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 the Mediterranean and English Channel data, we compare alternative model specifications through a comprehensive out-of-sample density forecasting exercise. Evaluating each model using log predictive scores and empirical coverage up to the 99th percentile, we find strong evidence for stochastic volatility in the migration innovations, with these models producing well-calibrated forecasts even at extreme quantiles. 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：受分析地中海（2015-2025年）和英吉利海峡（2018-2025年）每周海上越境动态的挑战所驱动，我们开发了一个贝叶斯动态框架用于建模异方差计数时间序列。基于理论考量和经验典型事实，我们的方法采用泊松随机游走模型，该模型允许重尾创新或随机波动动态，同时结合了分离结构零值与抽样零值的显式机制。后验推断通过直接的马尔可夫链蒙特卡洛算法实现。将此方法应用于地中海和英吉利海峡数据，我们通过全面的样本外密度预测实验比较了替代模型设定。使用对数预测分数和高达99百分位数的经验覆盖度评估每个模型，我们发现了移民创新过程中存在随机波动性的有力证据，这些模型即使在极端分位数下也能产生校准良好的预测。我们的框架可用于开发具有直接政策含义的风险指标，以改善对移民激增的治理和准备。更广泛地，该方法可扩展到其他零膨胀非平稳计数时间序列应用，包括流行病学监测和公共安全事件监控。