Forecasting Peruvian Blueberry Exports for Sustainable Agricultural Trade Management: Markov Chains, SARIMA, and Log-Linear Growth

Peruvian fresh blueberry exports have expanded rapidly since 2012, yet strong seasonality and price–volume fluctuations continue to complicate trade planning and export decision-making, thereby threatening the long-term economic sustainability of the sector. Using monthly series for 2012–2025, this study compares three forecasting approaches to export value (FOB), export volume and unit price: (i) a seasonal Markov chain with Monte Carlo simulation (Markov–Monte Carlo), (ii) a log-linear growth model, and (iii) a seasonal ARIMA (SARIMA) model estimated using logarithmic data. The models are evaluated under a common train–test design, with the last 12 months (September 2024–August 2025) reserved for out-of-sample assessment. Model performance was evaluated through standard metrics, specifically Mean Absolute Error (MAE) and Root Mean Square Error (RMSE), while model adequacy was examined through residual diagnostics, including Ljung–Box tests. For the Markov–Monte Carlo approach, simulated distributions were also used to characterize forecast uncertainty. Findings indicate that the log-linear growth model provides the most accurate short-term point forecasts for FOB values, and the SARIMA model performs better for export volume; the Markov–Monte Carlo approach, however, yields the best performance for export prices and provides additional insights into seasonal regimes. Overall, these results suggest that no single model dominates across all dimensions of the export chain. Instead, the combined use of forecast approaches offers a more comprehensive basis for sustainable trade management, export planning, and risk management in dynamic agricultural export sectors.