Diagnostic Methods in Time Series

This book provides new approaches to model diagnostics in time series analysis, covering nonstandard models, variable selection problems, and robust testing procedures. It discusses a unified view of portmanteau-type tests, asymptotic pivotal conditions, and Bartlett-type adjustments for heavy-tailed time series models. The results are applicable to financial data analysis and econometrics.

Format: Paperback / softback
Length: 108 pages
Publication date: 09 June 2021
Publisher: Springer Verlag, Singapore

This comprehensive book delves into novel aspects of model diagnostics in time series analysis, encompassing a wide range of topics. It addresses variable selection problems and higher-order asymptotics of tests, presenting comprehensive 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, derived from a likelihood ratio test, which is valuable for testing general parametric hypotheses inherent in statistical models. The conditions for the limit distribution of portmanteau-type tests to be asymptotically pivotal are established under general settings, providing insights into the relationships between the parameter of interest and the nuisance parameter through the use of Fisher-information matrices. Moreover, a robust testing procedure against heavy-tailed time series models is constructed within the context of variable selection problems, making it particularly relevant for financial data analysis and econometrics. In the final two sections, Bartlett-type adjustments for a class of test statistics are discussed when the parameter of interest lies on the boundary of the parameter space. A nonlinear adjustment procedure is proposed for a diverse range of test statistics, including the likelihood ratio, Wald, and score statistics, ensuring accurate and reliable inference in time series analysis.

Introduction:
This book offers a comprehensive exploration of model diagnostics in time series analysis, covering a diverse range of topics. It begins by introducing a unified view of a portmanteau-type test, derived from a likelihood ratio test, which is valuable for testing general parametric hypotheses inherent in statistical models. The conditions for the limit distribution of portmanteau-type tests to be asymptotically pivotal are established under general settings, providing insights into the relationships between the parameter of interest and the nuisance parameter through the use of Fisher-information matrices. Moreover, a robust testing procedure against heavy-tailed time series models is constructed within the context of variable selection problems, making it particularly relevant for financial data analysis and econometrics. In the final two sections, Bartlett-type adjustments for a class of test statistics are discussed when the parameter of interest lies on the boundary of the parameter space. A nonlinear adjustment procedure is proposed for a diverse range of test statistics, including the likelihood ratio, Wald, and score statistics, ensuring accurate and reliable inference in time series analysis.

Unified View of a Portmanteau-Type Test:
The book begins by introducing a unified view of a portmanteau-type test, derived from a likelihood ratio test, which is valuable for testing general parametric hypotheses inherent in statistical models. This test is useful in various applications, including testing for autocorrelation in time series data and testing for heteroscedasticity in panel data models. The conditions for the limit distribution of portmanteau-type tests to be asymptotically pivotal are established under general settings, providing insights into the relationships between the parameter of interest and the nuisance parameter through the use of Fisher-information matrices.

Robust Testing Procedure against Heavy-Tailed Time Series Models:
In addition to the unified view of a portmanteau-type test, the book also constructs a robust testing procedure against heavy-tailed time series models. 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. The robust testing procedure is based on a likelihood ratio test and uses a bootstrap procedure to estimate the limit distribution of the test statistics. This approach provides accurate and reliable inference even in the presence of heavy-tailed distributions, making it an invaluable tool for practitioners in the field.

Bartlett-Type Adjustments for a Class of Test Statistics:
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. These adjustments are useful in situations where the parameter of interest is close to the boundary of the parameter space, ensuring accurate and reliable inference even in such challenging scenarios.

Conclusion:
In conclusion, this comprehensive book provides a valuable resource for researchers and practitioners in time series analysis. It offers a unified view of a portmanteau-type test, robust testing procedures against heavy-tailed time series models, and Bartlett-type adjustments for a class of test statistics. The book's comprehensive coverage and practical applications make it an essential tool for anyone working with time series data and interested in developing accurate and reliable inference methods. By delving into novel aspects of model diagnostics, this book contributes to the ongoing development of time series analysis and provides valuable insights into the field's latest developments.

Weight: 454g
Dimension: 235 x 155 (mm)
ISBN-13: 9789811622632
Edition number: 1st ed. 2021