Diagnostic Checks in Time Series

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

• INTRODUCTIONDIAGNOSTIC CHECKS FOR UNIVARIATE LINEAR MODELSIntroductionThe Asymptotic Distribution of the Residual Autocorrelation DistributionModifications of the Portmanteau StatisticExtension to Multiplicative Seasonal ARMA ModelsRelation with the Lagrange Multiplier TestA Test Based on the Residual Partial Autocorrelation testA Test Based on the Residual Correlation Matrix testExtension to Periodic AutoregressionsTHE MULTIVARIATE LINEAR CASEThe Vector ARMA modelGranger Causality TestsTransfer Function Noise (TFN) ModelingROBUST MODELING AND ROBUST DIAGNOSTIC CHECKINGA Robust Portmanteau TestA Robust Residual Cross-Correlation TestA Robust Estimation Method for Vector Time SeriesThe Trimmed Portmanteau StatisticNONLINEAR MODELSIntroductionTests for General Nonlinear StructureTests for Linear vs. Specific Nonlinear ModelsGoodness-of-Fit Tests for Nonlinear Time SeriesChoosing Two Different Families of Nonlinear ModelsCONDITIONAL HETEROSCEDASTICITY MODELSThe Autoregressive Conditional Heteroscedastic ModelChecks for the Presence of ARCHDiagnostic Checking for ARCH ModelsDiagnostics for Multivariate ARCH modelsTesting for Causality in the VarianceFRACTIONALLY DIFFERENCED PROCESSIntroductionMethods of EstimationA Model Diagnostic StatisticDiagnostics for Fractional DifferencingMISCELLANEOUS MODELS AND TOPICSARMA Models with Non-Gaussian ErrorsOther Non-Gaussian time SeriesThe Autoregressive Conditional Duration ModelA Power Transformation to Induce NormalityEpilogue