Modelling and diagnostic checking multivariate and nonlinear time series

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In many areas of the human activity, the statistical analysis of time series data represents an important component in the decision making process. In various situations, the observations are observed over time and special techniques are needed in order to describe adequately the phenomenon of interest. One of the main goals of time series consists in synthesizing the information they contain in the form of statistical models, taking into account the dependence between the observations. Examples of applications include data coming from the social sciences (e.g., economic and finance), or coming from the physical sciences (e.g., hydrology, oceanography and climatology). The new theories and models rely often on the quantitative evaluation of statistical methods; the tools should be appropriate and efficient. Our research plays a central role in evaluating statistical models. The methodological evaluations of the last developments can be performed using the new tools that we propose, and new research avenues often emerge from the better understanding of the existing theories. More specifically, a univariate time series is composed of a single variable, and when several observations are recorded over time, multivariate data are observed. One goal of our research proposal is to propose and develop new powerful test statistics for serial correlation in univariate time series models. We are also interested in models for multivariate data allowing for seasonal, periodic and spatial behaviours; several data coming from the physical sciences present these characteristics and we will analyze such data. In general, aspects of the research proposal include the development of new models, and their statistical evaluation (with respect to the functional form of the model and the distributional assumptions) using test statistics. To study the relations between several financial time series using causality analysis and multivariate methods represents another component of our research. Determination of financial quantity such as the Value at Risk is also part of our research plan. Advanced univariate and multivariate techniques will be combined with data coming from economic, finance, and from the physical sciences, which will illustrate the potential of the new methods.