Optimization of Holt's Double Exponential Smoothing Model with Levenberg-Marquardt Algorithm for Forecasting Farmer Exchange Rate

Abstract

The Farmer Exchange Rate (NTP) is an indicator of farmer welfare calculated from the ratio of prices received by farmers to costs incurred in farming. East Java is one of the provinces with the agricultural sector as the main pillar of the regional economy. However, the NTP in this region shows a fluctuating pattern with a certain trend that reflects the economic instability of the agricultural sector. This instability may lower farmers' purchasing power and threaten production sustainability. Therefore, accurate forecasting models are needed to support data-driven policy making. Holt's Double Exponential Smoothing (DES) is an effective method for analyzing trend-patterned data, as it captures both level and trend components through exponential smoothing. However, the model's accuracy heavily relies on selecting smoothing parameters, typically determined through a time-consuming trial-and-error process that may yield suboptimal results. This study proposes using the Levenberg-Marquardt algorithm to optimize parameter smoothing. The algorithm effectively combines the Gauss-Newton and Gradient Descent methods to minimize prediction error. The data included monthly NTP values in East Java from 2014 to 2024, sourced from BPS. The results showed that the model with optimized parameters has higher accuracy, with MAPE decreasing from 1.28% to 1.06%.