A Distributed Lag Estimator with Piecewise Monotonic Coe-cients
Ioannis C. Demetriou, Evangelos E. Vassiliou · 2008
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 approach is proposed for the estimation of lag coe-cients sub- ject to the condition that the sequence of the coe-- cient estimates consists of a certain number of mono- tonic sections, where the positions of the extrema are also unknowns. The underlying algorithm is itera- tive, each iteration taking a descent direction, then forming an estimate of the coe-cients and flnally ad- justing this estimate to satisfy the given constraints. An immediate advantage of this approach is that the algorithm avoids inverting an ill-conditioned matrix that frequently occurs in practice. Moreover, the con- straints provide a realistic representation of the prior knowledge and the calculation results in a highly ef- flcient time series estimation. The algorithm is de- scribed, a proof of convergence is given and an appli- cation of the algorithm on real annual macroeconomic data concerning the personal consumption expendi- tures against the GDP for the U.S.A. during 1929 - 2006 is presented.