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Nonparametric pseudo-Lagrange multiplier stationarity testing

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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.

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References

  • Anderson T.W. (1971) The statistical analysis of time series. Wiley, New York

    MATH  Google Scholar 

  • Becker R., Enders W., Lee J. (2006) A stationarity test in the presence of an unknown number of smooth breaks. Journal of Time Series Analysis 27: 381–409

    Article  MathSciNet  MATH  Google Scholar 

  • Bhansali R.J., Giraitis L., Kokoszka P.S. (2007) Convergence of quadratic forms with nonvanishing diagonal. Statistics & Probability Letters 77: 726–734

    Article  MathSciNet  MATH  Google Scholar 

  • Bierens H.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 81: 29–64

    Article  MathSciNet  MATH  Google Scholar 

  • Billingsley P. (1968) Convergence of probability measures. Wiley, New York

    MATH  Google Scholar 

  • Brooks C. (2008) Introductory econometrics for finance. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Diebold F.X., Kilian L. (2000) Unit-root tests are useful for selecting forecasting models. Journal of Business and Economics Statistics 18: 265–273

    Google Scholar 

  • Dore, M. H. I., Johnston, M. (2000). The carbon cycle and the value of forests as a carbon sink: A boreal case study. In: Sustainable forest management and global climate change: Selected case studies from the Americas. Cheltenham, UK: Edward Elgar Publishing.

  • Escanciano J.C. (2006) Goodness-of-fit tests for linear and nonlinear time series models. Journal of the American Statistical Association 101: 531–541

    Article  MathSciNet  MATH  Google Scholar 

  • Gay-García C., Estrada F., Sánchez A. (2009) Global and hemispheric temperatures revised. Climatic Change 94: 333–349

    Article  Google Scholar 

  • Grenander U. (1981) Abstract inference. Wiley, New York

    MATH  Google Scholar 

  • Hashimzade N., Vogelsang T.J. (2008) Fixed-b asymptotic approximation of the sampling behaviour of nonparametric spectral density estimators. Journal of Time Series Analysis 29: 142–162

    Article  MathSciNet  MATH  Google Scholar 

  • Hong Y., Lee Y.J. (2003) Generalized spectral tests for conditional mean models in time series with conditional heteroscedasticity of unknown form. Review of Economic Studies 72: 499–541

    Article  MathSciNet  Google Scholar 

  • Hong Y., White H. (1995) Consistent specification testing via nonparametric series regression. Econometrica 63: 1133–1159

    Article  MathSciNet  MATH  Google Scholar 

  • Jewell T., Lee J., Tieslau M., Stracizich M.C. (2003) Stationarity of health expenditures and GDP: Evidence from panel unit root tests with heterogeneous structural breaks. Journal of Health Economics 22: 313–323

    Article  Google Scholar 

  • Kurozumi E. (2002) Testing for stationarity with a break. Journal of Econometrics 108: 63–99

    Article  MathSciNet  MATH  Google Scholar 

  • Kurozumi E., Tanaka S. (2010) Reducing the size distortion of the KPSS test. Journal of Time Series Analysis 31: 415–426

    Article  MathSciNet  MATH  Google Scholar 

  • Kwiatkowski D., Phillips P.C.B., Schmidt P., Shin Y. (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 54: 159–178

    Article  MATH  Google Scholar 

  • Landajo M., Presno M.J. (2010) Stationarity testing under nonlinear models. Some asymptotic results. Journal of Time Series Analysis 31: 392–405

    Article  MathSciNet  MATH  Google Scholar 

  • MacNeill I.B. (1978) Properties of sequences of partial sums of polynomial regression residuals with applications to tests for change of regression at unknown times. Annals of Statistics 6(2): 422–433

    Article  MathSciNet  MATH  Google Scholar 

  • Mills T.C., Markellos R.N. (2008) The econometric modelling of financial time series. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Nabeya S., Tanaka K. (1988) Asymptotic theory of a test for the constancy of regression coefficients against the random walk alternative. The Annals of Statistics 16: 218–235

    Article  MathSciNet  MATH  Google Scholar 

  • Pötscher B.M., Prucha I.R. (1991) Basic structure of the asymptotic theory in dynamic nonlinear econometric models. Part II: Asymptotic normality. Econometric Reviews 10: 253–325

    Article  MathSciNet  MATH  Google Scholar 

  • Sul D., Phillips P.C.B., Choi C. (2005) Prewhitening bias in HAC estimation. Oxford Bulletin of Economics and Statistics 67: 517–546

    Article  Google Scholar 

  • Sun Y.X., Phillips P.C.B., Jin S. (2008) Optimal bandwidth selection in heteroskedasticity-autocorrelation robust testing. Econometrica 76: 175–194

    Article  MathSciNet  MATH  Google Scholar 

  • Tanaka K. (1990) The Fredholm approach to asymptotic inference on nonstationary and noninvertible time series models. Econometric Theory 6: 411–432

    Article  MathSciNet  Google Scholar 

  • Tanaka K. (1996) Time series analysis: Nonstationary and noninvertible distribution theory. Wiley, New York

    MATH  Google Scholar 

  • Van Gelder, P. H. A. J. M., Wang, W., Vrijling, J. K. (2007). Statistical estimation methods for extreme hydrological events. In: Extreme hydrological events: New concepts for security. Netherlands: Springer.

  • Wang W. (2006) Stochasticity, nonlinearity and forecasting of streamflow processes. IOS Press, Amsterdam

    Google Scholar 

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Authors and Affiliations

  1. Unit of Statistics and Econometrics, Department of Applied Economics, University of Oviedo, Avenida del Cristo s/n, 33011, Oviedo, Spain

    Manuel Landajo & María José Presno

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  1. Manuel Landajo
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  2. María José Presno
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Correspondence to Manuel Landajo.

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Landajo, M., Presno, M.J. Nonparametric pseudo-Lagrange multiplier stationarity testing. Ann Inst Stat Math 65, 125–147 (2013). https://doi.org/10.1007/s10463-012-0363-z

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  • DOI: https://doi.org/10.1007/s10463-012-0363-z

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