Non-Linear Time Series : Extreme Events and Integer Value Problems

This book offers a useful combination of probabilistic and statistical tools for analyzing nonlinear time series. Key features of the book include a study of the extremal behavior of nonlinear time series and a comprehensive list of nonlinear models that address different aspects of nonlinearity. Several inferential methods, including quasi likelihood methods, sequential Markov Chain Monte Carlo Methods and particle filters, are also included so as to provide an overall view of the available tools for parameter estimation for nonlinear models. A chapter on integer time series models based on several thinning operations, which brings together all recent advances made in this area, is also included.

Readers should have attended a prior course on linear time series, and a good grasp of simulation-based inferential methods is recommended. This book offers a valuable resource for second-year graduate students and researchers in statistics and other scientific areas who need a basicunderstanding of nonlinear time series.

Kamil Feridun Turkman graduated from Middle East Technical University in 1976 and received a PhD degree in Statistics in 1980 from the University of Sheffield, England. Currently he is a Professor of Statistics at the Department of Statistics and Operations Research of the University of Lisbon, Portugal. His current research interests are on time series analysis, extreme value theory and environmental statistics.

Manuel G. Scotto is presently Assistant Professor at the Department of Mathematics of the University of Aveiro (Portugal). He completed his PhD in Statistics in 2001. His research interests center in applied probability and sometimes cross the boundary into statistics. Current topics of research gravitate towards problems in integer valued time series analysis, forecasting, classification, extreme value theory and applied statistics.

Patrícia de Zea Bermudez graduated in Applied Mathematics in 1990, received a MSc in Probability and Statistics in 1994 and a PhD in Probability and Statistics from the Faculty of Sciences of the University of Lisbon (FCUL) in 2003. She has been Assistant Professor at the Department of Statistics and Operations Research of FCUL since February 2003 (Tenure Track since February 2008). Her major research interests are Extreme Value Theory, Bayesian Statistics and Time Series.