An Algorithm for Distributed Lag Estimation Subject to Piecewise Monotonic Coe-cients
Ioannis C. Demetriou, Evangelos E. Vassiliou · 2009
Linearly distributed-lag models as a time series tool have very useful applications in many dis- ciplines. In these models, the dependent variable de- pends on one independent variable and its lags. The speciflcation of the lag coe-cients is a crucial ques- tion to the e-cacy of a model. A new algorithm is proposed for the estimation of lag coe-cients subject to the condition that the sequence of the coe-cient estimates consists of a certain number of monotonic sections, where the positions of the extrema are also unknowns. The algorithm is iterative, each iteration taking a conjugate gradient step, then forming an esti- mate of the coe-cients and flnally adjusting this esti- mate to satisfy the given constraints. An immediate advantage is that the inversion of an ill-conditioned matrix that frequently occurs in practice is avoided. Moreover, the constraints provide a realistic repre- sentation of the prior knowledge and the calculation results in a highly e-cient time series estimation. The algorithm and its convergence are described, results from simulation experiments are presented and an application of the algorithm on real annual macroe- conomic data concerning the personal consumption expenditures against the GDP for the U.S.A. during 1929 - 2006 is given.