STOCHASTIC DYNAMICS AND STRUCTURAL TREND MODELLING OF HOMICIDE IN JAMAICA: EVIDENCE FROM ARIMA AND ARIMAX TIME-SERIES ANALYSIS, 1970–2025

Abstract

This study develops an econometric homicide function for Jamaica using annual time-series data covering 1970–2025. The objective is to model internal dynamics, structural trends, and long-run persistence in homicide patterns using Autoregressive Integrated Moving Average (ARIMA) and Autoregressive Integrated Moving Average with Exogenous Variables (ARIMAX) specifications. The methodology employs first-differenced modelling to address non-stationarity, maximum likelihood estimation, diagnostic testing, structural break analysis, and forecast simulation. The results indicate strong volatility clustering, structural upward shifts during the 1980s and 2000s, and significant trend-driven persistence in homicide growth. The ARIMAX model incorporating a deterministic time trend produces superior explanatory power relative to the baseline ARIMA specification and generates an accelerating long-run trajectory under parameter stability assumptions. Forecast simulations for 2026–2035 suggest that if historical structural relationships persist, homicide levels may follow a renewed upward path driven by trend effects. However, robustness testing highlights sensitivity to structural breaks and model specification, suggesting that policy interventions could materially alter projected trajectories. Monte Carlo simulations demonstrate widening forecast uncertainty over longer horizons. The study contributes to the empirical criminology and time-series literature by formalising a dynamic homicide function for Jamaica and providing a quantitative baseline for policy evaluation.