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

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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.