Enhancing Forecast Reconciliation: A Study of Alternative Covariance Estimators

<p dir="ltr">A collection of time series connected via a set of linear constraints is known as <i>hierarchical time series</i>. Forecasting these series without respecting the hierarchical nature of the data can lead to incoherent forecasts across aggregation levels and, in practice, reduced accuracy. <i>Forecast reconciliation</i> corrects this by adjusting base forecasts to satisfy such constraints. Among modern reconciliation methods, <i>Minimum Trace</i> (MinT) is widely used, however, it requires a good estimate of the forecast error covariance matrix. The current practice uses linear shrinkage towards a diagonal target. Furthermore, the covariance estimate is based on in-sample 1-step-ahead forecast errors, then proportionally scale it to approximate h-step-ahead covariance matrix. This raises the question of the method’s appropriateness for all real-world applications. We study the shortcomings of current practice and assess the impacts of alternative covariance estimators on MinT, including the NOVELIST estimator (shrinkage towards a soft-thresholded target), PC-adjusted shrinkage (which utilises latent factor structures), and horizon-specific estimators that relax proportional scaling. We evaluate the accuracy of MinT using these covariance estimates for both point and probabilistic reconciled forecasts, and demonstrate their effectiveness and improvements over the shrinkage estimator in a complex, large-hierarchical dataset.</p><p dir="ltr"><b><i>Note:</i></b><i> This is an Honours research thesis, supervised by Dr. Shanika Wickramasuriya </i><i>and Prof. George Athanasopoulos, </i><i>Department of Econometrics and Business Statistics, Monash Business School.</i></p>