IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v36y2009i4p800-821.html
   My bibliography  Save this article

Frequency Domain Tests of Semiparametric Hypotheses for Locally Stationary Processes

Author

Listed:
  • MARIOS SERGIDES
  • EFSTATHIOS PAPARODITIS

Abstract

. Many time series in applied sciences obey a time‐varying spectral structure. In this article, we focus on locally stationary processes and develop tests of the hypothesis that the time‐varying spectral density has a semiparametric structure, including the interesting case of a time‐varying autoregressive moving‐average (tvARMA) model. The test introduced is based on a L2‐distance measure of a kernel smoothed version of the local periodogram rescaled by the time‐varying spectral density of the estimated semiparametric model. The asymptotic distribution of the test statistic under the null hypothesis is derived. As an interesting special case, we focus on the problem of testing for the presence of a tvAR model. A semiparametric bootstrap procedure to approximate more accurately the distribution of the test statistic under the null hypothesis is proposed. Some simulations illustrate the behaviour of our testing methodology in finite sample situations.

Suggested Citation

  • Marios Sergides & Efstathios Paparoditis, 2009. "Frequency Domain Tests of Semiparametric Hypotheses for Locally Stationary Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 800-821, December.
    • Handle: RePEc:bla:scjsta:v:36:y:2009:i:4:p:800-821
    DOI: 10.1111/j.1467-9469.2009.00652.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9469.2009.00652.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9469.2009.00652.x?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
    ---><---

    References listed on IDEAS

    as
    1. Sébastien Van Bellegem & Rainer Dahlhaus, 2006. "Semiparametric estimation by model selection for locally stationary processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(5), pages 721-746, November.
    2. Fryzlewicz, Piotr & van Bellegem, Sébastien & von Sachs, Rainer, 2003. "Forecasting non-stationary time series by wavelet process modelling," LSE Research Online Documents on Economics 25830, London School of Economics and Political Science, LSE Library.
    3. Kenji Sakiyama & Masanobu Taniguchi, 2003. "Testing Composite Hypotheses for Locally Stationary Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 483-504, July.
    4. Piotr Fryzlewicz & Sébastien Bellegem & Rainer Sachs, 2003. "Forecasting non-stationary time series by wavelet process modelling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(4), pages 737-764, December.
    5. Dahlhaus, Rainer & Neumann, Michael H., 2001. "Locally adaptive fitting of semiparametric models to nonstationary time series," Stochastic Processes and their Applications, Elsevier, vol. 91(2), pages 277-308, February.
    6. 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.
    7. Davis, Richard A. & Lee, Thomas C.M. & Rodriguez-Yam, Gabriel A., 2006. "Structural Break Estimation for Nonstationary Time Series Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 223-239, March.
    8. Marios Sergides & Efstathios Paparoditis, 2008. "Bootstrapping the Local Periodogram of Locally Stationary Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(2), pages 264-299, March.
    9. Ombao, Hernando & von Sachs, Rainer & Guo, Wensheng, 2005. "SLEX Analysis of Multivariate Nonstationary Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 519-531, June.
    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. Ruprecht Puchstein & Philip Preuß, 2016. "Testing for Stationarity in Multivariate Locally Stationary Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 3-29, January.
    2. Franziska Häfner & Claudia Kirch, 2017. "Moving Fourier Analysis for Locally Stationary Processes with the Bootstrap in View," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 895-922, November.
    3. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    4. Kawka, Rafael, 2022. "Convergence of spectral density estimators in the locally stationary framework," Econometrics and Statistics, Elsevier, vol. 24(C), pages 94-115.
    5. Chen, Yen-Hung & Hsu, Nan-Jung, 2014. "A frequency domain test for detecting nonstationary time series," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 179-189.
    6. Philip Preuss & Mathias Vetter & Holger Dette, 2013. "Testing Semiparametric Hypotheses in Locally Stationary Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 417-437, September.

    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. von Sachs, Rainer, 2019. "Spectral Analysis of Multivariate Time Series," LIDAM Discussion Papers ISBA 2019008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Cho, Haeran & Fryzlewicz, Piotr, 2015. "Multiple-change-point detection for high dimensional time series via sparsified binary segmentation," LSE Research Online Documents on Economics 57147, London School of Economics and Political Science, LSE Library.
    3. Guy Nason, 2013. "A test for second-order stationarity and approximate confidence intervals for localized autocovariances for locally stationary time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(5), pages 879-904, November.
    4. Tata Subba Rao & Granville Tunnicliffe Wilson & Alessandro Cardinali & Guy P. Nason, 2017. "Locally Stationary Wavelet Packet Processes: Basis Selection and Model Fitting," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(2), pages 151-174, March.
    5. Guy Nason & Kara Stevens, 2015. "Bayesian Wavelet Shrinkage of the Haar-Fisz Transformed Wavelet Periodogram," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-24, September.
    6. I A Eckley & G P Nason, 2018. "A test for the absence of aliasing or local white noise in locally stationary wavelet time series," Biometrika, Biometrika Trust, vol. 105(4), pages 833-848.
    7. 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.
    8. 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.
    9. Zhibiao Zhao, 2015. "Inference for Local Autocorrelations in Locally Stationary Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 296-306, April.
    10. Chen, Yen-Hung & Hsu, Nan-Jung, 2014. "A frequency domain test for detecting nonstationary time series," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 179-189.
    11. Holger Dette & Weichi Wu, 2020. "Prediction in locally stationary time series," Papers 2001.00419, arXiv.org, revised Jan 2020.
    12. 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.
    13. Zhang, Ting, 2015. "Semiparametric model building for regression models with time-varying parameters," Journal of Econometrics, Elsevier, vol. 187(1), pages 189-200.
    14. Dahlhaus, Rainer, 2009. "Local inference for locally stationary time series based on the empirical spectral measure," Journal of Econometrics, Elsevier, vol. 151(2), pages 101-112, August.
    15. Nowotarski, Jakub & Tomczyk, Jakub & Weron, Rafał, 2013. "Robust estimation and forecasting of the long-term seasonal component of electricity spot prices," Energy Economics, Elsevier, vol. 39(C), pages 13-27.
    16. 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.
    17. Triantafyllopoulos, K. & Nason, G.P., 2009. "A note on state space representations of locally stationary wavelet time series," Statistics & Probability Letters, Elsevier, vol. 79(1), pages 50-54, January.
    18. Cardinali Alessandro & Nason Guy P, 2011. "Costationarity of Locally Stationary Time Series," Journal of Time Series Econometrics, De Gruyter, vol. 2(2), pages 1-35, January.
    19. Ngai Hang Chan & Linhao Gao & Wilfredo Palma, 2022. "Simultaneous variable selection and structural identification for time‐varying coefficient models," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(4), pages 511-531, July.
    20. Honglu Zhu & Xu Li & Qiao Sun & Ling Nie & Jianxi Yao & Gang Zhao, 2015. "A Power Prediction Method for Photovoltaic Power Plant Based on Wavelet Decomposition and Artificial Neural Networks," Energies, MDPI, vol. 9(1), pages 1-15, December.

    More about this item

    Statistics

    Access and download statistics

    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:bla:scjsta:v:36:y:2009:i:4:p:800-821. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    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.