Application and Research Based on Exponential Weighted Moving Averages and GRU Modeling

In our study, we delve into statistical performance metric momentum prediction using Exponential Weighted Moving Averages (EWMA). To optimize performance, various <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha$</tex> values were tested against Mean Square Error (MSE), leading to the selection of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha=0.1$</tex> with an MSE of 0.529. This configuration achieved an 83.33% accuracy, reflecting a smoothness index of 1.308 and a robust STD of 0.791, highlighting the model's consistency and stability. Complementing this, we implemented a GRU-based prediction model, recognized for its computational efficiency. Our GRU model yielded a relative prediction error rate of 8.3519% and a relative RMSE of 6.4957%, affirming its precision in forecasting tasks. Overall, the integration of EWMA's trend sensitivity and GRU's advanced sequence handling capacity presents a robust framework for enhancing statistical performance metric predictions, balancing accuracy with computational speed.