Open AccessSize Distortion of Bootstrap Tests: an Example from Unit Root Testing
Author(s) -
Russell Davidson
Publication year - 2010
Publication title -
review of economic analysis
Language(s) - English
Resource type - Journals
ISSN - 1973-3909
DOI - 10.15353/rea.v2i2.1471
Subject(s) - unit root , distortion (music) , series (stratigraphy) , mathematics , statistics , root (linguistics) , statistical hypothesis testing , bootstrap model , unit root test , econometrics , computer science , physics , cointegration , boson , amplifier , computer network , paleontology , linguistics , philosophy , bandwidth (computing) , particle physics , particle decay , biology
Testing for a unit root in a series obtained by summing a stationary MA(1) process with a parameter close to -1 leads to serious size distortions under the null, on account of the near cancellation of the unit root by the MA component in the driving stationary series. The situation is analysed from the point of view of bootstrap testing, and an exact quantitative account is given of the error in rejection probability of a bootstrap test. A particular method of estimating the MA parameter is recommended, as it leads to very little distortion even when the MA parameter is close to -1. A new bootstrap procedure with still better properties is proposed. While more computationally demanding than the usual bootstrap, it is much less so than the double bootstrap.