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Bootstrap Tests for an Autoregressive Unit Root in the Presence of Weakly Dependent Errors

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  • Zacharias Psaradakis

Abstract

This paper examines bootstrap tests of the null hypothesis of an autoregressive unit root in models that may include a linear rend and/or an intercept and which are driven by innovations that belong to the class of stationary and invertible linear processes. Our approach makes use of a sieve bootstrap procedure based on residual resampling from autoregressive approximations, the order of which increases with the sample size at a suitable rate. We show that the sieve bootstrap provides asymptotically valid tests of the unit‐root hypothesis and demonstrate the small‐sample effectiveness of the method by means of simulation.

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  • Zacharias Psaradakis, 2001. "Bootstrap Tests for an Autoregressive Unit Root in the Presence of Weakly Dependent Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(5), pages 577-594, September.
    • Handle: RePEc:bla:jtsera:v:22:y:2001:i:5:p:577-594
    DOI: 10.1111/1467-9892.00242
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    Cited by:

    1. Mehmet Fatih Tra? & Esra Ball? & Çiler Sigeze, 2016. "Testing for Purchasing Power Parity for Selected CIS Countries Using the Sieve Bootstrap," Proceedings of International Academic Conferences 3506095, International Institute of Social and Economic Sciences.
    2. Fuertes, Ana-Maria, 2008. "Sieve bootstrap t-tests on long-run average parameters," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3354-3370, March.
    3. Franz C. Palm & Stephan Smeekes & Jean‐Pierre Urbain, 2008. "Bootstrap Unit‐Root Tests: Comparison and Extensions," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(2), pages 371-401, March.
    4. C. Jentsch & J.-P. Kreiss & P. Mantalos & E. Paparoditis, 2012. "Hybrid bootstrap aided unit root testing," Computational Statistics, Springer, vol. 27(4), pages 779-797, December.
    5. Bruce E. Hansen & Jeffrey S. Racine, 2024. "Bootstrap Model Averaging Unit Root Inference," Advances in Econometrics, in: Essays in Honor of Subal Kumbhakar, volume 46, pages 81-98, Emerald Group Publishing Limited.
    6. Christopoulos, Dimitris K. & Gente, Karine & León-Ledesma, Miguel A., 2012. "Net foreign assets, productivity and real exchange rates in constrained economies," European Economic Review, Elsevier, vol. 56(3), pages 295-316.
    7. Richard, Patrick, 2009. "Modified fast double sieve bootstraps for ADF tests," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4490-4499, October.
    8. Martin Sola & Zacharias Psaradakis & Fabio Spagnolo, 2005. "Testing the unbiased forward exchange rate hypothesis using a Markov switching model and instrumental variables," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(3), pages 423-437.
    9. Psaradakis, Zacharias, 2002. "On the asymptotic behaviour of unit-root tests in the presence of a Markov trend," Statistics & Probability Letters, Elsevier, vol. 57(1), pages 101-109, March.
    10. Rossi, Francesca & Lieberman, Offer, 2023. "Spatial autoregressions with an extended parameter space and similarity-based weights," Journal of Econometrics, Elsevier, vol. 235(2), pages 1770-1798.
    11. Davidson, Russell & Trokić, Mirza, 2020. "The fast iterated bootstrap," Journal of Econometrics, Elsevier, vol. 218(2), pages 451-475.
    12. Sebastian Kripfganz & Daniel C. Schneider, 2020. "Response Surface Regressions for Critical Value Bounds and Approximate p‐values in Equilibrium Correction Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(6), pages 1456-1481, December.
    13. Zou, Nan & Politis, Dimitris N., 2019. "Linear process bootstrap unit root test," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 74-80.
    14. Li, Haiqi & Zheng, Chaowen, 2018. "Unit root quantile autoregression testing with smooth structural changes," Finance Research Letters, Elsevier, vol. 25(C), pages 83-89.
    15. Christis Katsouris, 2023. "Bootstrapping Nonstationary Autoregressive Processes with Predictive Regression Models," Papers 2307.14463, arXiv.org.
    16. Anders Rygh Swensen, 2003. "Bootstrapping unit root tests for integrated processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(1), pages 99-126, January.
    17. Margherita Gerolimetto & Stefano Magrini, 2020. "Testing for boundary conditions in case of fractionally integrated processes," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(2), pages 357-371, June.
    18. Nunzio Cappuccio & Diego Lubian, 2016. "Unit Root Tests: The Role of the Univariate Models Implied by Multivariate Time Series," Econometrics, MDPI, vol. 4(2), pages 1-11, April.
    19. Bisaglia, Luisa & Procidano, Isabella, 2002. "On the power of the Augmented Dickey-Fuller test against fractional alternatives using bootstrap," Economics Letters, Elsevier, vol. 77(3), pages 343-347, November.
    20. Andrea Silvestrini, 2010. "Testing fiscal sustainability in Poland: a Bayesian analysis of cointegration," Empirical Economics, Springer, vol. 39(1), pages 241-274, August.

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