IDEAS home Printed from https://ideas.repec.org/p/aah/create/2013-11.html
   My bibliography  Save this paper

Changes in persistence, spurious regressions and the Fisher hypothesis

Author

Listed:
  • Robinson Kruse

    (Leibniz University Hannover and CREATES)

  • Daniel Ventosa-Santaulària

    (Centro de Investigación y Docencia Económicas, CIDE)

  • Antonio E. Noriega

    (Banco de México)

Abstract

Declining inflation persistence has been documented in numerous studies. When such series are analyzed in a regression framework in conjunction with other persistent time series, spurious regressions are likely to occur. We propose to use the coefficient of determination R2 as a test statistic to distinguish between spurious and genuine regressions in situations where time series possibly (but not necessarily) exhibit changes in persistence. To this end, we establish some limit theory for the R2 statistic and conduct a Monte Carlo study where we investigate its finite-sample properties. Finally, we apply the test to the Fisher equation for the U.S. and Mexico. Contrary to a rejection using cointegration techniques, the R2-based test offers strong evidence favourable to the Fisher hypothesis.

Suggested Citation

  • Robinson Kruse & Daniel Ventosa-Santaulària & Antonio E. Noriega, 2013. "Changes in persistence, spurious regressions and the Fisher hypothesis," CREATES Research Papers 2013-11, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2013-11
    as

    Download full text from publisher

    File URL: https://repec.econ.au.dk/repec/creates/rp/13/rp13_11.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Marmol, Francesc, 1996. "Nonsense Regressions between Integrated Processes of Different Orders," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 58(3), pages 525-536, August.
    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. & Ramos-Francia, Manuel, 2009. "The dynamics of persistence in US inflation," Economics Letters, Elsevier, vol. 105(2), pages 168-172, November.
    4. Christopher J. Neely & David E. Rapach, 2008. "Real interest rate persistence: evidence and implications," Review, Federal Reserve Bank of St. Louis, vol. 90(Nov), pages 609-642.
    5. Yiguo Sun & Cheng Hsiao & Qi Li, 2015. "Volatility Spillover Effect: A Semiparametric Analysis of Non-Cointegrated Process," Econometric Reviews, Taylor & Francis Journals, vol. 34(1-2), pages 127-145, February.
    6. Clive Granger & Namwon Hyung & Yongil Jeon, 2001. "Spurious regressions with stationary series," Applied Economics, Taylor & Francis Journals, vol. 33(7), pages 899-904.
    7. Tsong, Ching-Chuan & Lee, Cheng-Feng, 2013. "Quantile cointegration analysis of the Fisher hypothesis," Journal of Macroeconomics, Elsevier, vol. 35(C), pages 186-198.
    8. repec:bla:jfinan:v:43:y:1988:i:5:p:1095-1112 is not listed on IDEAS
    9. Joakim Westerlund, 2008. "Panel cointegration tests of the Fisher effect," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(2), pages 193-233.
    10. D. Ventosa-Santaulària, 2009. "Spurious Regression," Journal of Probability and Statistics, Hindawi, vol. 2009, pages 1-27, August.
    11. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    12. 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.
    13. Halunga, Andreea G. & Osborn, Denise R. & Sensier, Marianne, 2009. "Changes in the order of integration of US and UK inflation," Economics Letters, Elsevier, vol. 102(1), pages 30-32, January.
    14. Garcia, Rene & Perron, Pierre, 1996. "An Analysis of the Real Interest Rate under Regime Shifts," The Review of Economics and Statistics, MIT Press, vol. 78(1), pages 111-125, February.
    15. Kejriwal, Mohitosh & Perron, Pierre & Zhou, Jing, 2013. "Wald Tests For Detecting Multiple Structural Changes In Persistence," Econometric Theory, Cambridge University Press, vol. 29(2), pages 289-323, April.
    16. Eiji Kurozumi, 2005. "Detection of Structural Change in the Long‐run Persistence in a Univariate Time Series," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(2), pages 181-206, April.
    17. Philipp Sibbertsen & Robinson Kruse, 2009. "Testing for a break in persistence under long‐range dependencies," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(3), pages 263-285, May.
    18. 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.
    19. Mark J. Jensen, 2009. "The Long‐Run Fisher Effect: Can It Be Tested?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 41(1), pages 221-231, February.
    20. 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.
    21. Koustas, Zisimos & Serletis, Apostolos, 1999. "On the Fisher effect," Journal of Monetary Economics, Elsevier, vol. 44(1), pages 105-130, August.
    22. Mohitosh Kejriwal, 2009. "The Nature of Persistence in Euro Area Inflation: A Reconsideration," Purdue University Economics Working Papers 1218, Purdue University, Department of Economics.
    23. 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.
    24. Wolters Maik H. & Tillmann Peter, 2015. "The changing dynamics of US inflation persistence: a quantile regression approach," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(2), pages 161-182, April.
    25. Marmol, Francesc, 1998. "Spurious regression theory with nonstationary fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 84(2), pages 233-250, June.
    26. Alex Maynard & Aaron Smallwood & Mark E. Wohar, 2013. "Long Memory Regressors and Predictive Testing: A Two-stage Rebalancing Approach," Econometric Reviews, Taylor & Francis Journals, vol. 32(3), pages 318-360, November.
    27. Antonio Noriega & Carlos Capistrán & Manuel Ramos-Francia, 2013. "On the dynamics of inflation persistence around the world," Empirical Economics, Springer, vol. 44(3), pages 1243-1265, June.
    28. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    29. Busetti, Fabio & Taylor, A. M. Robert, 2004. "Tests of stationarity against a change in persistence," Journal of Econometrics, Elsevier, vol. 123(1), pages 33-66, November.
    30. Kim, Jae-Young & Belaire-Franch, Jorge & Amador, Rosa Badillo, 2002. "Corrigendum to "Detection of change in persistence of a linear time series" [J. Econom. 95 (2000) 97-116]," Journal of Econometrics, Elsevier, vol. 109(2), pages 389-392, August.
    31. Manmohan S. Kumar & Tatsuyoshi Okimoto, 2007. "Dynamics of Persistence in International Inflation Rates," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(6), pages 1457-1479, September.
    32. Francesc Marmol, 1995. "SPURIOUS REGRESSIONS BETWEEN I(d) PROCESSES," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(3), pages 313-321, May.
    33. Sun, Yiguo & Hsiao, Cheng & Li, Qi, 2011. "Measuring correlations of integrated but not cointegrated variables: A semiparametric approach," Journal of Econometrics, Elsevier, vol. 164(2), pages 252-267, October.
    34. Uwe Hassler & Barbara Meller, 2014. "Detecting multiple breaks in long memory the case of U.S. inflation," Empirical Economics, Springer, vol. 46(2), pages 653-680, March.
    35. Georgios P. Kouretas & Mark E. Wohar, 2012. "The dynamics of inflation: a study of a large number of countries," Applied Economics, Taylor & Francis Journals, vol. 44(16), pages 2001-2026, June.
    36. Malliaropulos, Dimitrios, 2000. "A note on nonstationarity, structural breaks, and the Fisher effect," Journal of Banking & Finance, Elsevier, vol. 24(5), pages 695-707, May.
    37. Kang Kyu Ho & Kim Chang-Jin & Morley James, 2009. "Changes in U.S. Inflation Persistence," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(4), pages 1-23, September.
    38. Dimitris K. Christopoulos & Miguel A. Le√N-Ledesma, 2007. "A Long-Run Non-Linear Approach to the Fisher Effect," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(2-3), pages 543-559, March.
    39. Martins, Luis F. & Rodrigues, Paulo M.M., 2014. "Testing for persistence change in fractionally integrated models: An application to world inflation rates," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 502-522.
    40. Stephen Leybourne & Robert Taylor & Tae‐Hwan Kim, 2007. "CUSUM of Squares‐Based Tests for a Change in Persistence," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(3), pages 408-433, May.
    41. Katsumi Shimotsu, 2006. "Simple (but Effective) Tests Of Long Memory Versus Structural Breaks," Working Paper 1101, Economics Department, Queen's University.
    42. Kruse, Robinson & Sibbertsen, Philipp, 2012. "Long memory and changing persistence," Economics Letters, Elsevier, vol. 114(3), pages 268-272.
    43. Leybourne Stephen & Kim Tae-Hwan & Taylor A.M. Robert, 2007. "Detecting Multiple Changes in Persistence," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 11(3), pages 1-34, September.
    44. Rapach, David E & Wohar, Mark E, 2005. "Regime Changes in International Real Interest Rates: Are They a Monetary Phenomenon?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(5), pages 887-906, October.
    45. Rapach, David E. & Weber, Christian E., 2004. "Are real interest rates really nonstationary? New evidence from tests with good size and power," Journal of Macroeconomics, Elsevier, vol. 26(3), pages 409-430, September.
    46. Gan, Li & Hsiao, Cheng & Xu, Shu, 2014. "Model specification test with correlated but not cointegrated variables," Journal of Econometrics, Elsevier, vol. 178(P1), pages 80-85.
    47. Lai, Kon S., 2008. "The puzzling unit root in the real interest rate and its inconsistency with intertemporal consumption behavior," Journal of International Money and Finance, Elsevier, vol. 27(1), pages 140-155, February.
    48. Stephen Leybourne & Tae-Hwan Kim & Vanessa Smith & Paul Newbold, 2003. "Tests for a change in persistence against the null of difference-stationarity," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 291-311, December.
    49. Uwe Hassler & Jan Scheithauer, 2011. "Detecting changes from short to long memory," Statistical Papers, Springer, vol. 52(4), pages 847-870, November.
    50. Kim, Jae-Young, 2000. "Detection of change in persistence of a linear time series," Journal of Econometrics, Elsevier, vol. 95(1), pages 97-116, March.
    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. 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.

    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. Martins, Luis F. & Rodrigues, Paulo M.M., 2014. "Testing for persistence change in fractionally integrated models: An application to world inflation rates," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 502-522.
    2. Soon, Siew-Voon & Baharumshah, Ahmad Zubaidi & Mohamad Shariff, Nurul Sima, 2017. "The persistence in real interest rates: Does it solve the intertemporal consumption behavior puzzle?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 50(C), pages 36-51.
    3. Noriega Antonio E. & Ventosa-Santaulària Daniel, 2011. "A Simple Test for Spurious Regressions," Working Papers 2011-05, Banco de México.
    4. Antonio Noriega & Carlos Capistrán & Manuel Ramos-Francia, 2013. "On the dynamics of inflation persistence around the world," Empirical Economics, Springer, vol. 44(3), pages 1243-1265, June.
    5. D. Ventosa-Santaulària, 2009. "Spurious Regression," Journal of Probability and Statistics, Hindawi, vol. 2009, pages 1-27, August.
    6. 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.
    7. Paulo M.M. Rodrigues & Philipp Sibbertsen, 2019. "Testing for breaks in the cointegrating relationship: On the stability of government bond markets’ equilibrium," Working Papers w201912, Banco de Portugal, Economics and Research Department.
    8. Noriega Antonio E. & Ventosa-Santaulària Daniel, 2006. "Spurious Regression and Econometric Trends," Working Papers 2006-05, Banco de México.
    9. 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.
    10. 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.
    11. Chen, Zhanshou & Xing, Yuhong & Li, Fuxiao, 2016. "Sieve bootstrap monitoring for change from short to long memory," Economics Letters, Elsevier, vol. 140(C), pages 53-56.
    12. Uwe Hassler & Jan Scheithauer, 2011. "Detecting changes from short to long memory," Statistical Papers, Springer, vol. 52(4), pages 847-870, November.
    13. Chen, Zhanshou & Jin, Zi & Tian, Zheng & Qi, Peiyan, 2012. "Bootstrap testing multiple changes in persistence for a heavy-tailed sequence," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2303-2316.
    14. Zhang, Lingxiang, 2013. "Partial unit root and linear spurious regression: A Monte Carlo simulation study," Economics Letters, Elsevier, vol. 118(1), pages 189-191.
    15. Heinen, Florian & Sibbertsen, Philipp & Kruse, Robinson, 2009. "Forecasting long memory time series under a break in persistence," Hannover Economic Papers (HEP) dp-433, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    16. Giorgio Canarella & Stephen M. Miller, 2016. "Inflation Persistence and Structural Breaks: The Experience of Inflation Targeting Countries and the US," Working papers 2016-11, University of Connecticut, Department of Economics.
    17. Paulo M. M. Rodrigues & Philipp Sibbertsen & Michelle Voges, 2024. "The stability of government bond markets’ equilibrium and the interdependence of lending rates," Empirical Economics, Springer, vol. 67(6), pages 2503-2538, December.
    18. 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.
    19. Zhanshou Chen & Yanting Xiao & Fuxiao Li, 2021. "Monitoring memory parameter change-points in long-memory time series," Empirical Economics, Springer, vol. 60(5), pages 2365-2389, May.
    20. Arnold, Stephan & Auer, Benjamin R., 2015. "What do scientists know about inflation hedging?," The North American Journal of Economics and Finance, Elsevier, vol. 34(C), pages 187-214.

    More about this item

    Keywords

    Changes in persistence; Spurious regression; Fisher hypothesis.;
    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
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:aah:create:2013-11. 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: the person in charge (email available below). General contact details of provider: http://www.econ.au.dk/afn/ .

    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.