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Quantile spectral analysis of long-memory processes

Author

Listed:
  • Yaeji Lim

    (Chung-Ang University)

  • Hee-Seok Oh

    (Seoul National University)

Abstract

This study examines the problem of robust spectral analysis of long-memory processes. We investigate the possibility of using Laplace and quantile periodograms for a non-Gaussian distribution structure. The Laplace periodogram, derived by the least absolute deviations in the harmonic regression procedure, demonstrates its superiority in handling heavy-tailed noise and nonlinear distortion. In this study, we discuss an asymptotic distribution of the Laplace periodogram for long-memory processes. We also derive an asymptotic distribution of the quantile periodogram. Through numerical experiments, we demonstrate the robustness of the Laplace periodogram and the usefulness of the quantile periodogram in detecting the hidden frequency for the spectral analysis of the long-memory process under non-Gaussian distribution. Moreover, as an application of robust periodograms under the long-memory process, we discuss the long-memory parameter estimation based on a log periodogram regression approach.

Suggested Citation

  • Yaeji Lim & Hee-Seok Oh, 2022. "Quantile spectral analysis of long-memory processes," Empirical Economics, Springer, vol. 62(3), pages 1245-1266, March.
    • Handle: RePEc:spr:empeco:v:62:y:2022:i:3:d:10.1007_s00181-021-02045-z
    DOI: 10.1007/s00181-021-02045-z
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    References listed on IDEAS

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    1. John Geweke & Susan Porter‐Hudak, 1983. "The Estimation And Application Of Long Memory Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(4), pages 221-238, July.
    2. Ta-Hsin Li, 2014. "Quantile Periodogram And Time-Dependent Variance," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(4), pages 322-340, July.
    3. Clifford M. Hurvich & Rohit Deo & Julia Brodsky, 1998. "The mean squared error of Geweke and Porter‐Hudak's estimator of the memory parameter of a long‐memory time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(1), pages 19-46, January.
    4. Valderio A. Reisen, 1994. "ESTIMATION OF THE FRACTIONAL DIFFERENCE PARAMETER IN THE ARIMA(p, d, q) MODEL USING THE SMOOTHED PERIODOGRAM," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(3), pages 335-350, May.
    5. Baillie, Richard T. & Chung, Sang-Kuck, 2002. "Modeling and forecasting from trend-stationary long memory models with applications to climatology," International Journal of Forecasting, Elsevier, vol. 18(2), pages 215-226.
    6. Koul, H. L. & Mukherjee, K., 1994. "Regression Quantiles and Related Processes Under Long Range Dependent Errors," Journal of Multivariate Analysis, Elsevier, vol. 51(2), pages 318-337, November.
    7. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    8. Clifford M. Hurvich & Kaizo I. Beltrao, 1993. "Asymptotics For The Low‐Frequency Ordinates Of The Periodogram Of A Long‐Memory Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(5), pages 455-472, September.
    9. Koul, Hira L., 1992. "M-estimators in linear models with long range dependent errors," Statistics & Probability Letters, Elsevier, vol. 14(2), pages 153-164, May.
    10. Stefan Birr & Stanislav Volgushev & Tobias Kley & Holger Dette & Marc Hallin, 2017. "Quantile spectral analysis for locally stationary time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1619-1643, November.
    11. 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.
    12. Ta-Hsin Li, 2012. "Quantile Periodograms," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 765-776, June.
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