1st Edition

Diagnostic Checks in Time Series

By Wai Keung Li Copyright 2004
    210 Pages 22 B/W Illustrations
    by Chapman & Hall

    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.

    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

    Biography

    Li, Wai Keung

    "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