IDEAS home Printed from https://ideas.repec.org/a/gam/jstats/v7y2024i4p72-1243d1501069.html
   My bibliography  Save this article

Prepivoted Augmented Dickey-Fuller Test with Bootstrap-Assisted Lag Length Selection

Author

Listed:
  • Somak Maitra

    (Department of Mathematics, University of California—San Diego, La Jolla, CA 92093, USA)

  • Dimitris N. Politis

    (Department of Mathematics and Halicioǧlu Data Science Institute, University of California—San Diego, La Jolla, CA 92093, USA)

Abstract

We investigate the application of prepivoting in conjunction with lag length selection to correct the size and power performance of the Augmented Dickey-Fuller test for a unit root. The bootstrap methodology used to perform the prepivoting is a residual based AR bootstrap that ensures that bootstrap replicate time series are created under the null irrespective of whether the originally observed series obeys the null hypothesis or not. Simulation studies wherein we examine the performance of our proposed method are given; we evaluate our method’s performance on ARMA(1,1) models with varying configurations for size and power performance. We also propose a novel data dependent lag selection technique that uses bootstrap data under the null to select an optimal lag length; the performance of our method is compared to existing lag length selection criteria.

Suggested Citation

  • Somak Maitra & Dimitris N. Politis, 2024. "Prepivoted Augmented Dickey-Fuller Test with Bootstrap-Assisted Lag Length Selection," Stats, MDPI, vol. 7(4), pages 1-18, October.
  • Handle: RePEc:gam:jstats:v:7:y:2024:i:4:p:72-1243:d:1501069
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2571-905X/7/4/72/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2571-905X/7/4/72/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Schwert, G William, 2002. "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 5-17, January.
    2. Efstathios Paparoditis & Dimitris N. Politis, 2018. "The asymptotic size and power of the augmented Dickey–Fuller test for a unit root," Econometric Reviews, Taylor & Francis Journals, vol. 37(9), pages 955-973, October.
    3. Pierre Perron & Serena Ng, 1996. "Useful Modifications to some Unit Root Tests with Dependent Errors and their Local Asymptotic Properties," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(3), pages 435-463.
    4. Christian Léger & Joseph Romano, 1990. "Bootstrap choice of tuning parameters," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(4), pages 709-735, December.
    5. Paparoditis, Efstathios & Politis, Dimitris N., 2005. "Bootstrapping Unit Root Tests for Autoregressive Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 545-553, June.
    6. 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.
    7. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
    8. Emre Aylar & Stephan Smeekes & Joakim Westerlund, 2019. "Lag truncation and the local asymptotic distribution of the ADF test for a unit root," Statistical Papers, Springer, vol. 60(6), pages 2109-2118, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:gam:jstats:v:7:y:2024:i:4:p:72-1244:d:1501069 is not listed on IDEAS
    2. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2013. "Unit roots, non-linearities and structural breaks," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 4, pages 61-94, Edward Elgar Publishing.
    3. Cláudia Duarte, 2015. "Covariate-augmented unit root tests with mixed-frequency data," Working Papers w201507, Banco de Portugal, Economics and Research Department.
    4. Gaowen Wang, 2017. "Modified Unit Root Tests with Nuisance Parameter Free Asymptotic Distributions," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 519-538, June.
    5. Vicente Esteve & Manuel Navarro-Ibáñez & María A. Prats, 2013. "The present value model of US stock prices revisited: long-run evidence with structural breaks, 1871-2010," Working Papers 04/13, Instituto Universitario de Análisis Económico y Social.
    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. Esteve, Vicente & Tamarit, Cecilio, 2012. "Threshold cointegration and nonlinear adjustment between CO2 and income: The Environmental Kuznets Curve in Spain, 1857–2007," Energy Economics, Elsevier, vol. 34(6), pages 2148-2156.
    8. repec:kap:iaecre:v:17:y:2011:i:3:p:315-333 is not listed on IDEAS
    9. 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.
    10. Vicente Esteve & Manuel Navarro-Ibáñez & María A. Prats, 2013. "The present value model of U.S. stock prices revisited: long-run evidence with structural breaks, 1871-2010," Working Papers 1305, Department of Applied Economics II, Universidad de Valencia.
    11. Sánchez, Ismael, 2000. "Spectral density estimators at frequency zero for nonstationarity tests in arma models," DES - Working Papers. Statistics and Econometrics. WS 10132, Universidad Carlos III de Madrid. Departamento de Estadística.
    12. Pedersen, Thomas Quistgaard & Schütte, Erik Christian Montes, 2020. "Testing for explosive bubbles in the presence of autocorrelated innovations," Journal of Empirical Finance, Elsevier, vol. 58(C), pages 207-225.
    13. Esteve, Vicente & Navarro-Ibáñez, Manuel & Prats, María A., 2013. "The Spanish term structure of interest rates revisited: Cointegration with multiple structural breaks, 1974–2010," International Review of Economics & Finance, Elsevier, vol. 25(C), pages 24-34.
    14. Emilio Congregado & Antonio A. Golpe & Vicente Esteve, 2019. "On the Substitutability between Paid-employment and Self-employment: Evidence from the Period 1969–2014 in the United States," Sustainability, MDPI, vol. 11(2), pages 1-17, January.
    15. Giorgio Canarella & Rangan Gupta & Stephen M. Miller & Stephen K. Pollard, 2019. "Unemployment rate hysteresis and the great recession: exploring the metropolitan evidence," Empirical Economics, Springer, vol. 56(1), pages 61-79, January.
    16. Kellard, Neil & Mark E Wohar, 2003. "Trends and Persistence in Primary Commodity Prices," Royal Economic Society Annual Conference 2003 118, Royal Economic Society.
    17. Ajmi, Ahdi Noomen & El Montasser, Ghassen & Nguyen, Duc Khuong, 2013. "Testing the relationships between energy consumption and income in G7 countries with nonlinear causality tests," Economic Modelling, Elsevier, vol. 35(C), pages 126-133.
    18. Thilo Reinschlussel & Martin C. Arnold, 2024. "Information-Enriched Selection of Stationary and Non-Stationary Autoregressions using the Adaptive Lasso," Papers 2402.16580, arXiv.org, revised Jul 2024.
    19. Antonio Cubel & Vicente Esteve & Maria Teresa Sanchis & Juan A. Sanchis-Llopis, 2014. "The effect of foreign and domestic patents on total factor productivity during the second half of the 20th century," Working Papers 06/14, Instituto Universitario de Análisis Económico y Social.
    20. Serena Ng & Pierre Perron, 2002. "PPP May not Hold Afterall: A Further Investigation," Annals of Economics and Finance, Society for AEF, vol. 3(1), pages 43-64, May.
    21. Stephan Smeekes, 2013. "Detrending Bootstrap Unit Root Tests," Econometric Reviews, Taylor & Francis Journals, vol. 32(8), pages 869-891, November.
    22. McElroy, Tucker S. & Jach, Agnieszka, 2023. "Identification of the differencing operator of a non-stationary time series via testing for zeroes in the spectral density," Computational Statistics & Data Analysis, Elsevier, vol. 177(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jstats:v:7:y:2024:i:4:p:72-1243:d:1501069. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.