Jiti Gao

This book introduces modern series methods with a focus on applications in econometrics and statistics. It explores how new orthogonal series techniques can address challenges in model building and estimation, particularly for variables with unbounded support, nonparametric nonstationary data, and high-dimensional models. By extending traditional series methods, which are typically limited to variables with bounded supports, this book provides tools to tackle emerging problems in econometrics and statistics effectively. The book is organized into the following key parts. Part one provides the mathematical foundation for modern series methods, offering the theoretical background needed for their application. Part two introduces fundamental econometric concepts, including conditional expectations and regression models, within the context of modern series techniques. The last part, part four examines advanced topics, such as the connections between series methods and generalized functions, and compares series methods with kernel methods, highlighting their respective strengths and use cases. With a balanced mix of theory and practical insights, this book is ideal for researchers, practitioners, and students looking to deepen their understanding of series methods and their applications in econometrics, statistics, and related fields.

Trends often play a dominant role in many empirical time series data, but do we truly understand these trends? What challenges arise when dealing with complex, nonstationary trending time series? How do we model such trends in fields like economics, finance, and climate change? This book provides an overview of recently developed models for trending time series and introduces new nonlinear, nonparametric, and semiparametric methods. Specifically, it offers practical approaches to address the problem of endogeneity in linear trending regression models where the trend component is either weak or strong. Additionally, it proposes a testing procedure for identifying common trends across multiple time series and includes illustrative examples from economics, finance, and climate change. As a practical toolbox, this book equips analysts with essential methods for investigating trends in their research and applications.

Useful in the theoretical and empirical analysis of nonlinear time series data, semiparametric methods have received extensive attention in the economics and statistics communities over the past twenty years. Recent studies show that semiparametric methods and models may be applied to solve dimensionality reduction problems arising from using fully nonparametric models and methods. Answering the call for an up-to-date overview of the latest developments in the field, Nonlinear Time Series: Semiparametric and Nonparametric Methods focuses on various semiparametric methods in model estimation, specification testing, and selection of time series data. After a brief introduction, the book examines semiparametric estimation and specification methods and then applies these approaches to a class of nonlinear continuous-time models with real-world data. It also assesses some newly proposed semiparametric estimation procedures for time series data with long-range dependence. Even though the book only deals with climatological and financial data, the estimation and specifications methods discussed can be applied to models with real-world data in many disciplines. This resource covers key methods in time series analysis and provides the necessary theoretical details. The latest applied finance and financial econometrics results and applications presented in the book enable researchers and graduate students to keep abreast of developments in the field.

Useful in the theoretical and empirical analysis of nonlinear time series data, semiparametric methods have received extensive attention in the economics and statistics communities over the past twenty years. Recent studies show that semiparametric methods and models may be applied to solve dimensionality reduction problems arising from using fully nonparametric models and methods. Answering the call for an up-to-date overview of the latest developments in the field, Nonlinear Time Series: Semiparametric and Nonparametric Methods focuses on various semiparametric methods in model estimation, specification testing, and selection of time series data. After a brief introduction, the book examines semiparametric estimation and specification methods and then applies these approaches to a class of nonlinear continuous-time models with real-world data. It also assesses some newly proposed semiparametric estimation procedures for time series data with long-range dependence. Even though the book only deals with climatological and financial data, the estimation and specifications methods discussed can be applied to models with real-world data in many disciplines. This resource covers key methods in time series analysis and provides the necessary theoretical details. The latest applied finance and financial econometrics results and applications presented in the book enable researchers and graduate students to keep abreast of developments in the field.

In the last ten years, there has been increasing interest and activity in the general area of partially linear regression smoothing in statistics. Many methods and techniques have been proposed and studied. This monograph hopes to bring an up-to-date presentation of the state of the art of partially linear regression techniques. The emphasis is on methodologies rather than on the theory, with a particular focus on applications of partially linear regression techniques to various statistical problems. These problems include least squares regression, asymptotically efficient estimation, bootstrap resampling, censored data analysis, linear measurement error models, nonlinear measurement models, nonlinear and nonparametric time series models.