Model diagnostics for count time series

在经济学和相关领域的许多不同情况下都会出现计数的时间序列。就其依赖结构或边际分布而言，它们可以有各种形式。由于经典的实值时间序列模型不能保持计数数据的离散性，大量为计数时间序列量身定制的模型被开发出来。对计票数据过程进行适当的建模对于进行预测、监测时间序列的后续过程以尽快揭示结构变化或只是为了更好地了解基本的计票数据过程都很重要。计划中的计数时间序列模型诊断研究项目包括建立模型的三个主要步骤：模型识别、模型选择和模型验证，虽然已经提出了大量用于实值（连续）时间序列的方法，而且这些方法很早就可以使用，但用于离散值时间序列的相应方法却远没有那么发达。现有的方法是稀缺的，其中大多数仅以初级形式可用（例如，作为启发式应用指南），以及更严格的基于理论的方法依赖于限制性模型假设或集中于过程的孤立特征，例如，分散体相应的问题也适用于拟合优度测试：虽然已经提出了许多连续值时间序列的拟合优度测试，这些测试不仅能够测试特定模型，而且能够测试整个模型类，但可用的拟合优度测试对计数时间序列的适用性受到限制，例如，计划中的研究项目具有两个互补的攻击线，用于在计数的时间序列中进行模型诊断。一方面，我们的目标是开发参数化的方法，模型诊断的时间序列的计数，考虑到各种特征的基础分布和/或依赖模式。此外，开发和广泛应用于实值时间序列的诊断工具也应该通过使用合适的参数引导实现而适用于计数的时间序列。另一方面，我们的目标是开发基于联合分布的拟合优度测试，这些分布能够始终如一地区分不同的模型类别。为了实施，而且为了允许上述诊断工具的更广泛的适用性，应开发用于计数时间序列的合适的半参数自举方法，并将其用于模型诊断。对于所提出的方法，我们要详细调查的性能和适用性，详细的比较模拟研究和应用程序的真实的数据集相关的经济科学。

Time Series of counts arise in many different situations in economics and related fields. They can have various forms with respect to their dependence structure or their marginal distribution. As classical models for real-valued time series are not able to maintain the discrete nature of count data, a great many of models tailor-made for time series of counts have been developed. An adequate modelling of count data processes is important, to do forecasting, to monitor the subsequent process of the time series to reveal structural changes as soon as possible, or just to obtain a better understanding of the underlying count data process. The planned research project on model diagnostics for time series of counts comprises three central steps of model building: model identification, model selection and model validation.While a large number of methods have been proposed for real-valued (continuous) time series and are available since a long time, corresponding approaches for discrete-valued time series are far less developed. The existing methods are scarce and most of them are available only in rudimentary form (e.g., as heuristic application guidelines), and more rigorous, theory-based methods rely on restrictive model assumptions or focus on isolated characteristics of the process as, e.g., dispersion. Corresponding issues do also hold for goodness-of-fit tests: while numerous goodness-of-fit tests for continuous-valued time series have been proposed that are not only capable to test for specific models but also whole model classes, the applicability of available goodness-of-fit tests for time series of counts is restricted, e.g., to parametric assumptions.The planned research project features two complimentary lines of attack for model diagnosis in time series of counts. On the one hand, we aim to develop parametric methods for model diagnosis for time series of counts, which take into account various characteristics of the underlying distribution and/or dependence pattern. Further, diagnostic tools developed and widely applied for real-valued time series shall be made applicable also to time series of counts by using suitable parametric bootstrap implementations. On the other hand, we aim to develop goodness-of-fit tests based on joint distributions that are capable to consistently distinguish between different model classes. For the implementation, but also to allow for a broader applicability of the above-mentioned diagnostic tools, suitable semi-parametric bootstrap methods for time series of counts shall be developed and employed for model diagnostics. For the proposed methods, we want to investigate in detail the performance and the applicability by elaborate comparative simulations studies and applications to real data sets relevant in economic sciences.