Multidimensional benchmarking of time series by Segmented Kalman Filtering / A. C. Singh and M. S. Kovacevic. : CS11-619/96-4E-PDF

"Benchmarking is essentially a method of signal estimation from time series under constraints. The final signal estimates satisfy the regression-adjusted benchmarks in the nonbinding case, but are forced to exactly satisfy benchmarks in the binding case; the latter case leads to sub-optimality in the case of random benchmarks. It is assumed that the source of benchmark series is independent of the source of target time series. Typically, the process of benchmarking consists of two stages: the first stage for finding initial signal estimates and the second stage for constrained regression. When the number of benchmarks is quite large as in the case of multidimensional benchmarking, the usual method of constrained regression may be computationally difficult due to high dimension of matrix inversion involved therein. If benchmarks are independent of each other, then the technique of recursive least squares can be adapted to avoid matrix inversion. For dependent benchmarks, a method termed Segmented Kalman Filtering (SKF) is proposed which alleviates the above computational difficulty under very general conditions"--Abstract.

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