IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v67y2013icp25-40.html
   My bibliography  Save this article

The spurious regression of AR(p) infinite-variance sequence in the presence of structural breaks

Author

Listed:
  • Jin, Hao
  • Zhang, Jinsuo
  • Zhang, Si
  • Yu, Cong

Abstract

This paper analyzes a spurious regression involving AR(p) infinite-variance processes in the presence of structural breaks by least squares using asymptotic theory. It is found that when regressing two independent infinite-variance sequence with breaks in the level and slope of trend, no matter whether the breaks occur at different points or not, the t-ratios become divergent and spurious phenomenon happens. The intuition behind this is that structural breaks can increase persistency in the level of regression errors, which then leads to spurious regressions. Simulation reveals that the effects of spurious regression not only depend on the autoregressive parameter and tailed index, but are sensitive to the presence of a linear trend in the regression model, and to the relative location of breaks with the sample. As a result, spurious effects might occur more often than we previously believed as they can arise even between AR(p) infinite-variance series with structural breaks.

Suggested Citation

  • Jin, Hao & Zhang, Jinsuo & Zhang, Si & Yu, Cong, 2013. "The spurious regression of AR(p) infinite-variance sequence in the presence of structural breaks," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 25-40.
    • Handle: RePEc:eee:csdana:v:67:y:2013:i:c:p:25-40
    DOI: 10.1016/j.csda.2013.04.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947313001527
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2013.04.011?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. McCallum, Bennett T., 2010. "Is the spurious regression problem spurious?," Economics Letters, Elsevier, vol. 107(3), pages 321-323, June.
    2. Clive Granger & Namwon Hyung & Yongil Jeon, 2001. "Spurious regressions with stationary series," Applied Economics, Taylor & Francis Journals, vol. 33(7), pages 899-904.
    3. Piotr S. Kokoszka & Murad S. Taqqu, 2001. "Can One Use the Durbin–Levinson Algorithm to Generate Infinite Variance Fractional ARIMA Time Series?," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(3), pages 317-337, May.
    4. Noriega, Antonio E. & de Alba, Enrique, 2001. "Stationarity and structural breaks -- evidence from classical and Bayesian approaches," Economic Modelling, Elsevier, vol. 18(4), pages 503-524, December.
    5. Martínez-Rivera, Berenice & Ventosa-Santaulària, Daniel, 2012. "A comment on ‘Is the spurious regression problem spurious?’," Economics Letters, Elsevier, vol. 115(2), pages 229-231.
    6. Entorf, Horst, 1997. "Random walks with drifts: Nonsense regression and spurious fixed-effect estimation," Journal of Econometrics, Elsevier, vol. 80(2), pages 287-296, October.
    7. Sollis, Robert, 2011. "Spurious regression: A higher-order problem," Economics Letters, Elsevier, vol. 111(2), pages 141-143, May.
    8. García-Belmonte, Lizeth & Ventosa-Santaulària, Daniel, 2011. "Spurious regression and lurking variables," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 2004-2010.
    9. Piotr Kokoszka & Michael Wolf, 2004. "Subsampling the mean of heavy‐tailed dependent observations," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(2), pages 217-234, March.
    10. Tsay, Wen-Jen, 1999. "Spurious Regression Between I(1) Processes With Infinite Variance Errors," Econometric Theory, Cambridge University Press, vol. 15(4), pages 622-628, August.
    11. Marmol, Francesc, 1998. "Spurious regression theory with nonstationary fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 84(2), pages 233-250, June.
    12. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    13. Jin, Hao & Tian, Zheng & Qin, Ruibing, 2009. "Bootstrap tests for structural change with infinite variance observations," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 1985-1995, October.
    14. Antonio E. Noriega & Daniel Ventosa‐Santaulària, 2006. "Spurious Regression Under Broken‐Trend Stationarity," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(5), pages 671-684, September.
    15. Tsay, Wen-Jen & Chung, Ching-Fan, 2000. "The spurious regression of fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 96(1), pages 155-182, May.
    16. Fox, Robert & Taqqu, Murad S., 1987. "Multiple stochastic integrals with dependent integrators," Journal of Multivariate Analysis, Elsevier, vol. 21(1), pages 105-127, February.
    17. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    18. Haldrup, Niels, 1994. "The asymptotics of single-equation cointegration regressions with I(1) and I(2) variables," Journal of Econometrics, Elsevier, vol. 63(1), pages 153-181, July.
    19. Jin, Hao & Zhang, Jinsuo, 2010. "Subsampling tests for variance changes in the presence of autoregressive parameter shifts," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2255-2265, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hao Jin & Si Zhang & Jinsuo Zhang, 2017. "Spurious regression due to neglected of non-stationary volatility," Computational Statistics, Springer, vol. 32(3), pages 1065-1081, September.
    2. Si Zhang & Hao Jin & Menglin Su, 2024. "Modified Block Bootstrap Testing for Persistence Change in Infinite Variance Observations," Mathematics, MDPI, vol. 12(2), pages 1-25, January.

    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. Noriega Antonio E. & Ventosa-Santaulària Daniel, 2006. "Spurious Regression and Econometric Trends," Working Papers 2006-05, Banco de México.
    2. Antonio E. Noriega & Daniel Ventosa‐Santaulària, 2007. "Spurious Regression and Trending Variables," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 69(3), pages 439-444, June.
    3. Noriega, Antonio E. & Ventosa-Santaulària, Daniel, 2005. "Spurious regression under deterministic and stochastic trends," MPRA Paper 58772, University Library of Munich, Germany.
    4. Antonio E. Noriega & Daniel Ventosa‐Santaulària, 2006. "Spurious Regression Under Broken‐Trend Stationarity," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(5), pages 671-684, September.
    5. Noriega Antonio E. & Ventosa-Santaulària Daniel, 2011. "A Simple Test for Spurious Regressions," Working Papers 2011-05, Banco de México.
    6. Stewart, Chris, 2006. "Spurious correlation of I(0) regressors in models with an I(1) dependent variable," Economics Letters, Elsevier, vol. 91(2), pages 184-189, May.
    7. Zhang, Lingxiang, 2013. "Partial unit root and linear spurious regression: A Monte Carlo simulation study," Economics Letters, Elsevier, vol. 118(1), pages 189-191.
    8. Kruse Robinson & Ventosa-Santaulària Daniel & Noriega Antonio E., 2017. "Changes in persistence, spurious regressions and the Fisher hypothesis," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(3), pages 1-28, June.
    9. D. Ventosa-Santaulària, 2009. "Spurious Regression," Journal of Probability and Statistics, Hindawi, vol. 2009, pages 1-27, August.
    10. Chris Stewart, 2011. "A note on spurious significance in regressions involving I(0) and I(1) variables," Empirical Economics, Springer, vol. 41(3), pages 565-571, December.
    11. Mármol, Francesc, 1999. "How spurious features arise in case of fractional cointegration," DES - Working Papers. Statistics and Econometrics. WS 6349, Universidad Carlos III de Madrid. Departamento de Estadística.
    12. Hao Jin & Si Zhang & Jinsuo Zhang, 2017. "Spurious regression due to neglected of non-stationary volatility," Computational Statistics, Springer, vol. 32(3), pages 1065-1081, September.
    13. Lee, Young-Sook & Kim, Tae-Hwan & Newbold, Paul, 2005. "Spurious nonlinear regressions in econometrics," Economics Letters, Elsevier, vol. 87(3), pages 301-306, June.
    14. Ferson, Wayne E. & Sarkissian, Sergei & Simin, Timothy, 2008. "Asset Pricing Models with Conditional Betas and Alphas: The Effects of Data Snooping and Spurious Regression," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 43(2), pages 331-353, June.
    15. Manuel Gómez Zaldivar & Oscar Manjarrez Castro & Daniel Ventosa-Santaulària, 2009. "Regresión espuria en especificaciones dinámicas," Ensayos Revista de Economia, Universidad Autonoma de Nuevo Leon, Facultad de Economia, vol. 0(1), pages 1-20, May.
    16. Granger, Clive W.J., 2012. "Useful conclusions from surprising results," Journal of Econometrics, Elsevier, vol. 169(2), pages 142-146.
    17. Kim, Tae-Hwan & Lee, Young-Sook & Newbold, Paul, 2004. "Spurious regressions with stationary processes around linear trends," Economics Letters, Elsevier, vol. 83(2), pages 257-262, May.
    18. Chu Ba & Kozhan Roman, 2010. "Spurious Regressions of Stationary AR(p) Processes with Structural Breaks," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(1), pages 1-25, December.
    19. Travaglini, Guido, 2007. "The U.S. Dynamic Taylor Rule With Multiple Breaks, 1984-2001," MPRA Paper 3419, University Library of Munich, Germany, revised 15 Jun 2007.
    20. Phillips, Peter C.B., 2005. "Challenges of trending time series econometrics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(5), pages 401-416.

    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:eee:csdana:v:67:y:2013:i:c:p:25-40. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.