Hybrid Metaheuristic Optimization for Time Series Forecasting:

Integrating Grey Wolf and Greylag Goose Strategies

Ghassan AL-Thabhawee 1,* Hussein Alkattan 2

1 Sciences of Mathematics, Computer Sciences, College of Health and Medical Techniques-Kufa Al-Furat Al-Awsat Technical

University, Kufa, Iraq

2 Department of System Programming, South Ural State University, Chelyabinsk, Russia; Directorate of Environment in Najaf,

Ministry of Environment, Najaf, Iraq

Received: April 05, 2026 Revised: June 05, 2026 Accepted: August 09, 2026 ⋆ Corresponding author

ABSTRACT

Time series forecasting is crucial in agricultural markets, where accurate predictions can enhance stakeholder

decision-making. Traditional statistical models such as ARIMA often struggle with capturing complex patterns,

necessitating the integration of metaheuristic optimization techniques to improve predictive performance. This study

introduces a novel hybrid optimizer, the Grey Wolf-Greylag Goose Optimizer (GGGWO), which combines the

strengths of the Grey Wolf Optimizer (GWO) and the Greylag Goose Optimizer (GGO) to enhance the forecasting

accuracy of ARIMA models. The proposed GGGWO-ARIMA model is evaluated on a dataset of daily potato prices

across multiple Indian cities and is compared against ARIMA, WOA-ARIMA, PSO-ARIMA, GWO-ARIMA, and

GGO-ARIMA. Experimental results demonstrate that GGGWO achieves the lowest MSE (0.0027), RMSE (0.0184),

and MAE (0.0116) while attaining the highest R-squared (0.9648) and Willmott Index (0.9565), outperforming all

baseline models. These findings highlight the efficacy of hybridizing GWO and GGO, offering a robust optimization

framework for improving time series forecasting in agricultural price prediction. This can aid policymakers, farmers,

and market analysts make data-driven decisions.

Keywords: Metaheuristic Optimization Time Series Forecasting Grey Wolf Optimizer (GWO) Greylag Goose

Optimizer (GGO) Hybrid ARIMA Model

1. INTRODUCTION

Time series forecasting is essential across nearly all domains,

such as finance, healthcare, energy, and agriculture. Accurate

forecasting aids stakeholders in decision-making, resource

optimization, and preventing potential risks. Price forecasting

is vital in agriculture because it directly influences farmers,

traders, policymakers, and consumers [1, 2]. Furthermore,

better predicting the price volatility of commodities, including

potatoes, provides market participants with a more reliable

forecast, leading to improved economic stability through

planning and reduced uncertainty. However, agricultural price

forecasting is challenging due to the influence of multiple

dynamic factors, such as seasonal variations, supply chain

disruptions, climate conditions, and policy changes [3, 4].

Time series forecasting has been extensively carried out using

traditional statistical models, with the Autoregressive

Integrated Moving Average (ARIMA) model being widely

utilized. ARIMA can capture linear dependencies observed

in the data and has been extensively applied in econometric

and financial forecasting [5, 6]. Nevertheless, it has several

limitations when modeling non-stationary and highly volatile

data. Since agricultural commodity prices often exhibit nonlinear

behaviors influenced by numerous external factors, no

statistical model can deliver optimal predictive performance