Improved model of ELASTIC NET regularization for financial time series

This paper proposes a modification of Elastic Net regression for short-term forecasting of financial time series by introducing Gaussian weight decay. The new approach is designed to smooth the abrupt “jumps” between the last historical observation and the first forecast—an issue typical of standard regularization. To assess its effectiveness, we formally derive the Elastic Net model with four weighting schemes (no decay, linear, exponential, and Gaussian) and conduct empirical experiments on the S&P 500, Dow Jones Industrial Average, and Nasdaq Composite indices over the period 2020–2025. The results demonstrate that Gaussian decay minimizes the transition gap and achieves the lowest RMSE and Deviation for the S&P 500 and Nasdaq Composite, whereas exponential decay proves optimal for the Dow Jones Industrial Average.