Introduction

Agriculture encompasses a set of activities related to various raw agricultural, horticultural, livestock, forestry and aquatic products by various groups of farmers (farmers, gardeners, livestock keepers, beekeepers, foresters, aquaculture, fishermen, etc.) that are produced in the context of the climate and through a combination of production factors of labor, capital and natural resources (land, water, etc.). Unlike industrial and service activities, the production of agricultural products is carried out in the context of nature (as an uncontrollable environment) and is completely and directly dependent on climate conditions and its changes.

This study investigates the nonlinear dynamics and multi-scale interactions between climate-economic variables and Iran's agricultural value added during 1981–2023 (1360–1402 in the Iranian calendar) through an innovative hybrid wavelet-machine learning framework. Given Iran's severe vulnerability as an arid nation experiencing accelerated climate change—characterized by 15% declining rainfall and 1.2°C rising temperatures over recent decades—understanding the complex mechanisms driving agricultural productivity has become critical for food security and sustainable development.

Materials and Methods

In order to answer the main question of the present study and achieve its objectives, a combination of parametric (econometric models) and non-parametric (intelligent models) methodologies has been used. The correct specification of an economic model means the correct selection of explanatory and dependent variables (based on economic theories), the type of relationship between these variables, and the precise definition of the relationships between variables and parameters. The explanatory variables affecting agricultural value added have been selected based on the theoretical foundations of economic growth and empirical studies.

The research methodology integrates three sequential analytical phases. First, the Brock-Dechert-Scheinkman (BDS) test confirmed strong nonlinear dynamics in all time series variables except annual rainfall, justifying the necessity of nonlinear modeling approaches. Second, discrete wavelet transform (DWT) was applied for multi-scale denoising using optimal wavelet functions (Daubechies 4–8, Haar 2) selected per variable to extract meaningful signals while eliminating noise. Third, three advanced machine learning algorithms—bootstrap neural network (NB), bootstrap forest (BF), and support vector machine (SVM)—were implemented on wavelet-denoised data to model complex relationships and rank variable importance through sensitivity analysis and total effect metrics.

Results and Discussion

Empirical results demonstrate the superior performance of the hybrid wavelet-bootstrap neural network (Wavelet-NB) model, achieving an exceptional coefficient of determination (R² = 0.99) in both training and validation phases—significantly outperforming Wavelet-BF (R² = 0.93 validation) and Wavelet-SVM (R² = 0.85 validation). Variable importance analysis within the optimal Wavelet-NB model revealed a distinctive ranking of influential factors: (1) agricultural labor productivity (total effect: 0.338), (2) lagged agricultural value added (0.216), and (3) annual mean temperature (0.162) emerged as the three dominant drivers. Notably, annual rainfall exhibited negligible influence (total effect: 0.007), while evapotranspiration showed virtually no impact—likely attributable to limitations in annual-scale climatic data aggregation that mask intra-annual variability critical for agricultural processes.

These findings carry significant theoretical and policy implications. The paramount importance of labor productivity underscores the diminishing returns of labor-intensive agricultural strategies in Iran's evolving economic landscape, signaling an urgent need for mechanization, skill development, and technological adoption. The substantial influence of temperature (third-ranked driver) confirms climate change as a direct threat to agricultural output, consistent with projections of 5–10% yield reductions per 1°C warming for staple crops. The weak impact of annual rainfall metrics does not imply water's unimportance—rather, it reflects methodological limitations in capturing irrigation-dependent production systems where groundwater and surface water dominate over direct rainfall reliance.

Conclusions

Methodologically, this research contributes to climate-agriculture literature through three innovations: (1) rigorous BDS testing to validate nonlinearity before model selection, (2) systematic wavelet denoising optimized per variable to enhance signal extraction across temporal scales, and (3) comparative assessment of three machine learning architectures with graphical sensitivity profiling for transparent variable ranking. The negligible performance of annual evapotranspiration metrics further suggests that monthly or seasonal climatic indicators would yield more accurate agricultural impact assessments.

Policy recommendations emphasize three strategic priorities: (1) shifting agricultural development policies from labor expansion toward productivity enhancement through precision agriculture and heat-resilient crop varieties; (2) integrating climate adaptation into agricultural planning with temperature thresholds as early warning indicators; and (3) improving climatic data infrastructure to capture sub-annual variability essential for modeling irrigation-dependent production systems. This hybrid wavelet-machine learning framework offers a replicable methodology for climate-vulnerable arid regions globally seeking robust analytical tools for sustainable agricultural planning under accelerating climate change.