Nonlinear Time Series Analysis

This book provides an overview of the current state-of-the-art of nonlinear time series analysis, richly illustrated with examples, pseudocode algorithms and real-world applications.

Books on time series models deal mainly with models based on Box-Jenkins methodology which is generally represented by autoregressive integrated moving average models or some nonlinear extensions of these models, such as generalized autoregressive conditional heteroscedasticity models. Statistical inference for these models is well developed and commonly used in practical applications, due also to statistical packages containing time series analysis parts. The present book is based on regression models used for time series. These models are used not only for modeling mean values of observed time se­ ries, but also for modeling their covariance functions which are often given parametrically. Thus for a given finite length observation of a time series we can write the regression model in which the mean value vectors depend on regression parameters and the covariance matrices of the observation depend on variance-covariance parameters. Both these dependences can be linear or nonlinear. The aim of this book is to give an unified approach to the solution of statistical problems for such time series models, and mainly to problems of the estimation of unknown parameters of models and to problems of the prediction of time series modeled by regression models.

This is the first book that integrates useful parametric and nonparametric techniques with time series modeling and prediction, the two important goals of time series analysis. Such a book will benefit researchers and practitioners in various fields such as econometricians, meteorologists, biologists, among others who wish to learn useful time series methods within a short period of time. The book also intends to serve as a reference or text book for graduate students in statistics and econometrics.