The Almon Liu-Type M-Estimator for the Distributed Lag Models in the Presence of Multicollinearity and Outliers

The Almon method is widely used for the estimation of the distributed lag models (DLM). The advantage of using the Almon technique lies in its capability to avoid some serious problems that may arise from the direct application of ordinary least squares (OLS). In the Almon technique, the OLS procedure is applied on transformed regressors, and these regressors correlate themselves leading to the problem of multicollinearity. Moreover, in the presence of outliers in the y-direction, the Almon estimator (AE) may become sensitive. The presence of multicollinearity and outliers jointly in the dataset can strongly distort the AE, leading to the unreliable estimation of the lagged coefficients. We propose the Almon Liu-type M-estimator (ALTME) to address the joint issue of multicollinearity and outliers in y-direction. To show that the proposed estimator has an advantage over the AE, the Almon M-estimator (AME), and the Almon ridge M-estimator (ARME), the Monte Carlo Simulation and two real-life numerical examples are given.