ARMA Sieve bootstrap unit root tests
AbstractAugmented Dickey-Fuller unit root tests may severely overreject when the DGP is a general linear process. The use of the AR sieve bootstrap, proposed by Park (2002) and Chang and Park (2003), may alleviate this problem. We propose sieve bootstraps based on MA and ARMA approximations. Invariance principles for the partial sum processes built from these sieve bootstrap DGPs are established and a proof of the asymptotic validity of the resulting ADF bootstrap tests is provided. Through Monte Carlo experiments, we find that the rejection probabilities of the MA and ARMA sieve bootstraps are often lower and more robust to the underlying DGP than that of the AR sieve bootstrap. In particular, the new sieve bootstraps perform much better than the AR sieve when a large MA root is present. We also find that the ARMA sieve bootstrap requires only a very parsimonious specification to achieve excellent results.
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Bibliographic InfoPaper provided by Departement d'Economique de la Faculte d'administration à l'Universite de Sherbrooke in its series Cahiers de recherche with number 07-05.
Length: 38 pages
Date of creation: 2007
Date of revision: Jul 2009
Sieve bootstrap; Unit root; ADF tests; ARMA approximations; Invariance Principle;
Find related papers by JEL classification:
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-04-09 (All new papers)
- NEP-ECM-2007-04-09 (Econometrics)
- NEP-ETS-2007-04-09 (Econometric Time Series)
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- Abadir, K.M., 1992.
"The Limiting Distribution of the T Ratio Under a Unit Root,"
1992-2, American Cairo - Economics and Political Sciences.
- Abadir, Karim M., 1995. "The Limiting Distribution of the t Ratio Under a Unit Root," Econometric Theory, Cambridge University Press, vol. 11(04), pages 775-793, August.
- repec:rus:hseeco:4965 is not listed on IDEAS
- Russell Davidson & James Mackinnon, 2006.
"Improving the reliability of bootstrap tests with the fast double bootstrap,"
- Davidson, Russell & MacKinnon, James G., 2007. "Improving the reliability of bootstrap tests with the fast double bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3259-3281, April.
- Russell Davidson & James G. MacKinnon, 2006. "Improving the Reliability of Bootstrap Tests with the Fast Double Bootstrap," Working Papers 1044, Queen's University, Department of Economics.
- Park, Joon Y., 2002. "An Invariance Principle For Sieve Bootstrap In Time Series," Econometric Theory, Cambridge University Press, vol. 18(02), pages 469-490, April.
- Joon Y. Park, 2003.
"Bootstrap Unit Root Tests,"
Econometric Society, vol. 71(6), pages 1845-1895, November.
- Joon Y. Park, 2000. "Bootstrap Unit Root Tests," Econometric Society World Congress 2000 Contributed Papers 1587, Econometric Society.
- Park, Joon, 2002. "Bootstrap Unit Root Tests," Working Papers 2003-04, Rice University, Department of Economics.
- Davidson, Russell & MacKinnon, James G, 1998.
"Graphical Methods for Investigating the Size and Power of Hypothesis Tests,"
The Manchester School of Economic & Social Studies,
University of Manchester, vol. 66(1), pages 1-26, January.
- Russell Davidson & James G. MacKinnon, 1994. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," Working Papers 903, Queen's University, Department of Economics.
- Donald W.K. Andrews, 2002.
"The Block-block Bootstrap: Improved Asymptotic Refinements,"
Cowles Foundation Discussion Papers
1370, Cowles Foundation for Research in Economics, Yale University.
- Donald W. K. Andrews, 2004. "the Block-Block Bootstrap: Improved Asymptotic Refinements," Econometrica, Econometric Society, vol. 72(3), pages 673-700, 05.
- Yoosoon Chang & Joon Y. Park, 2003. "A Sieve Bootstrap For The Test Of A Unit Root," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 379-400, 07.
- Yoosoon Chang & Joon Park, 2002. "On The Asymptotics Of Adf Tests For Unit Roots," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 431-447.
- Parker, Cameron & Paparoditis, Efstathios & Politis, Dimitris N., 2006. "Unit root testing via the stationary bootstrap," Journal of Econometrics, Elsevier, vol. 133(2), pages 601-638, August.
- repec:cup:etheor:v:11:y:1995:i:4:p:775-93 is not listed on IDEAS
- Stephan Smeekes, 2013.
"Detrending Bootstrap Unit Root Tests,"
Taylor & Francis Journals, vol. 32(8), pages 869-891, November.
- James G. MacKinnon, 2007. "Bootstrap Hypothesis Testing," Working Papers 1127, Queen's University, Department of Economics.
- Patrick Marsh, . "Saddlepoint Approximations for Optimal Unit Root Tests," Discussion Papers 09/31, Department of Economics, University of York.
- Richard, Patrick, 2009.
"Modified fast double sieve bootstraps for ADF tests,"
Computational Statistics & Data Analysis,
Elsevier, vol. 53(12), pages 4490-4499, October.
- Patrick Richard, 2008. "Modified Fast Double Sieve Bootstraps for ADF Tests," Cahiers de recherche 08-17, Departement d'Economique de la Faculte d'administration à l'Universite de Sherbrooke.
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