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A Parametric Bootstrap Test for Cycles

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Author Info
Violetta Dalla
Javier Hidalgo

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

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Find related papers by JEL classification:
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Miguel A. Delgado & Javier Hidalgo & Carlos Velasco, 2005. "Distribution Free Goodness-of-Fit Tests for Linear Processes," STICERD - Econometrics Paper Series /2005/482, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  2. 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. [Downloadable!]
  3. 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. [Downloadable!]
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  4. 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. [Downloadable!]
  5. 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. [Downloadable!] (restricted)
  6. Andrews, Donald W K, 2001. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, Econometric Society, vol. 69(3), pages 683-734, May.
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  7. Lobato, Ignacio N & Robinson, Peter M, 1998. "A Nonparametric Test for I(0)," Review of Economic Studies, Blackwell Publishing, vol. 65(3), pages 475-95, July. [Downloadable!] (restricted)
  8. 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. [Downloadable!]
  9. Dean Prichard & James Theiler, 1994. "Generating Surrogate Data for Time Series with Several Simultaneously Measured Variables," Working Papers 94-04-023, Santa Fe Institute.
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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. [Downloadable!] (restricted)
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  2. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2007. "Long Run and Cyclical Dynamics in the US Stock Market," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
    Other versions:
  3. 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. [Downloadable!]
  4. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2009. "Multi-Factor Gegenbauer Processes and European Inflation Rates," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
    Other versions:
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