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

点击翻译按钮获取中文摘要

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.