There are many books on time series analysis but this is the first monograph specialized to diagnostic checking. Construction of a model for time series data usually consists of three steps. At the beginning, a preliminary model is chosen. Then the parameters are estimated. The third stage is called model diagnostic checking. It involves techniques like residual plots and procedures for testing if the residuals are approximately uncorrelated. If it is found that the model is not adequate, the process starts with the first step again, this time with some new information from the previous analysis. The book describes a rich variety of diagnostic checks. It starts with the univariate and multivariate linear models. Although attention is paid mainly to ARMA models, the author also writes about periodic autoregression and Granger causality tests. A chapter is devoted to robust modelling and diagnostic checking, from a robust portmanteau test to the trimmed portmanteau statistic. An important part of the book describes results on nonlinear models. It contains goodness-of-fit tests, tests for general nonlinear structure, tests for linear vs. specific nonlinear time series, and methods for choosing two different families of nonlinear models. Then the models for conditional heteroscedasticity are presented. Finally, fractionally differenced processes are described and a few special topics are mentioned like non-Gaussian time series and power transformations. Unit root and co-integration tests are not included. The author is a known specialist in time series modelling. His approach is a practical one and each topic is presented from a model builder’s point of view. A long list of references is also appreciated as an important part of the publication. The monograph is very useful for statisticians working in time series analysis.