Diagnostic Checks in Time Series

Written by one of the world's foremost authorities in time series modeling, this book explores goodness of fit tests in time series analysis. Starting with linear models, the author proceeds to nonlinear modeling with extensions to long-memory and generalized linear models--all areas of interest and activity. The focus is firmly on practical matters, and the author presents a range of applications, particularly from the financial arena. Until now, published work in this area has been scattered throughout the literature. Researchers and practitioners alike will welcome this book as a reference that will guide them through the final stages of their modeling tasks.

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.

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

Li, Wai Keung