and computational efficiency to other methods for time series prediction.

Highlights

  • Data Availability Statement: All real-world datasets are available from the e-Stat, a portal site for official Japanese statistics

  • The experimental results reported evaluate the effectiveness of our structured regularization model when applied to artificial neural networks

  • We calculated the rootmean-squared error (RMSE) for each node i 2 N during the test period T^ as sfPifififififififififififififififififififif t2T^ ðyit À jT^ j if ififififififififi ~y it Þ2 ði 2 NÞ: We compared the performance of the following methods for time series prediction

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Summary

Objectives

This study aimed to produce better time series predictions by simultaneously completing these two phases. We aimed to develop a structured regularization method that takes full advantage of hierarchical structure for better time series predictions

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