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

多元和非线性时间序列的建模和预测以及复杂调查数据的分析

• 批准号: RGPIN-2020-05016
• 负责人: Duchesne, Pierre
• 金额: $ 1.31万
• 依托单位: Université de Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=759366
• 关键词: Modeling; Forecasting; Multivariate; Nonlinear; Time

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.

在人类活动的许多领域中，需要描述、综合和分析大型和复杂的数据集。例如，随着时间的推移而测量的观测值，以及来自复杂调查设计的样本所产生的调查数据。时间序列数据的统计分析涉及相依数据，其方法需要考虑到这一特点。研究建议的第二部分是关于调查抽样，调查数据的性质也需要特殊的技术，除了考虑数据的模型结构外，还要考虑如何收集观测数据。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以及获取预测和预测方法方面发挥了核心作用，这些预测和预测方法是决策过程中的基本组成部分。在这个研究计划的第一个轴上，问题涉及对一系列按时间排序的数据的观察，这些数据是从随时间测量的一些现象中获得的。单变量时间序列由感兴趣的单个变量组成。这里，当多变量时间序列可用时，也给予了特别的关注，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学模型，即高频数据，代表了涉及大量观察的应用的自然例子，已经提出了统计工具来对这种复杂的数据进行建模。检查统计模型误差项的规范，以及有效预测方法的发展，代表需要更多发展的主题。在这项研究方案中，我们试图提出新的多变量模型并开发创新的预测工具。我们还对考虑季节性、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呈现了这些特征，我们计划研究这种应用。在第二个轴上，复杂的调查需要考虑如何收集数据的特殊技术，因为通常情况下调查权重是可用的。这项研究的一个目标是为来自复杂调查设计的数据在这些方向上追求技术的发展。我们将继续进行一个正在进行的小区域估计项目，但我们也将考虑研究在存在无响应的情况下多变量数据和模型的校准方法。这些发展成果的应用将使人们更好地理解社会科学和官方机构的现象。为了实现这些目标，将把先进的调查抽样技术与多变量分析技术结合起来。这将大大提高拟议方法的效率。