Randall Douc, Eric Moulines and David S. Stoffer (2014) Nonlinear Time Series-Theory, Methods and Applications with R Examples. CRC Press, UK (A Chapman & Hall Book). Texts in Statistical Science.ISBN 978-1-4665-0225-3. pages 531

摘要

Often, one assumes when analysing time-series data that the data are linear, and quite possibly Gaussian. This assumption, in addition to the standard assumption of second-order stationarity, is sometimes unrealistic. Most of the literature available so far in time series is devoted to developing time-series methodology and is based on these crucial assumptions. In many instances, it has been observed that the assumption of Gaussianity is unrealistic because of lack symmetry in the data, and hence, there is a need for constructing nonlinear models (to cope with nonlinearity and non-Gaussianity). Since the early 1980s, many research workers developed statistical tests for linearity (and Gaussianity), and several nonlinear models have been proposed, and their properties have been investigated. The nonlinear area is very rich, and the literature is growing at a very fast rate. The methods developed for analysing time series are now used in many areas, such as biological and physical sciences, economics, and finance. One of the areas where the methods have been found to be most useful is in finance and economics. Some of the tools used for statistical analysis and modelling are quite mathematically oriented, and the existing literature is widely dispersed. In this book, one of the objects seems to be to bring all the mathematical details together in a systematic way. The authors clearly stated in their preface that the book is aimed at readers who want to acquire advanced skills in nonlinear time-series analysis, and therefore, the material presented is quite rigorous. To appreciate the contents, one needs to have a sound knowledge of linear Gaussian time series and measure theory and a deep knowledge of probability theory and stochastic processes. The authors have devoted the first three chapters as an introduction to linear and Gaussian time series, which may help to some extent readers who may not be familiar with the time-series literature. In my opinion, it would be helpful if the readers are familiar with the standard literature (the authors suggested several books) before they attempt to read the present book. The book is divided into three main sections (the fourth section is an appendix), containing altogether 13 chapters.