Statistical Modeling and Analysis for Multivariate and Nonlinear Time Series and for Complex Survey Data

时间序列和调查数据的统计分析是一个很大的研究领域。随着数据的巨大存储容量和高性能计算机的快速发展，对经济和社会科学数据的分析无疑是决策过程中的重要组成部分。在各种情况下，观测值是随时间推移观察的，需要特殊的技术来充分描述观测值之间的相关性。鉴于现有信息的数量，有必要而且有可能为这些数据开发复杂的模型，使决策者有可能更好地理解复杂的问题。调查数据来源于复杂调查设计的样本。近年来，调查方法有了相当大的扩展，分析人员要求对总体的一般参数进行有效推断，同时也要求对更精细的参数进行估计。发达的技术在评估现有理论方面发挥着核心作用，例如来自经济学和社会科学的理论，它们提供了理解一些程式化事实的机会，这些事实提供了额外的见解并提出了新的研究途径。使用时间序列应用程序，它们允许政策制定者提供更好的预测，这可能非常有价值。随着新的发展，提出了替代旧建议（例如，模型、测试）的方法，并提供了了解研究问题和提出可靠解决方案的机会。更具体地说，时间序列问题涉及对时间顺序数据序列的观察，这些数据序列是从随时间测量的某些现象中获得的。当在某一时间记录多个观测值时，涉及多个变量，观测到多变量数据；变量之间的动态也变得有趣起来。其中一个主要目标是综合它们以模型的形式包含的信息。由于此类数据的性质，对序列依赖性和非同质性的理解也占有重要地位。经典的统计工具，假设一个随机的样本是可用的，不适合在目前的情况下。因此，需要新的模型、工具和/或技术来描述时间序列数据。同样，调查数据的性质要求使用特殊技术，考虑到数据的收集方式（因此包括有关的抽样信息）和数据的模型结构。本研究的目标是在两个主要方向上追求方法的发展。为了达到我们的目标，我们将开发时间序列（如拟合优度检验、单变量、多变量、周期和/或协整数据的复杂模型）和调查抽样（如小区域估计）方面的先进技术，并用相关数据进行说明，这将显示新方法的潜力。

The statistical analysis of time series and survey data represents a large field of study. With the considerable storage capacity of data and the quick development of high performance computers, the analysis of data from economics and social sciences is certainly an important component in the decision making process. In various situations, the observations are observed over time and special techniques are needed to describe adequately the dependence between the observations. Given the quantity of available information, it becomes necessary and possible to develop sophisticated models for the data, giving the possibility to the policy makers to provide a better understanding of complex problems. Survey data arise with samples coming from complex survey designs. Survey methods have expanded considerably in recent years, and analysts are demanding valid inferences for general parameters of the population but also for estimators of parameters at a finer level. The developed techniques play a central role in evaluating existing theories, e.g. theories coming from economics and social sciences, and they give the opportunity to understand some stylized facts, which give additional insight and suggest new research avenues. With time series applications, they allow the policy makers to provide better forecasts, which can be very valuable. With the new developments, methodologies are proposed, which replace older proposals (e.g., models, tests) and give the opportunity to understand research questions and propose reliable solutions. More specifically, time series questions involve the observations of a sequence of time-ordered data, obtained from some phenomenon measured over time. When several observations are recorded at a certain time, several variables are involved and multivariate data are observed; the dynamics between the variables become also of interest. One of the main goals consists to synthesize the information they contain in the form of models. Because of the nature of such data, the understanding of the serial dependence and the non homogeneity take also an important place.  Classical statistical tools, which assume that a random sample is available are not appropriate in the present context. Thus, new models, tools and/or techniques are required to describe time series data. Similarly, the nature of survey data calls for special techniques taking into account how the data are collected (thus including the relevant sampling information) and the model structure of the data. The goal of this research is to pursue the development of methods in two main directions. To reach our objectives, advanced techniques in time series (e.g. goodness-of-fit tests, complex models for univariate, multivariate, periodic and/or cointegrated data) and in survey sampling (e.g. small area estimation) will be developed and illustrated with relevant data, which will show the potential of the new methods.