Likelihood-based inference in temporal hierarchies

Jan Kloppenborg Møller, Peter Nystrup and Henrik Madsen

International Journal of Forecasting, 2024, vol. 40, issue 2, 515-531

Abstract: We consider the importance of correctly specifying the variance–covariance matrix to allow information to be shared between aggregation levels when reconciling forecasts in a temporal hierarchy. We propose a novel framework for parametric modelling of the variance–covariance matrix, along with an iterative algorithm for maximum likelihood estimation. The covariance between aggregation levels can be modelled by aggregating the lower-level errors and disaggregating information from the higher levels. Using the likelihood approach, statistical inference can be applied to identify a parsimonious parametric structure for the variance–covariance matrix. We test and discuss different structures for how forecast errors are connected across aggregation levels and present a framework for simplifying these structures using Wald and likelihood-ratio tests. We evaluate the proposed method in a simulation study and through an application to day-ahead electricity load forecasting and find that it performs well compared to optimal shrinkage estimation.

Keywords: Maximum likelihood estimation; Dimensionality reduction; Forecast reconciliation; Hypothesis testing; Variance–covariance shrinkage; Statistical modelling; Load forecasting (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:intfor:v:40:y:2024:i:2:p:515-531

DOI: 10.1016/j.ijforecast.2022.12.005

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