Abstract

Forecasting hierarchical or grouped time series using a reconciliation approach involves two steps: computing base forecasts and reconciling the forecasts. Base forecasts can be computed by popular time series forecasting methods such as exponential smoothing (ETS) and Autoregressive Integrated Moving Average (ARIMA) models. The reconciliation step is a linear process that adjusts the base forecasts to ensure they are coherent. However, using ETS or ARIMA for base forecasts can be computationally challenging when there are a large number of series to forecast, as each model must be numerically optimized for each series. We propose a linear model that avoids this computational problem and handles the forecasting and reconciliation in a single step. The proposed method is very flexible in incorporating external data. We illustrate our approach using a dataset on monthly Australian domestic tourism, as well as a simulated dataset. We compare our approach to reconciliation using ETS and ARIMA, and show that our approach is much faster while providing similar levels of forecast accuracy. Supplementary files for this article are available online.

摘要

使用协调方法预测分层或分组时间序列涉及两个步骤：计算基础预测和协调预测。基础预测可以通过流行的时间序列预测方法计算，例如指数平滑 (ETS) 和自回归综合移动平均 (ARIMA) 模型。调节步骤是一个线性过程，它调整基本预测以确保它们是一致的。然而，当有大量序列要预测时，使用 ETS 或 ARIMA 进行基础预测可能在计算上具有挑战性，因为每个模型都必须针对每个序列进行数值优化。我们提出了一个线性模型，可以避免这种计算问题，并在一个步骤中处理预测和协调。所提出的方法在合并外部数据方面非常灵活。我们使用每月澳大利亚国内旅游的数据集以及模拟数据集来说明我们的方法。我们比较了我们使用 ETS 和 ARIMA 进行对账的方法，并表明我们的方法在提供相似水平的预测准确性的同时要快得多。本文的补充文件可在线获取。