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Higher-order improvements of the parametric bootstrap for long-memory Gaussian processes

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  • Andrews, Donald W.K.
  • Lieberman, Offer
  • Marmer, Vadim

Abstract

This paper determines coverage probability errors of both delta method and parametric bootstrap confidence intervals (CIs) for the covariance parameters of stationary long-memory Gaussian time series. CIs for the long-memory parameter d_0 are included. The results establish that the bootstrap provides higher-order improvements over the delta method. Analogous results are given for tests. The CIs and tests are based on one or other of two approximate maximum likelihood estimators. The first estimator solves the first-order conditions with respect to the covariance parameters of a "plug-in" log-likelihood function that has the unknown mean replaced by the sample mean. The second estimator does likewise for a plug-in Whittle log-likelihood. The magnitudes of the coverage probability errors for one-sided bootstrap CIs for covariance parameters for long-memory time series are shown to be essentially the same as they are with iid data. This occurs even though the mean of the time series cannot be estimated at the usual n^{1/2} rate.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 133 (2006)
Issue (Month): 2 (August)
Pages: 673-702

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Handle: RePEc:eee:econom:v:133:y:2006:i:2:p:673-702

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Cited by:
  1. Donald W.K. Andrews & Offer Lieberman, 2002. "Higher-order Improvements of the Parametric Bootstrap for Long-memory Gaussian Processes," Cowles Foundation Discussion Papers 1378, Cowles Foundation for Research in Economics, Yale University.
  2. George Kapetanios & Fotis Papailias, 2011. "Block Bootstrap and Long Memory," Working Papers 679, Queen Mary, University of London, School of Economics and Finance.
  3. Søren Johansen & Morten Ørregaard Nielsen, 2012. "The role of initial values in nonstationary fractional time series models," CREATES Research Papers 2012-47, School of Economics and Management, University of Aarhus.
  4. Arteche, J. & Orbe, J., 2005. "Bootstrapping the log-periodogram regression," Economics Letters, Elsevier, vol. 86(1), pages 79-85, January.
  5. D.S. Poskitt & Simone D. Grose & Gael M. Martin, 2012. "Higher Order Improvements of the Sieve Bootstrap for Fractionally Integrated Processes," Monash Econometrics and Business Statistics Working Papers 9/12, Monash University, Department of Econometrics and Business Statistics.
  6. Arteche, Josu & Orbe, Jesus, 2009. "Using the bootstrap for finite sample confidence intervals of the log periodogram regression," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 1940-1953, April.
  7. Banerjee, Anindya & Urga, Giovanni, 2005. "Modelling structural breaks, long memory and stock market volatility: an overview," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 1-34.
  8. Beran, Jan & Shumeyko, Yevgen, 2012. "Bootstrap testing for discontinuities under long-range dependence," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 322-347.
  9. Firouz Fallahi & Mohammad Karimi & Marcel-Cristian Voia, 2014. "Are Shocks to Energy Consumption Persistent? Evidence from Subsampling Confidence Intervals," Carleton Economic Papers 14-02, Carleton University, Department of Economics.
  10. Franco, G.C. & Reisen, V.A. & Alves, F.A., 2013. "Bootstrap tests for fractional integration and cointegration: A comparison study," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 87(C), pages 19-29.

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