Modelling and diagnostic checking multivariate and nonlinear time series

在人类活动的许多领域，时间序列数据的统计分析是决策过程中的一个重要组成部分。在各种情况下，观察结果是随着时间的推移而观察的，为了充分描述感兴趣的现象，需要特殊的技术。考虑到观测值之间的依赖性，时间序列的主要目标之一是以统计模型的形式综合它们所包含的信息。应用实例包括来自社会科学（如经济和金融）或来自物理科学（如水文学、海洋学和气候学）的数据。新的理论和模型往往依赖于统计方法的定量评价；这些工具应该是适当和有效的。我们的研究在评估统计模型中起着核心作用。对最新发展的方法学评估可以使用我们提出的新工具进行，新的研究途径通常来自对现有理论的更好理解。更具体地说，单变量时间序列由单个变量组成，当随时间记录多个观测值时，就可以观察到多变量数据。我们的研究计划的一个目标是提出和发展新的强大的检验统计序列的序列相关的单变量时间序列模型。我们也对允许季节性、周期性和空间行为的多变量数据模型感兴趣；来自物理科学的一些数据显示了这些特征，我们将分析这些数据。一般来说，研究计划的各个方面包括开发新模型，以及使用检验统计进行统计评估（关于模型的功能形式和分布假设）。利用因果分析和多变量方法研究几个金融时间序列之间的关系是我们研究的另一个组成部分。确定财务数量，如风险价值，也是我们研究计划的一部分。先进的单变量和多变量技术将与来自经济、金融和物理科学的数据相结合，这将说明新方法的潜力。

In many areas of the human activity, the statistical analysis of time series data represents an important component in the decision making process. In various situations, the observations are observed over time and special techniques are needed in order to describe adequately the phenomenon of interest. One of the main goals of time series consists in synthesizing the information they contain in the form of statistical models, taking into account the dependence between the observations. Examples of applications include data coming from the social sciences (e.g., economic and finance), or coming from the physical sciences (e.g., hydrology, oceanography and climatology). The new theories and models rely often on the quantitative evaluation of statistical methods; the tools should be appropriate and efficient. Our research plays a central role in evaluating statistical models. The methodological evaluations of the last developments can be performed using the new tools that we propose, and new research avenues often emerge from the better understanding of the existing theories. More specifically, a univariate time series is composed of a single variable, and when several observations are recorded over time, multivariate data are observed. One goal of our research proposal is to propose and develop new powerful test statistics for serial correlation in univariate time series models. We are also interested in models for multivariate data allowing for seasonal, periodic and spatial behaviours; several data coming from the physical sciences present these characteristics and we will analyze such data. In general, aspects of the research proposal include the development of new models, and their statistical evaluation (with respect to the functional form of the model and the distributional assumptions) using test statistics. To study the relations between several financial time series using causality analysis and multivariate methods represents another component of our research. Determination of financial quantity such as the Value at Risk is also part of our research plan. Advanced univariate and multivariate techniques will be combined with data coming from economic, finance, and from the physical sciences, which will illustrate the potential of the new methods.