Optimal Forecast Reconciliation with Time Series Selection

Xiaoqian Wang (), Rob Hyndman and Shanika Wickramasuriya ()

No 5/24, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: Forecast reconciliation ensures forecasts of time series in a hierarchy adhere to aggregation constraints, enabling aligned decision making. While forecast reconciliation can enhance overall accuracy in hierarchical or grouped structures, the most substantial improvements occur in series with initially poor-performing base forecasts. Nevertheless, certain series may experience deteriorations in reconciled forecasts. In practical settings, series in a structure often exhibit poor base forecasts due to model misspecification or low forecastability. To prevent their negative impact, we propose two categories of forecast reconciliation methods that incorporate time series selection based on out-of-sample and in-sample information, respectively. These methods keep "poor" base forecasts unused in forming reconciled forecasts, while adjusting weights allocated to the remaining series accordingly when generating bottom-level reconciled forecasts. Additionally, our methods ameliorate disparities stemming from varied estimates of the base forecast error covariance matrix, alleviating challenges associated with estimator selection. Empirical evaluations through two simulation studies and applications using Australian labour force and domestic tourism data demonstrate improved forecast accuracy, particularly evident in higher aggregation levels, longer forecast horizons, and cases involving model misspecification.

Keywords: Forecasting; Hierarchical Time Series; Grouped Time Series; Linear Forecast Reconciliation; Integer Programming (search for similar items in EconPapers)
Pages: 35
Date: 2024
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-for
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