Benchmarking time series according to a growth rates preservation principle

We present a new technique for temporally benchmarking a time series according to a Growth Rates Preservation (GRP) principle. This procedure basically looks for the solution to a non linear program, according to which a smooth, non-convex function of the unknown values of the target time series has to be minimized subject to linear equality constraints which link the more frequent series to a given, less frequent benchmark series. We develop a Newton’s method with Hessian modification applied to a suitably reduced-unconstrained problem. This method exploits the analytic Hessian of the GRP objective 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 currently used by statistical agencies.