IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i12p3921-3934.html
   My bibliography  Save this article

Comparing non-stationary and irregularly spaced time series

Author

Listed:
  • Salcedo, Gladys E.
  • Porto, Rogério F.
  • Morettin, Pedro A.

Abstract

In this paper, we present approximate distributions for the ratio of the cumulative wavelet periodograms considering stationary and non-stationary time series generated from independent Gaussian processes. We also adapt an existing procedure to use this statistic and its approximate distribution in order to test if two regularly or irregularly spaced time series are realizations of the same generating process. Simulation studies show good size and power properties for the test statistic. An application with financial microdata illustrates the test usefulness. We conclude advocating the use of these approximate distributions instead of the ones obtained through randomizations, mainly in the case of irregular time series.

Suggested Citation

  • Salcedo, Gladys E. & Porto, Rogério F. & Morettin, Pedro A., 2012. "Comparing non-stationary and irregularly spaced time series," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3921-3934.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:12:p:3921-3934
    DOI: 10.1016/j.csda.2012.05.022
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947312002216
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2012.05.022?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Duchesne, Pierre & Lafaye De Micheaux, Pierre, 2010. "Computing the distribution of quadratic forms: Further comparisons between the Liu-Tang-Zhang approximation and exact methods," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 858-862, April.
    2. Porto, Rogério F. & Morettin, Pedro A. & Aubin, Elisete C.Q., 2008. "Wavelet regression with correlated errors on a piecewise Hölder class," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2739-2743, November.
    3. Timmer, J. & Lauk, M. & Vach, W. & Lucking, C. H., 1999. "A test for a difference between spectral peak frequencies," Computational Statistics & Data Analysis, Elsevier, vol. 30(1), pages 45-55, March.
    4. Marc Paolella & Ronald W. Butler, 1999. "Calculating the Density and Distribution Function of a Singly and Doubly Noncentral F Random Variable," Computing in Economics and Finance 1999 532, Society for Computational Economics.
    5. 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.
    6. Giovanni Forchini, "undated". "The Distribution of a Ratio of Quadratic Forms in Noncentral Normal Variables," Discussion Papers 01/12, Department of Economics, University of York.
    7. 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.
    8. Iain M. Johnstone & Bernard W. Silverman, 1997. "Wavelet Threshold Estimators for Data with Correlated Noise," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 319-351.
    9. Rainer Von Sachs & Brenda Macgibbon, 2000. "Non‐parametric Curve Estimation by Wavelet Thresholding with Locally Stationary Errors," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(3), pages 475-499, September.
    10. Ibbotson, Roger G., 1975. "Price performance of common stock new issues," Journal of Financial Economics, Elsevier, vol. 2(3), pages 235-272, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jin, Lei, 2021. "Robust tests for time series comparison based on Laplace periodograms," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    2. Liu, Shen & Maharaj, Elizabeth Ann & Inder, Brett, 2014. "Polarization of forecast densities: A new approach to time series classification," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 345-361.
    3. Mahmoudi, Mohammad Reza, 2021. "A computational technique to classify several fractional Brownian motion processes," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fryzlewicz, Piotr & Nason, Guy P., 2006. "Haar-Fisz estimation of evolutionary wavelet spectra," LSE Research Online Documents on Economics 25227, London School of Economics and Political Science, LSE Library.
    2. Mahmoudi, Mohammad Reza, 2021. "A computational technique to classify several fractional Brownian motion processes," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. Fryzlewicz, Piotr & Nason, Guy P., 2004. "Smoothing the wavelet periodogram using the Haar-Fisz transform," LSE Research Online Documents on Economics 25231, London School of Economics and Political Science, LSE Library.
    4. Winkelmann, Lars, 2013. "Quantitative forward guidance and the predictability of monetary policy: A wavelet based jump detection approach," SFB 649 Discussion Papers 2013-016, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    5. Capobianco, Enrico, 2003. "Independent Multiresolution Component Analysis and Matching Pursuit," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 385-402, March.
    6. Marcelo M. Taddeo & Pedro A. Morettin, 2023. "Bayesian P-Splines Applied to Semiparametric Models with Errors Following a Scale Mixture of Normals," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1331-1355, August.
    7. Antonis A. Michis & Guy P. Nason, 2017. "Case study: shipping trend estimation and prediction via multiscale variance stabilisation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(15), pages 2672-2684, November.
    8. 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.
    9. Euan T. McGonigle & Rebecca Killick & Matthew A. Nunes, 2022. "Trend locally stationary wavelet processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(6), pages 895-917, November.
    10. Linyuan Li & Kewei Lu, 2013. "On rate-optimal nonparametric wavelet regression with long memory moving average errors," Statistical Inference for Stochastic Processes, Springer, vol. 16(2), pages 127-145, July.
    11. Madison Giacofci & Sophie Lambert-Lacroix & Franck Picard, 2018. "Minimax wavelet estimation for multisample heteroscedastic nonparametric regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(1), pages 238-261, January.
    12. Zhang, Ting, 2015. "Semiparametric model building for regression models with time-varying parameters," Journal of Econometrics, Elsevier, vol. 187(1), pages 189-200.
    13. Beran, Jan & Shumeyko, Yevgen, 2012. "Bootstrap testing for discontinuities under long-range dependence," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 322-347.
    14. repec:hum:wpaper:sfb649dp2013-016 is not listed on IDEAS
    15. 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.
    16. Taylor, Larry W., 2009. "Using the Haar wavelet transform in the semiparametric specification of time series," Economic Modelling, Elsevier, vol. 26(2), pages 392-403, March.
    17. Winkelmann, Lars, 2010. "The Norges Bank's key rate projections and the news element of monetary policy: A wavelet based jump detection approach," SFB 649 Discussion Papers 2010-062, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    18. Amit Sinha, 2024. "Daily and Weekly Geometric Brownian Motion Stock Index Forecasts," JRFM, MDPI, vol. 17(10), pages 1-22, September.
    19. Antonio Acconcia & Alfredo Del Monte & Luca Pennacchio & Germana Scepi, 2011. "IPO Underpricing and the Location of Firms," CSEF Working Papers 295, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy, revised 04 Feb 2021.
    20. Schroeder, Anna Louise & Fryzlewicz, Piotr, 2013. "Adaptive trend estimation in financial time series via multiscale change-point-induced basis recovery," LSE Research Online Documents on Economics 54934, London School of Economics and Political Science, LSE Library.
    21. Fu, Fangjian & Lin, Leming & Officer, Micah S., 2013. "Acquisitions driven by stock overvaluation: Are they good deals?," Journal of Financial Economics, Elsevier, vol. 109(1), pages 24-39.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:56:y:2012:i:12:p:3921-3934. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.