Modelling the effect of weather variables on maize production using copula methods

Abstract

This study investigates the interplay between weather variables and maize production, employing advanced statistical and copula modeling techniques. The framework integrates: data pre-treatment (autocorrelation, stationarity testing and detrending); exploratory dependence analysis using Pearson correlation coefficient, Kendall’s tau, and Spearman’s rho, supplemented by graphical diagnostics; bivariate and trivariate copula selection using semi-parametric Canonical Maximum Likelihood estimation and further modeling by vine copulas; and goodness-of-fit validation by AIC and BIC criteria. This structured approach ensures robust modeling of complex dependencies between climatic and agricultural variables while addressing temporal biases and non-linear interactions. Maize production, precipitation and temperature data from Uasin Gishu County, Kenya over the period 1990 to 2020 was used in the analysis. This study establishes that copula-based models, particularly when enhanced with semi-parametric methods and vine structures, significantly improve the modeling of nonlinear, multivariate dependencies between weather variables and maize production compared to traditional linear approaches. Particularly, copula models overcome linear correlation limitations and estimate the maize production-weather variables nexus with greater precision. The semi-parametric approach also ensures robustness through rank-based margins. Vine structures identified conditional relationships, with precipitation-temperature conditioning amplifying maize-precipitation dependence. Nonparametric vine copulas used for comparison with the parametric class offered superior fit, though interpretability favored parametric models. Hence, this study demonstrated copulas’ utility in disentangling multivariate dependencies in agroclimatic systems, advocating for nuanced, data-driven approaches in agricultural planning.

Keywords: Maize production, Copula modeling, Weather variables, Nonlinear dependencies, Semi-parametric estimation