UNIT GRAPH ESTIMATION AND STABILIZATION USING QUADRATIC-PROGRAMMING AND DIFFERENCE NORMS

For a rainfall-runoff event, quadratic programming is particularly sui ted to the estimation of unit graph as linear and positivity constrain ts on unit graph ordinates can be naturally implemented. In this paper , the quadratic programming framework is invoked in a novel way to sta bilize the unit graph estimation procedure via the use of difference n orms. The advantage of the latter over standard ridge regression is th at penalties are placed on oscillations of the unit graph rather than on the size of its ordinates. Application of the methodology to real r ainfall-runoff data is provided and comparisons with existing approach es are made. The latter indicate that our approach generally yields un it graph estimates of more realistic shape and smaller variance result ing in a better fit to the runoff data.