The nonparametric and the nuisance parameter approaches to consistently testing statistical models are both attempts to estimate topological measures of distance between a parametric and a nonparametric fit, and neither dominates in experiments. This topological unification allows us to greatly extend the nuisance parameter approach. How and why the nuisance parameter approach works and how it can be extended bear closely on recent developments in artificial neural networks. Statistical content is provided by viewing specification tests with nuisance parameters as tests of hypotheses about Banach-valued random elements and applying the Banach central limit theorem and law of iterated logarithm, leading to simple procedures that can be used as a guide to when computationally more elaborate procedures may be warranted.

This paper investigates the behavior of the maximum likelihood estimator of a Gaussian autoregressive moving average model with a unit root in the moving average polynomial. The results are primarily of interest in testing hypotheses that involve moving average unit roots as, for example, when testing for stationarity of a series.

The distribution of sums of squared random variables with heavy-tailed distributions is investigated. Considering random variables in the domain of attraction of a stable Paretian law we derive the limiting distribution as the degrees of freedom approach infinity. The finite-degrees-of-freedom behavior for stable Paretian variates is simulated. Response surface techniques are employed to compactly summarize the simulation results for a relevant range of significance levels.

This article analyzes the asymptotic behavior of the Dickey–Fuller unit root tests when the variable is generated under the breaking trend hypothesis. Our results show that the asymptotic behavior of these statistics allows for the rejection of the unit root hypothesis. This asymptotic finding contrasts with the results that can be found in the literature devoted to the analysis of the integration order of a variable in the presence of a structural break. However, some Monte Carlo exercises show that the argument of Perron (1989, Econometrica 57, 1361–1401) that the tests are biased in favor of nonrejection of the unit root hypothesis remains valid for sample sizes of practical interest.

“Notoriously, works on mathematical finance can be precise, and they can be comprehensible. Sadly, as Dr. Johnson might have put it, the ones which are precise are not necessarily comprehensible, and those comprehensible are not necessarily precise.” So starts the preface to Baxter and Rennie's recent treatise on financial calculus. The book attempts to give an introduction to modern continuous time finance in a precise and comprehensible fashion. Does it succeed? Yes, it is a very clear and precise little (233 pages) book, although the claim that the book is accessible to a reader with only “some knowledge of (classical) differential calculus and experience with symbolic notation” is exaggerated. Such a reader would find the material hard going indeed.

This book, Topics in Advanced Econometrics, is written primarily as a textbook for an advanced graduate econometrics course. The topics covered include consistent model specification testing, unit roots and cointegration, and nonparametric regression estimation; they are mainly the topics in which Professor Bierens has made significant contributions to the literature over the last 15 years. This book is unusual as a textbook in the sense that it treats both cross-sectional and time series (i.e., both subscript i and t) issues in econometrics at an advanced level. Most of the results given, other than those available in standard econometrics or statistics textbooks, are drawn from the published work of the author. The book is very useful because it puts together a number of important current issues that have been treated separately in the literature and presents them systematically using a well-organized set of statistical tools. Another advantage of this book is that the materials given are almost self-contained, making this book suitable for self-tuition. This book thus ideally suits students who need tools for independent research especially in the area of nonlinear and nonparametric models and time series analysis. It will also be useful to more advanced researchers who are interested in a thorough understanding of some of the author's original and influential work in these areas.

Since the influential work by Nelson and Plosser (1982) and Engle and Granger (1987), many new and exciting developments have been made in the analysis of time series involving autoregressive unit roots. Hatanaka (1996; hereafter HT) reviewed the literature on unit roots and cointegration up to 1994 and provided new perspectives on this research area.

This book is a collection of matrix results that the author found important for his own work. To make the book reasonably self-contained, the author has also added many elementary results. The book contains definitions and results only and no proofs.