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Quantile Spectral Analysis for Locally Stationary Time Series

Author

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  • Stefan Skowronek
  • Stanislav Volgushev
  • Tobias Kley
  • Holger Dette
  • Marc Hallin

Abstract

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Suggested Citation

  • Stefan Skowronek & Stanislav Volgushev & Tobias Kley & Holger Dette & Marc Hallin, 2014. "Quantile Spectral Analysis for Locally Stationary Time Series," Working Papers ECARES ecares 2014-24, ULB -- Universite Libre de Bruxelles.
  • Handle: RePEc:eca:wpaper:2013/159999
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    References listed on IDEAS

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    1. Stefan Birr & Holger Dette & Marc Hallin & Tobias Kley & Stanislav Volgushev, 2016. "On Wigner-Ville Spectra and the Unicity of Time-Varying Quantile-Based Spectral Densities," Working Papers ECARES ECARES 2016-38, ULB -- Universite Libre de Bruxelles.
    2. Koenker, Roger & Xiao, Zhijie, 2006. "Quantile Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 980-990, September.
    3. Zhou Zhou, 2013. "Heteroscedasticity and Autocorrelation Robust Structural Change Detection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 726-740, June.
    4. Han, Heejoon & Linton, Oliver & Oka, Tatsushi & Whang, Yoon-Jae, 2016. "The cross-quantilogram: Measuring quantile dependence and testing directional predictability between time series," Journal of Econometrics, Elsevier, vol. 193(1), pages 251-270.
    5. Davis, Richard A. & Mikosch, Thomas & Zhao, Yuwei, 2013. "Measures of serial extremal dependence and their estimation," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2575-2602.
    6. Fryzlewicz, Piotr & Sapatinas, Theofanis & Subba Rao, Suhasini, 2008. "Normalized least-squares estimation in time-varying ARCH models," LSE Research Online Documents on Economics 25187, London School of Economics and Political Science, LSE Library.
    7. Zhao, Zhibiao & Wu, Wei Biao, 2009. "Nonparametric inference of discretely sampled stable Lévy processes," Journal of Econometrics, Elsevier, vol. 153(1), pages 83-92, November.
    8. Rajae Azrak & Guy Mélard, 2006. "Asymptotic Properties of Quasi-Maximum Likelihood Estimators for ARMA Models with Time-Dependent Coefficients," Statistical Inference for Stochastic Processes, Springer, vol. 9(3), pages 279-330, October.
    9. Holger Dette & Marc Hallin & Tobias Kley & Stanislav Volgushev, 2011. "Of Copulas, Quantiles, Ranks and Spectra - An L1-Approach to Spectral Analysis," Working Papers ECARES ECARES 2011-038, ULB -- Universite Libre de Bruxelles.
    10. G. P. Nason & R. von Sachs & G. Kroisandt, 2000. "Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 271-292.
    11. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, March.
    12. Linton, O. & Whang, Yoon-Jae, 2007. "The quantilogram: With an application to evaluating directional predictability," Journal of Econometrics, Elsevier, vol. 141(1), pages 250-282, November.
    13. Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus, 2000. "Stationary Arch Models: Dependence Structure And Central Limit Theorem," Econometric Theory, Cambridge University Press, vol. 16(01), pages 3-22, February.
    14. Li, Ta-Hsin, 2008. "Laplace Periodogram for Time Series Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 757-768, June.
    15. Hallin, Marc & Ingenbleek, Jean-François, 1983. "Nonstationary Yule-Walker equations," Statistics & Probability Letters, Elsevier, vol. 1(4), pages 189-195, June.
    16. Dahlhaus, R., 1996. "On the Kullback-Leibler information divergence of locally stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 139-168, March.
    17. Ta-Hsin Li, 2012. "Quantile Periodograms," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 765-776, June.
    18. Michael Vogt, 2012. "Nonparametric regression for locally stationary time series," CeMMAP working papers CWP22/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    19. Guy Nason, 2013. "A test for second-order stationarity and approximate confidence intervals for localized autocovariances for locally stationary time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(5), pages 879-904, November.
    20. Marc Hallin, 1984. "Spectral factorization of nonstationary moving average processes," ULB Institutional Repository 2013/2001, ULB -- Universite Libre de Bruxelles.
    21. Ta-Hsin Li, 2014. "Quantile Periodogram And Time-Dependent Variance," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(4), pages 322-340, July.
    22. Rajae Azrak & Guy Melard, 2006. "Asymptotic properties of quasi-maximum likelihood estimators for ARMA models with time-dependent coefficients," ULB Institutional Repository 2013/13758, ULB -- Universite Libre de Bruxelles.
    23. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    24. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
    25. Liu, Weidong & Wu, Wei Biao, 2010. "Asymptotics Of Spectral Density Estimates," Econometric Theory, Cambridge University Press, vol. 26(04), pages 1218-1245, August.
    26. R. Dahlhaus & M. Neumann & R. von Sachs, 1997. "Nonlinear Wavelet Estimation of Time-Varying Autoregressive Processes," SFB 373 Discussion Papers 1997,34, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    27. Fryzlewicz, Piotr & Sapatinas, Theofanis & Subba Rao, Suhasini, 2006. "A Haar-Fisz technique for locally stationary volatility estimation," LSE Research Online Documents on Economics 25225, London School of Economics and Political Science, LSE Library.
    28. repec:jss:jstsof:v:070:i03 is not listed on IDEAS
    29. Longla, Martial & Peligrad, Magda, 2012. "Some aspects of modeling dependence in copula-based Markov chains," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 234-240.
    30. Yongmiao Hong, 2000. "Generalized spectral tests for serial dependence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(3), pages 557-574.
    31. Francq, Christian & Zako an, Jean-Michel, 2005. "A Central Limit Theorem For Mixing Triangular Arrays Of Variables Whose Dependence Is Allowed To Grow With The Sample Size," Econometric Theory, Cambridge University Press, vol. 21(06), pages 1165-1171, December.
    32. Roueff, François & von Sachs, Rainer, 2011. "Locally stationary long memory estimation," Stochastic Processes and their Applications, Elsevier, vol. 121(4), pages 813-844, April.
    33. Tobias Kley & Stanislav Volgushev & Holger Dette & Marc Hallin, 2014. "Quantile Spectral Processes: Asymptotic Analysis and Inference," Working Papers ECARES ECARES 2014-07, ULB -- Universite Libre de Bruxelles.
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    Citations

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    Cited by:

    1. Jozef Barun'ik & Tobias Kley, 2015. "Quantile Cross-Spectral Measures of Dependence between Economic Variables," Papers 1510.06946, arXiv.org.
    2. Stefan Birr & Holger Dette & Marc Hallin & Tobias Kley & Stanislav Volgushev, 2016. "On Wigner-Ville Spectra and the Unicity of Time-Varying Quantile-Based Spectral Densities," Working Papers ECARES ECARES 2016-38, ULB -- Universite Libre de Bruxelles.
    3. Yaeji Lim & Hee-Seok Oh, 2016. "Composite Quantile Periodogram for Spectral Analysis," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(2), pages 195-221, March.

    More about this item

    Keywords

    time series; spectral analysis; periodogram; quantile regression; copulas; ranks; local stationarity;

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