Modeling and Forecasting Multivariate and Nonlinear Time Series, and Analysis of Complex Survey Data

在人类活动的许多领域，需要对大量复杂的数据集进行描述、综合和分析。例子包括随时间测量的观察结果，也包括来自复杂调查设计的样本的调查数据。时间序列数据的统计分析处理的是相关数据，其方法需要考虑这一特性。研究计划的第二个组成部分是调查抽样，调查数据的性质也需要特殊的技术，考虑到如何收集观察，除了数据的模型结构。应用的例子包括来自社会科学和国家统计局的数据或来自物理科学的数据。我们的研究在评估统计模型的理论、获取预测和预测方法方面发挥着核心作用，这些都是决策过程中的基本组成部分。在这个研究项目的第一个轴中，问题涉及到对一系列时间顺序数据的观察，这些数据是由一些随时间测量的现象获得的。单变量时间序列由单个感兴趣的变量组成。在这里，当多元时间序列可用时，也要特别注意，即随着时间的推移收集了几个变量，外生变量也可能是动态系统的一部分。股票市场日内活动的计量经济模型，高频数据，代表了涉及大量观察的应用的自然例子，并且已经提出了统计工具来模拟这种复杂的数据。检验统计模型误差项的规定性，开发有效的预测方法，是有待进一步发展的课题。在这项研究计划中，我们试图提出新的多元模型，并开发创新的预测工具。我们也对季节性、周期性和空间行为的统计模型感兴趣；来自统计水文学等物理科学的观测数据显示了这些特征，我们计划研究这些应用。在第二个轴中，复杂的调查需要考虑到如何收集数据的特殊技术，因为通常调查权重是可用的。本研究的一个目标是追求这些方向的技术发展，以获取来自复杂调查设计的数据。我们将继续进行一个正在进行的小面积估计项目，但我们也将考虑在无响应的情况下研究多元数据和模型的校准方法。这些发展的应用将有助于更好地理解来自社会科学和官方机构的现象。为了达到这些目标，调查抽样的先进技术将与多元分析技术相结合。这将使所提议的方法在效率方面取得重大进展。

In many areas of the human activity, large and complex data sets need to be described, synthetized and analyzed. Exemples include observations that are measured over time and also survey data which arise with samples coming from complex survey designs. The statistical analysis of time series data deals with dependent data and the methods need to take into account that characteristic. The second component of the research proposal is on survey sampling, and the nature of survey data also calls for special techniques, taking into consideration how the observations are collected, in addition to the model structure of the data. Examples of applications include data coming from the social sciences and national statistical offices or coming from the physical sciences. Our research plays a central role in evaluating theories of the statistical models, and in procuring predictions and forecasting methods which are fundamental components in the decision making process. In the first axis of this research program, questions involve the observations of a sequence of time-ordered data, obtained from some phenomenon measured over time. A univariate time series is composed of a single variable of interest. Here, special attention is also given when multivariate time series are available, that is several variables are collected over time, and exogenous variables may also be part of the dynamic system. Econometric modelling of stock market intraday activity, high-frequency data, represent natural examples of applications which involve a large number of observations, and statistical tools have been proposed to model such complex data. To check the specification of the error term of statistical models, and development of valid forecasting methods, represent topics which need more developments. In this research proposal, we seek to propose new multivariate models and to develop innovative forecasting tools. We are also interested in statistical models allowing for seasonal, periodic and spatial behaviours; observed data coming from the physical sciences such as statistical hydrology, present these characteristics and we plan to study such applications. In the second axis, complex surveys call for special techniques taking into account how the data are collected, because typically survey weights are available. A goal of this research is to pursue the development of techniques in these directions for data coming from complex survey designs. We will pursue an on-going project on small area estimation, but we will also consider the study of calibration methods for multivariate data and models in the presence of non-response. The applications of these developments will provide a better understanding of phenomena coming from social sciences and from official agencies. To reach these goals, advanced techniques in survey sampling will be combined with multivariate analysis techniques. This will lead to important gains in efficiency for the proposed methodologies.