Topics in Nonlinear and Functional Time Series

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The investigators examine statistical inference techniques for nonlinear and functional time series models that work in both stationary and nonstationary regimes, thereby providing unified procedures that help advance statistical theory. Since determining whether a given set of (functional) observations is stationary can be a vexing problem, the proposed research also helps to lighten the statistical analysis for practitioners. Moreover, the investigators develop a new framework to deal with dependent Hilbert space-valued random functions which is both mathematically challenging and important for statistical applications in various areas such as finance, econometrics, astronomy, geophysics, climatology and genetics. This research is based on delicately fusing elements of statistical and probability theory with time series and functional data analysis.The investigators' research is aimed at providing flexible statistical tools for practitioners that are less sensitive to underlying model assumptions and time dependent changes in environment. In view of the economic crisis in the Fall of 2008, this seems to be of particular importance for the analysis of financial data, but may also prove relevant in other scientific fields such as climatology. To enhance our understanding of these complex scientific questions, the investigators' research will provide novel data-analytic tools for practitioners by advancing statistical theory.