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 22-25) 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