Authors:George Box, Gwilym Jenkins, Gregory Reinsel

Time series analysis techniques are applicable in a wide range of fields and hence there is a strong interest in both researchers and practitioners. The book Time Series Analysis by Box, Jenkins and Reinsel is a key foundation book in this field and covers the full breadth of topics that will appeal to readers in a diverse range of fields.

A salient aspect of the book is that the book covers the fundamentals of time series in a comprehensive manner including details of models techniques and how they can be estimated. Although most users will depend on a statistical software for model estimation, the book provides the much needed intuitive understanding for proper use of the models.

Time Series Analysis addresses practical problems such as forecasting, estimation of transfer function, effects of  unusual intervention events to a system, analysis of multivariate time series and discrete control system.

Basic concepts behind model building such as parsimony and iterative stages in model building are explained ahead of moving into the core material.

The basics of time series and stochastic processes such as auto correlation and auto covariance functions, estimation and standard errors are covered in the section on stochastic processes and their forecasting.

Building on the basic material, the book explores linear stationary and non-stationary models in depth. Auto regressive, moving average and mixed auto regressive processes, their properties and estimation of the parameters are covered clearly and in detail.

Forecasting is taken up next with calculating the forecasting functions and their updation, followed by many examples of forecasting functions. The section closes with the use of state space formulation of ARIMA models for forecasting.

Stochastic model building is explained in detailed in the next part of the book. Intuitive and rigorous treatment is given to identification of models and initial estimation of model parameters. 

Regarding model estimation, the book explains key issues including likelihood and sum of squares functions, and non linear estimation. Unit roots and estimation using bayes's theorem are covered apart from useful reviews of normal distribution theory and linear least squares.

General guidelines for model diagnostics and testing are dealt with, covering issues such as diagnostic checks for residuals. The section concludes with some topics of broader interest including seasonal models, and non linear and long memory models.

The final two sections of the book goes into transfer function and multivariate modeling as well as using these models for design of discrete control systems. Both theoretical and practical insights into identification, fitting and checking of models are covered.

Time Series Analysis by George Box, Gwilym Jenkins, Gregory Reinsel is a classic. This latest edition has updated some of the recent developments in the field and provides a strong foundation to the subject in a very structured way. The book will be highly useful to both students and practitioners in variety of fields that involve applied statistics and engineering.

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