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Likelihood-based inference in temporal hierarchies
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DOI：10.1016/j.ijforecast.2022.12.005.png)
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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 dayahead electricity load forecasting and find that it performs well compared to optimal shrinkage estimation. (c) 2022 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.
Keyword:
Maximum likelihood estimation
Dimensionality reduction
Forecast reconciliation
Hypothesis testing
Variance-covariance shrinkage
Statistical modelling
Load forecasting
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