Diagnostic Methods in Time Series (SpringerBriefs in Statistics)

✍ Scribed by Fumiya Akashi

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 117
• Category: Library

✦ Synopsis

This book contains new aspects of model diagnostics in time series analysis, including variable selection problems and higher-order asymptotics of tests. This is the first book to cover systematic approaches and widely applicable results for nonstandard models including infinite variance processes. The book begins by introducing a unified view of a portmanteau-type test based on a likelihood ratio test, useful to test general parametric hypotheses inherent in statistical models. The conditions for the limit distribution of portmanteau-type tests to be asymptotically pivotal are given under general settings, and very clear implications for the relationships between the parameter of interest and the nuisance parameter are elucidated in terms of Fisher-information matrices. A robust testing procedure against heavy-tailed time series models is also constructed in the context of variable selection problems. The setting is very reasonable in the context of financial data analysis and econometrics, and the result is applicable to causality tests of heavy-tailed time series models. In the last two sections, Bartlett-type adjustments for a class of test statistics are discussed when the parameter of interest is on the boundary of the parameter space. A nonlinear adjustment procedure is proposed for a broad range of test statistics including the likelihood ratio, Wald and score statistics.

✦ Table of Contents

Preface
Contents
1 Elements of Stochastic Processes
1.1 Introduction
References
2 Systematic Approach for Portmanteau Tests
2.1 Introduction
2.2 Interpretation of Portmanteau Tests as Special Forms …
2.3 Asymptotic Properties for the Natural Whittle Likelihood Ratio
2.4 Numerical Study
References
3 A New Look at Portmanteau Test
3.1 Introduction
3.2 Portmanteau Test for General Statistical Models
3.3 Bias Adjustment and the Local Power of the Modified Portmanteau-Type Test
3.4 Applications and Numerical Examples
3.4.1 Serial Correlation in Linear Regression Models
3.4.2 Variable Selection in Linear Regression Models
3.4.3 Serial Correlation in Regression Models with Lagged Dependent Variable
3.5 Concluding Remarks
References
4 Adjustments for a Class of Tests Under Nonstandard Conditions
4.1 Introduction
4.2 Higher Order Asymptotic Theory
4.3 General Asymptotic Theory
4.4 Numerical Analysis
4.5 Concluding Remarks
References
5 Adjustments for Variance Component Tests in ANOVA Models
5.1 Introduction
5.2 Likelihood Inference
5.3 Bartlett-Corrected Likelihood Ratio Test
5.4 Wald Test
5.5 Wald Type Test When the Nuisance Parameters Are Unknown
5.6 Numerical Experiments
5.6.1 Likelihood Ratio Test
5.6.2 Wald Test
5.6.3 Wald Type Test with Unknown Nuisance Parameters
References
6 Robust Causality Test of Infinite Variance Processes
6.1 Introduction
6.2 Linear Process with Possibly Infinite Variance Innovations
6.3 Causality Test in Frequency Domain
6.4 Causality Test in Time Domain
6.5 Numerical Example
6.5.1 Case 1
6.5.2 Case 2
6.6 Concluding Remarks
References
Appendix A Index
Index