Bootstrap union tests for unit roots in the presence of nonstationary volatility

Discussion Papers from University of Nottingham, Granger Centre for Time Series Econometrics

Abstract: We provide a joint treatment of three major issues that surround testing for a unit root in practice: uncertainty as to whether or not a linear deterministic trend is present in the data, uncertainty as to whether the initial condition of the process is (asymptotically) negligible or not, and the possible presence of nonstationary volatility in the data. Harvey, Leybourne and Taylor (2010, Journal of Econometrics, forthcoming) propose decision rules based on a four-way union of rejections of QD and OLS detrended tests, both with and without allowing for a linear trend, to deal with the first two problems. However, in the presence of nonstationary volatility these test statistics have limit distributions which depend on the form of the volatility process, making tests based on the standard asymptotic critical values invalid. We construct bootstrap versions of the four-way union of rejections test, which, by employing the wild bootstrap, are shown to be asymptotically valid in the presence of nonstationary volatility. These bootstrap union tests therefore allow for a joint treatment of all three of the aforementioned problems.

Keywords: Unit root; local trend; initial condition; asymptotic power; union of rejections decision rule; nonstationary volatility; wild bootstrap (search for similar items in EconPapers)
Date: 2010-02
New Economics Papers: this item is included in nep-ecm and nep-ets
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Related works:
Journal Article: BOOTSTRAP UNION TESTS FOR UNIT ROOTS IN THE PRESENCE OF NONSTATIONARY VOLATILITY (2012)
Working Paper: Bootstrap union tests for unit roots in the presence of nonstationary volatility (2010)
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Persistent link: https://EconPapers.repec.org/RePEc:not:notgts:10/03

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