This book provides the limit theorems that can be used in the development of nonlinear cointegrating regression. The topics include weak convergence to a local time process, weak convergence to a mixture of normal distributions and weak convergence to stochastic integrals. This book also investigates estimation and inference theory in nonlinear contegrating regression.
The core context of this book comes from the author and his collaborator’s current researches in past years, which is wide enough to cover the knowledge bases in nonlinear cointegrating regression. It may be used as a main reference book for future researchers.
○ First of all, this book extends the classical martingale limit theorem. Unlike previous books, for a certain class of martingales, weak convergence to a mixture of normal distributions is established under the convergence in distribution for the conditional variance
○ This extension partially removes a barrier in applications of the classical martingale limit theorem to non-parametric estimation and inference with non-stationarity
○ This extension enhances the effectiveness of the classical martingale limit theorem in the investigation of asymptotics in statistics, econometrics and other fields
○ Secondly, this book systemically introduces weak convergence to a local time process and weak convergence to stochastic integrals beyond martingale and semi-martingale structures (This kind of context is new to the field and is particularly useful in the framework of nonlinear cointegration)
○ Finally, this book does not look for the most general theory from the view of probability, but provides enough details for those who are interested in nonlinear cointegrating regression