Modeling the uncertainty on the covariance matrix for probabilistic forecast reconciliation

In minimum trace (MinT) forecast reconciliation, the covariance matrix of the base forecasts errors plays a crucial role. Typically, this matrix is estimated and then treated as known. This can lead to underestimation of the variance of the predictive distribution. To address the problem, we propose a Bayesian reconciliation model that accounts for the uncertainty in the estimation of the covariance matrix. By adopting an Inverse-Wishart prior and assuming Gaussian residuals, the reconciled predictive distribution follows a multivariate t-distribution, obtained in closed-form, rather than a multivariate Gaussian distribution. We evaluate our method on three tourism-related datasets, including a new publicly available dataset. Empirical results show that our approach consistently improves prediction intervals compared to MinT reconciliation. Hierarchical time series are collections of time series that adhere to a set of linear constraints. For example, the sales of individual items (the

Modeling the uncertainty on the covariance matrix for probabilistic forecast reconciliation Chiara Carrara University of Pavia chiara.carrara03@universitadipavia.it Dario Azzimonti Giorgio Corani Lorenzo Zambon SUPSI, Istituto Dalle Molle di Studi sull’Intelligenza Artificiale (IDSIA) Abstract In minimum trace (MinT) forecast reconciliation, the covariance matrix of the base forecasts errors plays a crucial role. Typically, this matrix is estimated and then treated as known. This can lead to underestimation of the variance of the predictive distribution. To address the problem, we propose a Ba

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