Adaptive Exponential Smoothing with Embedded Fuzzy Adjustment for Nonlinear Time Series Forecasting

Nonlinear time series forecasting is one of the challenges to be handled in traditional exponential smoothing (ES) due to its fixed smoothing parameter. In this study, a novel Adaptive Exponential Smoothing with Embedded Fuzzy Adjustment (AES-FA) method is proposed to dynamically change its smoothing parameter based on data characteristics. This study aims to develop an adaptive exponential smoothing model with embedded fuzzy adjustment, in which the smoothing parameters are dynamically updated to capture nonlinear patterns in time series data; to validate and evaluate the performance of the proposed model against the traditional exponential smoothing method; and to apply the best-performing model to a real-world nonlinear dataset for improved forecasting accuracy. An empirical study is used to compare AES-FA to traditional ES methods, Exponential Brownian Motion and Neural Network for 52 weeks for 2021-2024. A fuzzy logic system is embedded into the ES which is Single Exponential Smoothing, Double Exponential Smoothing and Holt-Winters to dynamically adjust its smoothing parameter based on volatility, trend and seasonality. Results are validated using MAE and RMSE. Results show that AES-FA has a lower value of MAE and RMSE between traditional ES. AES-FA has more stable residuals even during abrupt changes. In conclusion, AES-FA has improved forecasting performance for nonlinear time series data and has potential for real-world applications like forecasting agricultural product prices.