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Quantile and Copula Spectrum: A New Approach to Investigate Cyclical Dependence in Economic Time Series

  • Gilles Dufrénot
  • Takashi MatsukiEmail author
  • Kimiko Sugimoto
Chapter
  • 12 Downloads
Part of the Dynamic Modeling and Econometrics in Economics and Finance book series (DMEF, volume 27)

Abstract

This chapter presents a survey of some recent methods used in economics and finance to account for cyclical dependence and account for their multifaced dynamics: nonlinearities, extreme events, asymmetries, non-stationarity, time-varying moments. To circumvent the caveats of the standard spectral analysis, new tools are now used based on copula spectrum, quantile spectrum and Laplace periodogram in both non-parametric and parametric contexts. The chapter presents a comprehensive overview of both theoretical and empirical issues as well as a computational approach to explain how the methods can be implemented using the R Package.

References

  1. Baruník, J., & Kley, T. (2019). Quantile coherency: A general measure for dependence between cyclical economic variables. Econometrics Journal, 22(2), 131–152.CrossRefGoogle Scholar
  2. Brockwell, P. J., & Davis, R. A. (1991). Time series: Theory and methods (2nd ed.). New York: Springer.CrossRefGoogle Scholar
  3. Dette, H., Hallin, M., Kley, T., & Volgushev, S. (2015). Of copulas, quantiles, ranks and spectra: An L1-approach to spectral analysis. Bernoulli, 21(2), 781–831.CrossRefGoogle Scholar
  4. Hagemann, A. (2013). Robust spectral analysis. arXiv e-prints. https://arxiv.org/abs/1111.1965.
  5. Hill, J. B., & McCloskey, A. (2014). Heavy tail robust frequency domain estimation, mimeo.Google Scholar
  6. Hong, Y. (1999). Hypothesis testing in time series via the empirical characteristic function: A general spectral density approach. Journal of the American Statistical Association, 94(448), 1201–1220.CrossRefGoogle Scholar
  7. Hong, Y. (2000). Generalized spectral tests for serial dependence. Journal of the Royal Statistical Association. Series B, 62, 557–574.CrossRefGoogle Scholar
  8. Katkovnik, V. (1998). Robust M-periodogram. IEEE Transactions on Signal Processing, 46(11), 3104–3109.CrossRefGoogle Scholar
  9. Kleiner, B., Martin, R. D., & Thomson, D. J. (1979). Robust estimation of power spectra. Journal of the Royal Statistical Society B, 41(3), 313–351.Google Scholar
  10. Kley, T. (2016). Quantile-based spectral analysis in an object-oriented framework and a reference implementation in R: The Quantspect package. Journal of Statistical Software, 70(3), 1–27.CrossRefGoogle Scholar
  11. Kley, T., Volgushev, S., Dette, H., & Hallin, M. (2016). Quantile spectral processes: Asymptotic analysis and inference. Bernoulli, 22(3), 1770–1807.CrossRefGoogle Scholar
  12. Klüppelberg, C., & Mikosch, T. (1994). Some limit theory for the self-normalized periodogram of stable processes. Scandinavian Journal of Statistics, 21(4), 485–491.Google Scholar
  13. Koenker, R. (2005). Quantile regression. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  14. Lee, J., & Subba Rao, S. S. (2012). The quantile spectral density and comparison-based tests for nonlinear time series. arXiv e-prints. https://arxiv.org/abs/1112.2759.
  15. Li, T.-H. (2008). Laplace periodogram for time series analysis. Journal of the American Statistical Association, 103(482), 757–768.CrossRefGoogle Scholar
  16. Li, T.-H. (2012). Quantile periodograms. Journal of the American Statistical Association, 107(498), 765–776.CrossRefGoogle Scholar
  17. Li, T.-H. (2013). Time series with mixed spectra: Theory and methods. Boca Raton: CRC Press.Google Scholar
  18. Li, T.-H. (2014). Quantile periodogram and time-dependent variance. Journal of Time Series Analysis, 35(4), 322–340.CrossRefGoogle Scholar
  19. Li, T. H. (2019). Quantile-frequency analysis and spectral divergence metrics for diagnostic checks of time series with nonlinear dynamics. arXiv:1908.02545.
  20. Lim, Y., & Oh, H.-S. (2015). Composite quantile periodogram for spectral analysis. Journal of Time Series Analysis, 37, 195–211.CrossRefGoogle Scholar
  21. Mikosch, T. (1998). Periodogram estimates from heavy-tailed data. In R. A. Adler, R. Feldman, & M. S. Taqqu (Eds.), A practical guide to heavy tails: Statistical techniques for analyzing heavy tailed distributions (pp. 241–258). Boston: Birkhäuser.Google Scholar
  22. Patton, A. J. (2012). A review of copula models for economic time series. Journal of Multivariate Analysis, 110(C), 4–18.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2021

Authors and Affiliations

  • Gilles Dufrénot
    • 1
  • Takashi Matsuki
    • 2
    Email author
  • Kimiko Sugimoto
    • 3
  1. 1.Aix-Marseille School of EconomicsMarseilleFrance
  2. 2.Osaka Gakuin UniversitySuitaJapan
  3. 3.Konan UniversityNishinomiyaJapan

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