The main goal of this paper is to improve the existing methods and tools used for solving penalized quantile regression problems. We modified the quantile regression method by implementing the extreme learning machine (ELM) algorithm and features of locally weighted regression. Also, we used different penalty functions. A modified method was used for the one-step-ahead prediction of the composite indicator (CI) of the Lithuanian economy. Our analysis showed that the prediction error of the modified locally weighted quantile regression is smaller in comparison to the other quantile regression.