Probabilistic Forecast Reconciliation: Theory and Applications

A collection of multiple time series with an inherent aggregation structure is referred to as a "hierarchical time series". For such time series, it is important to have forecasts that adhere to the aggregate constraints across the hierarchy. The process that involves revising the incoherent forecasts so that they become coherent is known as "forecast reconciliation". Although there is a substantial literature on point forecast reconciliation for hierarchical time series, the focus on probabilistic forecasting is limited. This thesis attempts to address this gap by extending the idea of coherency and reconciliation into the probabilistic framework.