Bootstrap M Unit Root Tests
AbstractIn this article we propose wild bootstrap implementations of the local generalized least squares (GLS) de-trended M and ADF unit root tests of Stock (1999), Ng and Perron (2001), and Elliott et al. (1996), respectively. The bootstrap statistics are shown to replicate the first-order asymptotic distributions of the original statistics, while numerical evidence suggests that the bootstrap tests perform well in small samples. A recolored version of our bootstrap is also proposed which can further improve upon the finite sample size properties of the procedure when the shocks are serially correlated, in particular ameliorating the significant under-size seen in the M tests against processes with autoregressive or moving average roots close to -1. The wild bootstrap is used because it has the desirable property of preserving in the resampled data the pattern of heteroskedasticity present in the original shocks, thereby allowing for cases where the series under test is driven by martingale difference innovations.
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Bibliographic InfoArticle provided by Taylor & Francis Journals in its journal Econometric Reviews.
Volume (Year): 28 (2009)
Issue (Month): 5 ()
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- Su, Jen-Je & Cheung, Adrian (Wai-Kong) & Roca, Eduardo, 2014. "Does Purchasing Power Parity hold? New evidence from wild-bootstrapped nonlinear unit root tests in the presence of heteroskedasticity," Economic Modelling, Elsevier, vol. 36(C), pages 161-171.
- Smeekes Stephan, 2009. "Detrending Bootstrap Unit Root Tests," Research Memorandum 056, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- Cavaliere Giuseppe & Phillips Peter C.B. & Smeekes Stephan & Taylor A.M. Robert, 2011. "Lag Length Selection for Unit Root Tests in the Presence of Nonstationary Volatility," Research Memorandum 056, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- Cavaliere Giuseppe & Phillips Peter C.B. & Smeekes Stephan & Taylor A.M. Robert, 2011.
"Lag Length Selection for Unit Root Tests in the Presence of Nonstationary Volatility,"
056, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- Giuseppe Cavaliere & Peter C.B. Phillips & Stephan Smeekes & A.M. Robert Taylor, 2012. "Lag Length Selection for Unit Root Tests in the Presence of Nonstationary Volatility," Cowles Foundation Discussion Papers 1844, Cowles Foundation for Research in Economics, Yale University.
- Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2012. "Unit roots, nonlinearities and structural breaks," CREATES Research Papers 2012-14, School of Economics and Management, University of Aarhus.
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