Diagnostic checking is an important step in the modeling process. But while the literature on diagnostic checks is quite extensive and many texts on time series modeling are available, it still remains difficult to find a book that adequately covers methods for performing diagnostic checks.
Diagnostic Checks in Time Series helps to fill that gap. Author Wai Keung Li--one of the world's top authorities in time series modeling--concentrates on diagnostic checks for stationary time series and covers a range of different linear and nonlinear models, from various ARMA, threshold type, and bilinear models to conditional non-Gaussian and autoregressive heteroscedasticity (ARCH) models. Because of its broad applicability, the portmanteau goodness-of-fit test receives particular attention, as does the score test. Unlike most treatments, the author's approach is a practical one, and he looks at each topic through the eyes of a model builder rather than a mathematical statistician.
This book brings together the widely scattered literature on the subject, and with clear explanations and focus on applications, it guides readers through the final stages of their modeling efforts. With Diagnostic Checks in Time Series, you will understand the relative merits of the models discussed, know how to estimate these models, and often find ways to improve a model.
Table of Contents
DIAGNOSTIC CHECKS FOR UNIVARIATE LINEAR MODELS
The Asymptotic Distribution of the Residual Autocorrelation Distribution
Modifications of the Portmanteau Statistic
Extension to Multiplicative Seasonal ARMA Models
Relation with the Lagrange Multiplier Test
A Test Based on the Residual Partial Autocorrelation test
A Test Based on the Residual Correlation Matrix test
Extension to Periodic Autoregressions
THE MULTIVARIATE LINEAR CASE
The Vector ARMA model
Granger Causality Tests
Transfer Function Noise (TFN) Modeling
ROBUST MODELING AND ROBUST DIAGNOSTIC CHECKING
A Robust Portmanteau Test
A Robust Residual Cross-Correlation Test
A Robust Estimation Method for Vector Time Series
The Trimmed Portmanteau Statistic
Tests for General Nonlinear Structure
Tests for Linear vs. Specific Nonlinear Models
Goodness-of-Fit Tests for Nonlinear Time Series
Choosing Two Different Families of Nonlinear Models
CONDITIONAL HETEROSCEDASTICITY MODELS
The Autoregressive Conditional Heteroscedastic Model
Checks for the Presence of ARCH
Diagnostic Checking for ARCH Models
Diagnostics for Multivariate ARCH models
Testing for Causality in the Variance
FRACTIONALLY DIFFERENCED PROCESS
Methods of Estimation
A Model Diagnostic Statistic
Diagnostics for Fractional Differencing
MISCELLANEOUS MODELS AND TOPICS
ARMA Models with Non-Gaussian Errors
Other Non-Gaussian time Series
The Autoregressive Conditional Duration Model
A Power Transformation to Induce Normality
"There are many books on time series analysis but this is the first monograph specialized to diagnostic checking. … 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. … [V]ery useful for statisticians working in time series analysis."
- EMS Newsletter
"[T]he author has adopted an easy-to-follow style which takes the reader to the frontier of the literature painlessly."
- Journal of the Royal Statistical Society
"There have been several excellent monographs on the diagnostics of linear models, but this is the first and possibly definitive one for stationary time series modeling. It is of great value in bringing together the diverse literature on the topic, over three hundred references are given, and integrating them into a coherent whole…Whatever type of time series model you are fitting, linear or nonlinear, volatile or not, turn to this monograph for help in testing its goodness-of-fit."
- ISI Short Book Reviews