An IHS-ARIMAX Framework for Modeling Cnaphalocrocis medinalis with Potential Implications for Sustainable Pest Management in Rice Fields

The rice leaffolder (Cnaphalocrocis medinalis) is a major migratory pest whose population dynamics are synergistically driven by endogenous biological factors and exogenous meteorological conditions. Developing precise quantification models for its occurrence is a prerequisite for sustainable pest management. This study applied the Inverse Hyperbolic Sine (IHS) transformation to handle non-normally distributed pest population data with five years of continuous monitoring (2020–2024). We construct two dynamic predictive models: a simplified early warning model (Model I) and a multi-factor coupling model (Model II) by employing the Autoregressive Integrated Moving Average model with exogenous variables (ARIMAX) to integrate exogenous meteorological drivers (rainfall level during the monitoring interval, Rlt–1,2), endogenous biological indicator (local population development abundance index, LPDAI), and endogenous population dynamic factor (IHS-transformed daily average trap catch increment of the previous interval, IHS_IIPTn–1). Correlation analysis revealed that the trap catch was highly significant and positively correlated with LPDAI and Rlt–1,2 (p < 0.01). Parameter estimation of the IHS-ARIMAX models indicated that the exogenous rainfall factor (Rlt−1,2, Model I: B = 0.996; Model II: B = 0.947) reached significance levels (p < 0.05) in both models; IHS_IIPTn–1 (B = 1.535) in Model I and LPDAI (B = 0.846) in Model II exhibited strong positive effects. Robust fitting performance was shown by both ARIMAX models (Model I: total R2 = 0.903, stationary R2 = 0.860, RMSE = 8.58; Model II: total R2 = 0.922, stationary R2 = 0.898, RMSE = 8.34). Ljung-Box Q test (Model I: Q(18) = 21.500, p = 0.160; Model II: Q(18) = 13.729, p = 0.619) confirmed that the residuals are independently distributed white noise with no remaining significant autocorrelation. Both models stably captured the outbreak trends of C. medinalis. Crucially, an independent out-of-sample validation using field data from 2025 showed the high robustness and generalization power of Model II. It achieved highly significant trend synchronization with the observed values (Spearman’s ρ = 0.499, p = 0.005) and maintained complete numerical unbiasedness (p = 0.157). The IHS-ARIMAX framework developed here effectively addresses the statistical challenges of autocorrelation and non-linear fluctuations in ecological data and offers a robust tool to potentially support future decision making for sustainable pest management.