Reconciliation of Time Series according to a Growth Rates Preservation Principle

The reconciliation of a system of time series is known in the literature as the statistical process of adjusting preliminary values of the series to satisfy both temporal and contemporaneous constraints. In this paper we propose new reconciliation procedures based on the Growth Rates Preservation (GRP) principle, which explicitly preserves the period-to-period growth rates of the preliminary series. A non-linear constrained minimization problem is solved through a Newton’s optimization method, which exploits the analytical gradient and Hessian of the GRP objective function.We apply these procedures to two real-life applications and compare them with the state-of-the-art reconciliation procedures. The results show that simultaneous and two-step reconciliation procedures based on the GRP criterion are worthy candidates in terms of both quality of results and computational time, even for large systems with many constraints.