A Generalised Fractional Differencing Bootstrap for Long Memory Processes
A Generalised Fractional Differencing Bootstrap for Long Memory Processes

Author: George Kappetanios

Publisher:

Published: 2020

Total Pages: 0

ISBN-13:

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A bootstrap methodology suitable for use with stationary and non-stationary fractionally integrated time series is further developed in this article. The resampling algorithm involves estimating the degree of fractional integration, applying the fractional differencing operator, resampling the resulting approximation to the underlying short memory series and, finally, cumulating to obtain a resample of the original fractionally integrated process. This approach extends existing methods in the literature by allowing for general bootstrap schemes including blockwise bootstraps. Furthermore, we show that it can also be validly used for non-stationary fractionally integrated processes. We establish asymptotic validity results for the general method and provide simulation evidence which highlights a number of favourable aspects of its finite sample performance, relative to other commonly used bootstrap methods.

Almost All About Unit Roots
Almost All About Unit Roots

Author: In Choi

Publisher: Cambridge University Press

Published: 2015-05-12

Total Pages: 301

ISBN-13: 1107097339

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Many economic theories depend on the presence or absence of a unit root for their validity, making familiarity with unit roots extremely important to econometric and statistical theory. This book introduces the literature on unit roots in a comprehensive manner to empirical and theoretical researchers in economics and other areas.

Bootstrap Methods
Bootstrap Methods

Author: Gerhard Dikta

Publisher: Springer Nature

Published: 2021-08-10

Total Pages: 256

ISBN-13: 3030734803

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This book provides a compact introduction to the bootstrap method. In addition to classical results on point estimation and test theory, multivariate linear regression models and generalized linear models are covered in detail. Special attention is given to the use of bootstrap procedures to perform goodness-of-fit tests to validate model or distributional assumptions. In some cases, new methods are presented here for the first time. The text is motivated by practical examples and the implementations of the corresponding algorithms are always given directly in R in a comprehensible form. Overall, R is given great importance throughout. Each chapter includes a section of exercises and, for the more mathematically inclined readers, concludes with rigorous proofs. The intended audience is graduate students who already have a prior knowledge of probability theory and mathematical statistics.