A Newton's Method for Benchmarking Time Series according to a Growth Rates Preservation Principle

Abstract

We present a new technique for temporally benchmarking a time series according to the Growth Rates Preservation (GRP) principle by Causey and Trager (1981). This procedure basically looks for the solution to a non linear program, according to which f(x), a smooth, non-convex function of the unknown values of the target time series xt, t = 1, . . . , n, has to be minimized subject to linear equality constraints which link the more frequent series xt to a given, less frequent benchmark series bT, T = 1, . . . ,m. We develop a Newton's method with Hessian modification applied to a suitably reducedunconstrained problem. This method exploits the analytic Hessian of the GRPobjective function, making full use of all the derivative information at disposal. We show that the proposed technique is easy to implement, computationally robust and efficient, all features which make it a plausible competitor of other benchmarking procedures (Denton, 1971; Dagum and Cholette, 2006) also in a data-production process involving a considerable amount of series.