arXiv subjects

Shanika L Wickramasuriya

Publications and source records attributed to Shanika L Wickramasuriya.

3 recordsLinked to original sources

arXiv2026

Hierarchical forecasting: The role of information

In hierarchical forecasting, the process of forecast reconciliation transforms a set of "base" or "raw" forecasts, which do not satisfy the hierarchical aggregation constraints in the real data, into a set of "coherent" forecasts, which do satisfy those constraints. The academic literature provides ample simulation evidence and real-world examples demonstrating the value of forecast reconciliation in improving forecasts of hierarchical time series. This improvement is attributed to the imposition of aggregation constraints. However, this evidence is derived from base forecasts, each generated using a distinct information set, usually the univariate information set corresponding to each time series. Since reconciliation algorithms combine forecasts, it is difficult to determine the extent to which the improvement is due to the imposition of constraints versus the combination of information carried by different forecasts. In this paper, we demonstrate that when base forecasts are based on different information sets and historical data are available, there is scope for improving these forecasts by combining the information that each one carries, even when they are already coherent. We propose a new method, called the information combination (IComb) method, which combines the information content of forecasts during the reconciliation process. The method is regression-based and can be implemented using existing penalised regression packages. We provide simulation evidence to illustrate the role of information sets, as distinct from the role of aggregation constraints, in forecasting hierarchical time series. Finally, we apply our method to datasets previously used in the literature and demonstrate that it achieves superior results compared to traditional approaches.

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arXiv2021

Probabilistic forecast reconciliation under the Gaussian framework

Forecast reconciliation of multivariate time series is the process of mapping a set of incoherent forecasts into coherent forecasts to satisfy a given set of linear constraints. Commonly used projection matrix based approaches for point forecast reconciliation are OLS (ordinary least squares), WLS (weighted least squares), and MinT (minimum trace). Even though point forecast reconciliation is a well-established field of research, the literature on generating probabilistic forecasts subject to linear constraints is somewhat limited. Available methods follow a two-step procedure. Firstly, it draws future sample paths from the univariate models fitted to each series in the collection (which are incoherent). Secondly, it uses a projection matrix based approach or empirical copula based reordering approach to account for contemporaneous correlations and linear constraints. The projection matrices are estimated either by optimizing a scoring rule such as energy or variogram score, or simply using a projection matrix derived for point forecast reconciliation. This paper proves that (a) if the incoherent predictive distribution is Gaussian then MinT minimizes the logarithmic scoring rule; and (b) the logarithmic score of MinT for each marginal predictive density is smaller than that of OLS. We show these theoretical results using a set of simulation studies. We also evaluate them using the Australian domestic tourism data set.

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arXiv2021

Properties of point forecast reconciliation approaches

Point forecast reconciliation of collection of time series with linear aggregation constraints has evolved substantially over the last decade. A few commonly used methods are GLS (generalized least squares), OLS (ordinary least squares), WLS (weighted least squares), and MinT (minimum trace). GLS and MinT have similar mathematical expressions, but they differ by the covariance matrix used. OLS and WLS can be considered as special cases of MinT where they differ by the assumptions made about the structure of the covariance matrix. All these methods ensure that the reconciled forecasts are unbiased, provided that the base forecasts are unbiased. The ERM (empirical risk minimizer) approach was proposed to relax the assumption of unbiasedness. This paper proves that (a) GLS and MinT reduce to the same solution; (b) on average, a method similar to ERM (which we refer to as MinT-U) can produce better forecasts than MinT (lowest total mean squared error) which is then followed by OLS and then by base; and (c) the mean squared error of each series in the structure for MinT-U is smaller than that for MinT which is then followed by that for either OLS or base forecasts. We show these theoretical results using a set of simulation studies. We also evaluate them using the Australian domestic tourism data set.

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