# Stochastic Limit Theory: An Introduction for Econometricians

## James Davidson

### Abstract

This book aims to introduce modern asymptotic theory to students and practitioners of econometrics. It falls broadly into two parts. The first half provides a handbook and reference for the underlying mathematics (Part I, Chapters 1‐6), statistical theory (Part II, Chapters 7‐11) and stochastic process theory (Part III, Chapters 12‐17). The second half provides a treatment of the main convergence theorems used in analysing the large sample behaviour of econometric estimators and tests. These are the law of large numbers (Part IV, Chapters 18‐21), the central limit theorem (Part V, Chapters 22‐ ... More

This book aims to introduce modern asymptotic theory to students and practitioners of econometrics. It falls broadly into two parts. The first half provides a handbook and reference for the underlying mathematics (Part I, Chapters 1‐6), statistical theory (Part II, Chapters 7‐11) and stochastic process theory (Part III, Chapters 12‐17). The second half provides a treatment of the main convergence theorems used in analysing the large sample behaviour of econometric estimators and tests. These are the law of large numbers (Part IV, Chapters 18‐21), the central limit theorem (Part V, Chapters 22‐25) and the functional central limit theorem (Part VI, Chapters 26‐30). The focus in this treatment is on the nonparametric approach to time series properties, covering topics such as nonstationarity, mixing, martingales, and near‐epoch dependence. While the approach is not elementary, care is taken to keep the treatment self‐contained. Proofs are provided for almost all the results.

*Keywords: *
asymptotic theory,
central limit theorem,
convergence theorems,
econometrics,
law of large numbers,
statistical theory,
stochastic process

### Bibliographic Information

Print publication date: 1994 |
Print ISBN-13: 9780198774037 |

Published to Oxford Scholarship Online: November 2003 |
DOI:10.1093/0198774036.001.0001 |