Modeling the uncertainty on the covariance matrix for probabilistic forecast reconciliation

In forecast reconciliation, the covariance matrix of the base forecasts errors plays a crucial role. Typically, this matrix is estimated, and then treated as known. In contrast, we propose a Bayesian reconciliation model that accounts for the uncertainty in the estimation of the covariance matrix. This leads to a reconciled predictive distribution that follows a multivariate t-distribution, obtained in closed-form, rather than a multivariate Gaussian. 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 Gaussian reconciliation.