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Nonparametric Comparison of Cumulative Periodograms

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  • Peter J. Diggle
  • Nicholas I. Fisher

Abstract

Motivated by a problem in the analysis of hormonal time series data, this paper proposes a simple graphical method for comparing two periodograms and describes a new nonparametric approach to testing the hypothesis that the two underlying spectra are the same. Simulation studies show that the new test has power characteristics that are competitive with existing procedures. The relative merits of nonparametric and semiparametric tests are discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssc:v:40:y:1991:i:3:p:423-434
    DOI: 10.2307/2347522
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    1. repec:cep:stiecm:/2013/563 is not listed on IDEAS
    2. Shibin Zhang & Xin M. Tu, 2022. "Tests for comparing time‐invariant and time‐varying spectra based on the Anderson–Darling statistic," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(3), pages 254-282, August.
    3. Caiado, Jorge & Crato, Nuno & Peña, Daniel, 2007. "Comparison of time series with unequal length," MPRA Paper 6605, University Library of Munich, Germany.
    4. Caiado, Jorge & Crato, Nuno & Pena, Daniel, 2006. "A periodogram-based metric for time series classification," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2668-2684, June.
    5. Alonso, Andres M. & Maharaj, Elizabeth A., 2006. "Comparison of time series using subsampling," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2589-2599, June.
    6. 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.
    7. 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.
    8. Daniel M Keenan & Amy W Quinkert & Donald W Pfaff, 2015. "Stochastic Modeling of Mouse Motor Activity under Deep Brain Stimulation: The Extraction of Arousal Information," PLOS Computational Biology, Public Library of Science, vol. 11(2), pages 1-24, February.
    9. Hidalgo, Javier & Souza, Pedro, 2013. "Testing for equality of an increasing number of spectral density functions," LSE Research Online Documents on Economics 58195, London School of Economics and Political Science, LSE Library.
    10. 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.
    11. Jin, Lei, 2021. "Robust tests for time series comparison based on Laplace periodograms," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    12. Mahmoudi, Mohammad Reza & Heydari, Mohammad Hossein & Roohi, Reza, 2019. "A new method to compare the spectral densities of two independent periodically correlated time series," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 160(C), pages 103-110.
    13. Dette, Holger & Paroditis, Efstathios, 2007. "Testing equality of spectral densities," Technical Reports 2007,29, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    14. Jan Beran & Theo Gasser, 1995. "Testing Equality Of Variances For Paired Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(2), pages 165-176, March.
    15. 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.
    16. Dette, Holger & Hildebrandt, Thimo, 2012. "A note on testing hypotheses for stationary processes in the frequency domain," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 101-114, February.
    17. Jorge Caiado & Nuno Crato & Pilar Poncela, 2020. "A fragmented-periodogram approach for clustering big data time series," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(1), pages 117-146, March.
    18. Daniel Cirkovic & Thomas J. Fisher, 2021. "On testing for the equality of autocovariance in time series," Environmetrics, John Wiley & Sons, Ltd., vol. 32(7), November.
    19. Mahmoudi, Mohammad Reza, 2021. "A computational technique to classify several fractional Brownian motion processes," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    20. Dette, Holger & Paparoditis, Efstathios, 2008. "Bootstrapping frequency domain tests in multivariate time series with an application to comparing spectral densities," Technical Reports 2008,28, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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