From data to berthing: ARMA prediction in logarithms of the weekly influx of import containers in Puerto Bolívar (Ecuador)

Abstract

Container terminals face week-to-week variability that strains berth, yard, and gate operations; therefore, short-horizon predictive signals are essential to schedule resources and prevent bottlenecks. In Puerto Bolívar (Machala, Ecuador), import flows display occasional surges and weeks without operations, calling for transparent, auditable models aligned with tactical decision-making. Objective: to estimate and validate a parsimonious weekly forecasting scheme for imported container handling that is directly usable for operational management. Methodology: we used weekly observations from August 2021 to May 2025; the target series was transformed to a logarithmic scale to stabilize variance, and an ARMA(1,1) model was estimated by maximum likelihood, using the Kalman filter to accommodate missing weeks. Validation comprised a unit-root test for stationarity, inspection of autocorrelation and partial autocorrelation functions, the Ljung–Box white-noise test on residuals, verification of inverse roots for stability and invertibility, and checks on the squared residuals to rule out conditional heteroskedasticity. Main findings: the log series was stationary with short memory; residuals showed no serial correlation and no ARCH effects; AR and MA roots lay within the unit circle. The ARMA(1,1) captured weekly persistence and dampened transient shocks, delivering one-step predictions with coherent bands. Operationally, the scheme supports a continuous week-by-week update to coordinate staffing, yard allocation, and gate appointments, providing an actionable, traceable signal for terminal planning.