The problem of testing the equality of the generating processes of two categorical time series is addressed in this work. To this aim, we propose three tests relying on a dissimilarity measure between categorical processes. Particular versions of these tests are constructed by considering three specific distances evaluating discrepancy between the marginal distributions and the serial dependence patterns of both processes. Proper estimates of these dissimilarities are an essential element of the constructed tests, which are based on the bootstrap. Specifically, a parametric bootstrap method assuming the true generating models and extensions of the moving blocks bootstrap and the stationary bootstrap are considered. The approaches are assessed in a broad simulation study including several types of categorical models with different degrees of complexity. Advantages and disadvantages of each one of the methods are properly discussed according to their behavior under the null and the alternative hypothesis. The impact that some important input parameters have on the results of the tests is also analyzed. An application involving biological sequences highlights the usefulness of the proposed techniques.

翻译：本文研究了检验两个分类时间序列生成过程一致性的问题。为此，我们提出了三种基于分类过程间相异度度量的检验方法。通过考虑三种特定距离来构建这些检验的具体版本——这些距离分别评估两个过程的边际分布与序列依赖模式之间的差异。对这些相异度的恰当估计是所构建检验的核心要素，而这些估计基于Bootstrap方法。具体而言，我们采用了假设真实生成模型的参数Bootstrap方法，并扩展了移动块Bootstrap与平稳Bootstrap方法。通过涵盖多种复杂度不同的分类模型的大规模模拟研究评估了这些方法的性能。根据各方法在原假设与备择假设下的表现，详细讨论了其他缺点。同时分析了若干重要输入参数对检验结果的影响。基于生物序列的应用实例突显了所提技术的实用性。