Diagnostic Checks in Time Series: (Chapman & Hall/CRC Monographs on Statistics & Applied Probability)

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:
INTRODUCTION DIAGNOSTIC CHECKS FOR UNIVARIATE LINEAR MODELS Introduction 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 NONLINEAR MODELS Introduction 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 Introduction 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 Epilogue