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Comparing spectral densities of stationary time series with unequal sample sizes

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  • Preuß, Philip
  • Hildebrandt, Thimo

Abstract

This paper deals with the comparison of stationary processes with unequal sample sizes. We provide a detailed theoretical framework on a test for equality of spectral densities in the bivariate case, after which the generalization of our approach to the m-dimensional case and to other statistical applications is straightforward.

Suggested Citation

  • Preuß, Philip & Hildebrandt, Thimo, 2013. "Comparing spectral densities of stationary time series with unequal sample sizes," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1174-1183.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:4:p:1174-1183
    DOI: 10.1016/j.spl.2013.01.015
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    References listed on IDEAS

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    1. Maharaj, Elizabeth Ann, 2002. "Comparison of non-stationary time series in the frequency domain," Computational Statistics & Data Analysis, Elsevier, vol. 40(1), pages 131-141, July.
    2. Holger Dette & Efstathios Paparoditis, 2009. "Bootstrapping frequency domain tests in multivariate time series with an application to comparing spectral densities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(4), pages 831-857, September.
    3. Peter J. Diggle & Nicholas I. Fisher, 1991. "Nonparametric Comparison of Cumulative Periodograms," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 40(3), pages 423-434, November.
    4. B. M. Pötscher & E. Reschenhofer, 1988. "Discriminating Between Two Spectral Densities In Case Of Replicated Observations," Journal of Time Series Analysis, Wiley Blackwell, vol. 9(3), pages 221-224, May.
    5. Caiado, Jorge & Crato, Nuno & Peña, Daniel, 2009. "Comparison of time series with unequal length in the frequency domain," MPRA Paper 15310, University Library of Munich, Germany.
    6. Jentsch, Carsten & Pauly, Markus, 2012. "A note on using periodogram-based distances for comparing spectral densities," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 158-164.
    7. Dette, Holger & Preuß, Philip & Vetter, Mathias, 2011. "A Measure of Stationarity in Locally Stationary Processes With Applications to Testing," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1113-1124.
    8. Eichler, Michael, 2008. "Testing nonparametric and semiparametric hypotheses in vector stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 968-1009, May.
    9. Holger Dette & Tatjana Kinsvater & Mathias Vetter, 2011. "Testing non‐parametric hypotheses for stationary processes by estimating minimal distances," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(5), pages 447-461, September.
    10. D. S. Coates & P. J. Diggle, 1986. "Tests For Comparing Two Estimated Spectral Densities," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(1), pages 7-20, January.
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    Cited by:

    1. Andrew J. Grant & Barry G. Quinn, 2017. "Parametric Spectral Discrimination," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 838-864, November.

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