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On bootstrap implementation of likelihood ratio test for a unit root

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  • Skrobotov, Anton

Abstract

In this paper we investigate a bootstrap implementation of the likelihood ratio test for a unit root recently proposed by Jansson and Nielsen (2012). We demonstrate that the likelihood ratio test shows poor finite sample properties under strongly autocorrelated errors, i.e. if the autoregressive or moving average roots are close to −1. The size distortions in these case are more pronounced in comparison to the bootstrap M and ADF tests. We found that the bootstrap version of likelihood ratio test (with autoregressive recolouring) demonstrates better performance than bootstrap M tests. Moreover, the bootstrap likelihood ratio test show better finite sample properties in comparison to the bootstrap ADF in some cases.

Suggested Citation

  • Skrobotov, Anton, 2018. "On bootstrap implementation of likelihood ratio test for a unit root," Economics Letters, Elsevier, vol. 171(C), pages 154-158.
    • Handle: RePEc:eee:ecolet:v:171:y:2018:i:c:p:154-158
    DOI: 10.1016/j.econlet.2018.07.030
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    1. Jansson Michael & Nielsen Morten Ørregaard, 2011. "Nearly Efficient Likelihood Ratio Tests for Seasonal Unit Roots," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-21, February.
    2. 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.
    3. Giuseppe Cavaliere & A. M. Robert Taylor, 2009. "Bootstrap M Unit Root Tests," Econometric Reviews, Taylor & Francis Journals, vol. 28(5), pages 393-421.
    4. Michael Jansson & Morten Ørregaard Nielsen, 2012. "Nearly Efficient Likelihood Ratio Tests of the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 80(5), pages 2321-2332, September.
    5. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2009. "Heteroskedastic Time Series With A Unit Root," Econometric Theory, Cambridge University Press, vol. 25(5), pages 1228-1276, October.
    6. Smeekes, Stephan & Taylor, A.M. Robert, 2012. "Bootstrap Union Tests For Unit Roots In The Presence Of Nonstationary Volatility," Econometric Theory, Cambridge University Press, vol. 28(2), pages 422-456, April.
    7. Joon Y. Park, 2003. "Bootstrap Unit Root Tests," Econometrica, Econometric Society, vol. 71(6), pages 1845-1895, November.
    8. Park, Joon Y., 2006. "A bootstrap theory for weakly integrated processes," Journal of Econometrics, Elsevier, vol. 133(2), pages 639-672, August.
    9. 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, July.
    10. Stephan Smeekes, 2013. "Detrending Bootstrap Unit Root Tests," Econometric Reviews, Taylor & Francis Journals, vol. 32(8), pages 869-891, November.
    11. Boswijk, H. Peter & Jansson, Michael & Nielsen, Morten Ørregaard, 2015. "Improved likelihood ratio tests for cointegration rank in the VAR model," Journal of Econometrics, Elsevier, vol. 184(1), pages 97-110.
    12. Perron, Pierre & Qu, Zhongjun, 2007. "A simple modification to improve the finite sample properties of Ng and Perron's unit root tests," Economics Letters, Elsevier, vol. 94(1), pages 12-19, January.
    13. Park, Joon Y., 2002. "An Invariance Principle For Sieve Bootstrap In Time Series," Econometric Theory, Cambridge University Press, vol. 18(2), pages 469-490, April.
    14. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    15. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2008. "Bootstrap Unit Root Tests For Time Series With Nonstationary Volatility," Econometric Theory, Cambridge University Press, vol. 24(1), pages 43-71, February.
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    Cited by:

    1. Walter Distaso & Rustam Ibragimov & Alexander Semenov & Anton Skrobotov, 2020. "COVID-19: Tail Risk and Predictive Regressions," Papers 2009.02486, arXiv.org, revised Oct 2021.
    2. Kassouri, Yacouba & Altıntaş, Halil, 2020. "Threshold cointegration, nonlinearity, and frequency domain causality relationship between stock price and Turkish Lira," Research in International Business and Finance, Elsevier, vol. 52(C).

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    More about this item

    Keywords

    Likelihood ratio test; Unit root test; Bootstrap;
    All these keywords.

    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; Diffusion Processes

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