Bootstrap Model Averaging Unit Root Inference

Classical unit root tests are known to suffer from potentially crippling size distortions, and a range of procedures have been proposed to attenuate this problem, including the use of bootstrap procedures. It is also known that the estimating equation's functional form can affect the outcome of the test, and various model selection procedures have been proposed to overcome this limitation. In this paper, we adopt a model averaging procedure to deal with model uncertainty at the testing stage. In addition, we leverage an automatic model-free dependent bootstrap procedure where the null is imposed by simple differencing (the block length is automatically determined using recent developments for bootstrapping dependent processes). Monte Carlo simulations indicate that this approach exhibits the lowest size distortions among its peers in settings that confound existing approaches, while it has superior power relative to those peers whose size distortions do not preclude their general use. The proposed approach is fully automatic, and there are no nuisance parameters that have to be set by the user, which ought to appeal to practitioners.

It is the editor’s distinct privilege to gather this collection of papers that honors Subhal Kumbhakar’s many accomplishments, drawing further attention to the various areas of scholarship that he has touched.

This book presents a selection of peer-reviewed contributions on the latest developments in time series analysis and forecasting, presented at the 7th International Conference on Time Series and Forecasting, ITISE 2021, held in Gran Canaria, Spain, July 19-21, 2021. It is divided into four parts. The first part addresses general modern methods and theoretical aspects of time series analysis and forecasting, while the remaining three parts focus on forecasting methods in econometrics, time series forecasting and prediction, and numerous other real-world applications. Covering a broad range of topics, the book will give readers a modern perspective on the subject. The ITISE conference series provides a forum for scientists, engineers, educators and students to discuss the latest advances and implementations in the foundations, theory, models and applications of time series analysis and forecasting. It focuses on interdisciplinary research encompassing computer science, mathematics, statistics and econometrics.

"This book is. . . clear and well-written. . . anyone with any interest in the basis of quantitative analysis simply must read this book. . . . well-written, with a wealth of explanation. . ." --Dougal Hutchison in Educational Research Using real data examples, this volume shows how to apply bootstrapping when the underlying sampling distribution of a statistic cannot be assumed normal, as well as when the sampling distribution has no analytic solution. In addition, it discusses the advantages and limitations of four bootstrap confidence interval methods--normal approximation, percentile, bias-corrected percentile, and percentile-t. The book concludes with a convenient summary of how to apply this computer-intensive methodology using various available software packages.

This article proposes a hybrid bootstrap approach to approximate the augmented Dickey-Fuller test by perturbing both the residual sequence and the minimand of the objective function. Since innovations can be dependent, this allows the inclusion of conditional heteroscedasticity models. The new bootstrap method is also applied to least absolute deviation-based unit root test statistics, which are efficient in handling heavy-tailed time-series data. The asymptotic distributions of resulting bootstrap tests are presented, and Monte Carlo studies demonstrate the usefulness of the proposed tests.

A comprehensive review of unit roots, cointegration and structural change from a best-selling author.

In this paper, we consider a sieve bootstrap for the test of a unit root in models driven by general linear processes. The given model is first approximated by a finite autoregressive integrated process of order increasing with the sample size, and then the method of bootstrap is applied for the approximated autoregression to obtain the critical values for the usual unit root tests. The resulting tests, which may simply be viewed as the bootstrapped versions of Augmented Dickey-Fuller (ADF) unit root tests by Said and Dickey (1984), are shown to be consistent under very general conditions. The asymptotic validity of the bootstrap ADF unit root tests is thus established. Our conditions are significantly weaker than those used by Said and Dickey. Simulations show that bootstrap provides substantial improvements on finite sample sizes of the tests.

This book discusses the econometric foundations of structural vector autoregressive modeling, as used in empirical macroeconomics, finance, and related fields.