New Procedures for the Reconciliation of Time Series

We propose new simultaneous and two-step procedures for reconciling systems of time series subject to temporal and contemporaneous constraints according to a Growth Rates Preservation (GRP) principle. Two nonlinear optimization algorithms are used: an interior-point method applied to the constrained problem and a Newton’s method with Hessian modification applied to a suitably reduced-unconstrained problem. Both techniques exploit the analytic gradient and Hessian of the GRP objective function, making full use of all the derivative information at disposal. We apply the proposed GRP procedures to two large systems of economic series, and compare the results with those of other reconciliation procedures based on the Proportional First Differences (PFD) principle, a linear approximation of the GRP principle widely used by data-producing agencies. Our experiments show that (i) an optimal solution to the nonlinear GRP problem can be efficiently achieved through the proposed Newton’s optimization algorithms, and (ii) GRP-based procedures preserve better the growth rates in the system than linear PFD solutions, especially for series with high temporal discrepancy and high volatility.