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A Parametric Bootstrap Test for Cycles

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  • Violetta Dalla
  • Javier Hidalgo

Abstract

The paper proposes a simple test for the hypothesis of strong cycles and as a by-product a test for weak dependence for linear processes. We show that the limit distribution of the test is the maximum of a (semi)Gaussian process G(t), t ? [0; 1]. Because the covariance structure of G(t) is a complicated function of t and model dependent, to obtain the critical values (if possible) of maxt?[0;1] G(t) may be difficult. For this reason we propose a bootstrap scheme in the frequency domain to circumvent the problem of obtaining (asymptotically) valid critical values. The proposed bootstrap can be regarded as an alternative procedure to existing bootstrap methods in the time domain such as the residual-based bootstrap. Finally, we illustrate the performance of the bootstrap test by a small Monte Carlo experiment and an empirical example.

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Bibliographic Info

Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2005/486.

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Date of creation: Feb 2005
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Handle: RePEc:cep:stiecm:/2005/486

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Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

Related research

Keywords: Cyclical data; strong and weak dependence; spectral density functions; Whittle estimator; bootstrap algorithms;

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References

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  1. Hidalgo, Javier, 2003. "An alternative bootstrap to moving blocks for time series regression models," Journal of Econometrics, Elsevier, vol. 117(2), pages 369-399, December.
  2. Lobato, Ignacio N & Robinson, Peter M, 1998. "A Nonparametric Test for I(0)," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 475-95, July.
  3. Peter M Robinson & Carlos Velasco, 2000. "Whittle Pseudo-Maximum Likelihood Estimation for Nonstationary Time Series - (Now published in Journal of the American Statistical Association, 95, (2000), pp.1229-1243.)," STICERD - Econometrics Paper Series /2000/391, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  4. Pham, Tuan D. & Tran, Lanh T., 1985. "Some mixing properties of time series models," Stochastic Processes and their Applications, Elsevier, vol. 19(2), pages 297-303, April.
  5. Josu Artech & Peter M Robinson, 1998. "Semiparametric Inference in Seasonal and Cyclical Long Memory Processes - (Now published in Journal of Time Series Analysis, 21 (2000), pp.1-25.)," STICERD - Econometrics Paper Series /1998/359, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  6. L Giraitis & J Hidalgo & Peter M. Robinson, 2001. "Gaussian estimation of parametric spectral density with unknown pole," LSE Research Online Documents on Economics 297, London School of Economics and Political Science, LSE Library.
  7. Hidalgo, J. & Kreiss, J.-P., 2006. "Bootstrap specification tests for linear covariance stationary processes," Journal of Econometrics, Elsevier, vol. 133(2), pages 807-839, August.
  8. Miguel A. Delgado & Javier Hidalgo & Carlos Velasco, 2005. "Distribution free goodness-of-fit tests for linear processes," LSE Research Online Documents on Economics 6840, London School of Economics and Political Science, LSE Library.
  9. Hall, Peter, 1990. "On the relative performance of bootstrap and Edgeworth approximations of a distribution function," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 108-129, October.
  10. Liudas Giraitis & Javier Hidalgo & Peter M Robinson, 2001. "Gaussian Estimation of Parametric Spectral Density with Unknown Pole," STICERD - Econometrics Paper Series /2001/424, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  11. Donald W.K. Andrews, 1999. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Cowles Foundation Discussion Papers 1229, Cowles Foundation for Research in Economics, Yale University.
  12. Javier Hidalgo & Peter M Robinson, 1997. "Time Series Regression with Long Range Dependence - (Now published in 'Annals of Statistics', 25, (1997)pp.2054-2083.)," STICERD - Econometrics Paper Series /1997/318, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  13. Dean Prichard & James Theiler, 1994. "Generating Surrogate Data for Time Series with Several Simultaneously Measured Variables," Working Papers 94-04-023, Santa Fe Institute.
  14. Javier Hidalgo, 2003. "An Alternative Bootstrap to Moving Blocks for Time Series Regression Models," STICERD - Econometrics Paper Series /2003/452, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
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Citations

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Cited by:
  1. Faria, João Ricardo & Cuestas, Juan Carlos & Gil-Alana, Luis A., 2009. "Unemployment and entrepreneurship: A cyclical relation?," Economics Letters, Elsevier, vol. 105(3), pages 318-320, December.
  2. Uwe Hassler, 2011. "Estimation of fractional integration under temporal aggregation," Post-Print peer-00815563, HAL.
  3. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2010. "Long Memory and Volatility Dynamics in the US Dollar Exchange Rate," Discussion Papers of DIW Berlin 975, DIW Berlin, German Institute for Economic Research.
  4. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2009. "Multi-Factor Gegenbauer Processes and European Inflation Rates," Discussion Papers of DIW Berlin 879, DIW Berlin, German Institute for Economic Research.
  5. Luis A. Gil-Alana, 2009. "Time series modelling of sunspot numbers using long range cyclical dependence," Faculty Working Papers 06/09, School of Economics and Business Administration, University of Navarra.
  6. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2005. "Long Run And Cyclical Dynamics In The Us Stock Market," Economics and Finance Discussion Papers 05-09, Economics and Finance Section, School of Social Sciences, Brunel University.
  7. Joao Ricardo Faria & Juan Carlos Cuestas & Luis Gil-Alana, 2008. "Unemployment and entrepreneurship: a cyclical relationship?," Working Papers 2008/2, Nottingham Trent University, Nottingham Business School, Economics Division.
  8. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2011. "Persistence and Cyclical Dependence in the Monthly Euribor Rate," CESifo Working Paper Series 3653, CESifo Group Munich.
  9. Gil-Alana, Luis A. & Yaya, OlaOluwa S. & Shittu, Olanrewaju I., 2014. "Global temperatures and sunspot numbers. Are they related?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 396(C), pages 42-50.
  10. Caporale, Guglielmo Maria & Gil-Alana, Luis A., 2014. "Persistence and cycles in US hours worked," Economic Modelling, Elsevier, vol. 38(C), pages 504-511.
  11. Juan Carlos Cuestas & Luis A. Gil-Alana, 2012. "A Non-Linear Approach with Long Range Dependence Based on Chebyshev Polynomials," Working Papers 2012013, The University of Sheffield, Department of Economics.
  12. Guglielmo Caporale & Luis Gil-Alana, 2007. "Testing for deterministic and stochastic cycles in macroeconomic time series," Empirica, Springer, vol. 34(2), pages 155-169, April.

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