Restricted estimation of distributed lag model from a Bayesian point of view

This article addresses the issue of multicollinearity for the distributed lag model via Bayesian approach. We introduce the Bayes Almon ridge estimator under this approach by employing prior information. Specifically, the resulting estimator is a new Bayesian estimator that is the mean of posterior density function for the coefficient of the Almon model. Also, a restricted version of this estimator is proposed by using Lagrange multipliers to optimize the coefficients under the additional exact linear constraints. In mathematical sense, theoretical comparisons are carried out by employing mean squared error utilizing matrix theory. Additionally, we investigate a selection method for the biasing parameter of the new estimators with the help of the mean squared error comparisons. To test the theoretical suggestions, we perform a real-life data analysis as a means of applied mathematics. Moreover, we benefit from Monte Carlo simulation techniques where we use several levels of different parameters. The outcomes of numerical example and simulation study favor the new estimators and, hence we succeed in eliminating the multicollinearity.