How global warming data are modeled via some novel mathematical programming scenarios in distributed lag model?

The method of Almon reduces multicollinearity in some degree in distributed lag model, however multicollinearity may not be recovered since Almon estimator depends on the use of ordinary least squares technique. In this context, Almon ridge estimator including one biasing parameter is commonly preferred in this model. Based on recent advances, biased estimators that have more than one biasing parameter are stated as advantageous to one biasing parameter estimators. One of two-parameter estimators is Almon two-parameter ridge estimator of Özbay (Iran J Sci Tech Trans Sci 43: 1819–1828, 2019) which regulates the multicollinearity with its first biasing parameter and improves the quality of fit of regression with its second biasing parameter. As for another method to eliminate multicollinearity, exact linear restrictions are employed for the Almon two-parameter ridge estimator and restricted Almon two-parameter ridge estimator was introduced by Özbay and Toker (Considering linear constraints for Almon two parameter ridge estimation. 11th International Statistics Congress (ISC 2019), Muğla, Turkey, 2019). In this article, the issue of selecting the biasing parameters of the restricted and unrestricted Almon two-parameter ridge estimators is handled with the approach of mathematical programming instead of traditional selection methods. Different scenarios in which mean square error is minimized or coefficient of multiple determination is maximized are constituted by this mathematical programming approach. In real-life data analysis, we focus on global warming as a trend topic to demonstrate the effect of mathematical programming approach on the mentioned estimators. The dataset in question comprises carbon dioxide emission that has adverse effects on global warming via increasing average global temperature.