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Nonparametric pseudo-Lagrange multiplier stationarity testing

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  • Landajo, Manuel
  • Presno, María José

Abstract

The framework of stationarity testing is extended to allow a generic smooth trend function estimated nonparametrically. The asymptotic behavior of the pseudo-Lagrange Multiplier test is analyzed in this setting. The proposed implementation delivers a consistent test whose limiting null distribution is standard normal. Theoretical analyses are complemented with simulation studies and some empirical applications.

Suggested Citation

  • Landajo, Manuel & Presno, María José, 2010. "Nonparametric pseudo-Lagrange multiplier stationarity testing," MPRA Paper 25659, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:25659
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    File URL: https://mpra.ub.uni-muenchen.de/25659/1/MPRA_paper_25659.pdf
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    References listed on IDEAS

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    1. Phillips, Peter C.B., 2005. "Hac Estimation By Automated Regression," Econometric Theory, Cambridge University Press, vol. 21(1), pages 116-142, February.
    2. Junsoo Lee & Walter Enders, 2004. "Testing for a unit-root with a nonlinear Fourier function," Econometric Society 2004 Far Eastern Meetings 457, Econometric Society.
    3. Kapetanios, George & Shin, Yongcheol & Snell, Andy, 2003. "Testing for a unit root in the nonlinear STAR framework," Journal of Econometrics, Elsevier, vol. 112(2), pages 359-379, February.
    4. Fabio Busetti & Andrew Harvey, 2001. "Testing for the Presence of a Random Walk in Series with Structural Breaks," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(2), pages 127-150, March.
    5. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    6. Mills,Terence C. & Markellos,Raphael N., 2008. "The Econometric Modelling of Financial Time Series," Cambridge Books, Cambridge University Press, number 9780521710091.
    7. Yongmiao Hong & Yoon-Jin Lee, 2005. "Generalized Spectral Tests for Conditional Mean Models in Time Series with Conditional Heteroscedasticity of Unknown Form," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(2), pages 499-541.
    8. María Presno & Manuel Landajo, 2010. "Computation of limiting distributions in stationarity testing with a generic trend," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(2), pages 165-183, March.
    9. Manuel Landajo & María José Presno, 2010. "Stationarity testing under nonlinear models. Some asymptotic results," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(5), pages 392-405, September.
    10. Junsoo Lee & Mark C. Strazicich, 2003. "Minimum Lagrange Multiplier Unit Root Test with Two Structural Breaks," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 1082-1089, November.
    11. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-1159, September.
    12. George Kapetanios, 2000. "Testing for a Unit Root against Nonlinear STAR Models," National Institute of Economic and Social Research (NIESR) Discussion Papers 164, National Institute of Economic and Social Research.
    13. David I. Harvey & Terence C. Mills, 2004. "Tests for Stationarity in Series with Endogenously Determined Structural Change," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 66(5), pages 863-894, December.
    14. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(6), pages 1130-1164, December.
    15. Gustavsson, Magnus & Osterholm, Par, 2006. "The informational value of unemployment statistics: A note on the time series properties of participation rates," Economics Letters, Elsevier, vol. 92(3), pages 428-433, September.
    16. Mohammed H.I. Dore & Rubén Guevara (ed.), 2000. "Sustainable Forest Management and Global Climate Change," Books, Edward Elgar Publishing, number 1849.
    17. Escanciano, J. Carlos, 2006. "Goodness-of-Fit Tests for Linear and Nonlinear Time Series Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 531-541, June.
    18. Jewell, Todd & Lee, Junsoo & Tieslau, Margie & Strazicich, Mark C., 2003. "Stationarity of health expenditures and GDP: evidence from panel unit root tests with heterogeneous structural breaks," Journal of Health Economics, Elsevier, vol. 22(2), pages 313-323, March.
    19. Terasvirta, Timo, 2006. "Forecasting economic variables with nonlinear models," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 8, pages 413-457, Elsevier.
    20. Enders, Walter & Granger, Clive W J, 1998. "Unit-Root Tests and Asymmetric Adjustment with an Example Using the Term Structure of Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 304-311, July.
    21. Kurozumi, Eiji, 2002. "Testing for stationarity with a break," Journal of Econometrics, Elsevier, vol. 108(1), pages 63-99, May.
    22. Jakob Madsen & Vinod Mishra & Russell Smyth, 2008. "Are Labour Force Participation Rates Non‐Stationary? Evidence From 130 Years For G7 Countries," Australian Economic Papers, Wiley Blackwell, vol. 47(2), pages 166-189, June.
    23. Junsoo Lee & Mark Strazicich, 2001. "Testing the null of stationarity in the presence of a structural break," Applied Economics Letters, Taylor & Francis Journals, vol. 8(6), pages 377-382.
    24. Diebold, Francis X & Kilian, Lutz, 2000. "Unit-Root Tests Are Useful for Selecting Forecasting Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 265-273, July.
    25. Mehmet Caner & Bruce E. Hansen, 2001. "Threshold Autoregression with a Unit Root," Econometrica, Econometric Society, vol. 69(6), pages 1555-1596, November.
    26. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    27. Yixiao Sun & Peter C. B. Phillips & Sainan Jin, 2008. "Optimal Bandwidth Selection in Heteroskedasticity-Autocorrelation Robust Testing," Econometrica, Econometric Society, vol. 76(1), pages 175-194, January.
    28. Bhansali, R.J. & Giraitis, L. & Kokoszka, P.S., 2007. "Convergence of quadratic forms with nonvanishing diagonal," Statistics & Probability Letters, Elsevier, vol. 77(7), pages 726-734, April.
    29. Tanaka, Katsuto, 1990. "The Fredholm Approach to Asymptotic Inference on Nonstationary and Noninvertible Time Series Models," Econometric Theory, Cambridge University Press, vol. 6(4), pages 411-432, December.
    30. Dore, M. & Johnston, M., 1996. "The Carbon Cycle and the Value of Canadian Forests," Working Papers 1996-01, Brock University, Department of Economics.
    31. Nigar Hashimzade & Timothy J. Vogelsang, 2008. "Fixed‐b asymptotic approximation of the sampling behaviour of nonparametric spectral density estimators," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(1), pages 142-162, January.
    32. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    33. Brooks,Chris, 2019. "Introductory Econometrics for Finance," Cambridge Books, Cambridge University Press, number 9781108436823.
    34. Donggyu Sul & Peter C. B. Phillips & Chi‐Young Choi, 2005. "Prewhitening Bias in HAC Estimation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(4), pages 517-546, August.
    35. Paulo M.M. Rodrigues & A. M. Robert Taylor, 2009. "The Flexible Fourier Form and Local GLS De-trended Unit Root Tests," Working Papers w200919, Banco de Portugal, Economics and Research Department.
    36. Robert Sollis, 2004. "Asymmetric adjustment and smooth transitions: a combination of some unit root tests," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(3), pages 409-417, May.
    37. Bierens, Herman J., 1997. "Testing the unit root with drift hypothesis against nonlinear trend stationarity, with an application to the US price level and interest rate," Journal of Econometrics, Elsevier, vol. 81(1), pages 29-64, November.
    38. Mills,Terence C. & Markellos,Raphael N., 2008. "The Econometric Modelling of Financial Time Series," Cambridge Books, Cambridge University Press, number 9780521883818.
    39. Leybourne, S J & McCabe, B P M, 1994. "A Consistent Test for a Unit Root," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 157-166, April.
    40. Ralf Becker & Walter Enders & Junsoo Lee, 2006. "A Stationarity Test in the Presence of an Unknown Number of Smooth Breaks," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(3), pages 381-409, May.
    41. Bart Hobijn & Philip Hans Franses & Marius Ooms, 2004. "Generalizations of the KPSS‐test for stationarity," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(4), pages 483-502, November.
    42. Riccardo DiCecio & Kristie M. Engemann & Michael T. Owyang & Christopher H. Wheeler, 2008. "Changing trends in the labor force: a survey," Review, Federal Reserve Bank of St. Louis, vol. 90(Jan), pages 47-62.
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    Cited by:

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    More about this item

    Keywords

    Time series; stationarity testing; limiting distribution; nonparametric regression; nonparametric hypothesis testing;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: 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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