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This book presents the contemporary statistical methods and theory of nonlinear time series analysis. The principal focus is on nonparametric and semiparametric techniques developed in the last decade. It covers the techniques for modelling in state-space, in frequency-domain as well as in time-domain. To reflect the integration of parametric and nonparametric methods in analyzing time series data, the book also presents an up-to-date exposure of some parametric nonlinear models, including ARCH/GARCH models and threshold models. A compact view on linear ARMA models is also provided. Data arising in real applications are used throughout to show how nonparametric approaches may help to reveal local structure in high-dimensional data. Important technical tools are also introduced.