Motivated by the challenge of analyzing the dynamics of weekly sea border crossings in the Mediterranean (2015-2025) and the English Channel (2018-2025), we develop a Bayesian dynamic framework for modeling heteroskedastic count time series. Building on theoretical considerations and empirical stylized facts, our approach utilizes a Poisson random walk model that allows for heavy-tailed innovations or stochastic volatility dynamics, while incorporating an explicit mechanism to separate structural from sampling zeros. Posterior inference is carried out via a straightforward Markov chain Monte Carlo algorithm. Applying this methodology to Mediterranean and English Channel data, we compare alternative model specifications through a comprehensive out-of-sample forecasting exercise. Using log predictive scores and empirical coverage at predictive quantiles to evaluate each model, we find strong evidence for stochastic volatility in migration innovations. These models deliver the strongest out-of-sample forecasts with empirical coverage close to nominal levels up to the 99th percentile. Our framework can be used to develop risk indicators with direct policy implications for improving governance and preparedness for migration surges. More broadly, the methodology extends to other zero-inflated non-stationary count time series applications, including epidemiological surveillance and public safety incident monitoring.

翻译：受地中海（2015-2025年）和英吉利海峡（2018-2025年）周度海上边境穿越动态分析挑战的驱动，我们开发了一个用于建模异方差计数时间序列的贝叶斯动态框架。基于理论考量与经验风格化事实，该方法采用泊松随机游走模型，允许厚尾创新或随机波动率动态，同时融入显式机制区分结构性零值和抽样零值。后验推断通过直接的马尔可夫链蒙特卡洛算法完成。将该方法应用于地中海与英吉利海峡数据，我们通过全面的样本外预测实验比较了不同模型规格。利用对数预测评分与预测分位数处经验覆盖度评估各模型，发现迁移创新中存在强随机波动率证据。这些模型提供了最优的样本外预测，经验覆盖度在高达第99百分位处接近名义水平。我们的框架可用于开发具有直接政策含义的风险指标，以改善对移民潮的治理与准备。更广泛而言，该方法可扩展至其他零膨胀非平稳计数时间序列应用，包括流行病学监测与公共安全事件监控。