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Statistical modelling and analysis for stochastic processes

Many applications in engineering, telecommunication, economy, finance and computer science, suggest the modelling of data by dependent stochastic processes. Among many exciting developments in statistics over the last two decades, nonlinear time series, long range dependent models and nonparametric methods have greatly advanced and have been shown to offer excellent alternatives to well established short memory linear processes and parametric methods.

Robert F. Engle and Clive W. J. Granger obtained in 2003 the Nobel prize in Economy for their work on time series models for financial and macroeconomic data.

Natural questions that arise with the development of these new models cover the estimation of parameters or functions, which characterise them, the detection of some features and their ability to describe and predict the data. In the same way, the recent impressive and successful researches in statistical machine learning has yet to be fully extended to this case of dependent and possibly highly structured data.

This exploratory field is then related to many topics addressed in Digiteo (such as classification and clustering, extremal and rare events, long-memory behaviour, non stationarity modelling, multivariate analysis, robustness) and a large scope of methods (kernel methods for learning, independent component analysis, spectral and multiscale approaches etc.).