IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v24y2003i4p483-504.html

Testing Composite Hypotheses for Locally Stationary Processes

Author

Listed:
  • KENJI SAKIYAMA
  • MASANOBU TANIGUCHI

Abstract

For a class of locally stationary processes introduced by Dahlhaus, this paper discusses the problem of testing composite hypotheses. First, for the Gaussian likelihood ratio test (GLR), Wald test (W) and Lagrange multiplier test (LM), we derive the limiting distribution under a composite hypothesis in parametric form. It is shown that the distribution of GLR, W and LM tends to a χ2 distribution under the hypothesis. We also evaluate their local powers under a sequence of local alternatives, and discuss their asymptotic optimality. The results can be applied to testing for stationarity. Some examples are given. They illuminate the local power property via simulation. On the other hand, we provide a nonparametric LAN theorem. Based on this result, we obtain the limiting distribution of the GLR under both null and alternative hypotheses described in nonparametric form. Finally, the numerical studies are given.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:24:y:2003:i:4:p:483-504
    DOI: 10.1111/1467-9892.00317
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1467-9892.00317
    Download Restriction: no
    File URL: https://libkey.io/10.1111/1467-9892.00317?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. Dahlhaus, R., 1996. "On the Kullback-Leibler information divergence of locally stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 139-168, March.
    2. M. Taniguchi & L. Zhao & P. Krishnaiah & Z. Bai, 1989. "Statistical analysis of dyadic stationary processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(2), pages 205-225, June.
    3. M. B. Priestley, 1988. "The Spectral Analysis of Time Series," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 151(3), pages 573-574, May.
    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.

    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. Chen, Qitong & Hong, Yongmiao & Li, Haiqi, 2024. "Time-varying forecast combination for factor-augmented regressions with smooth structural changes," Journal of Econometrics, Elsevier, vol. 240(1).
    2. Bonsoo Koo & Oliver Linton, 2010. "Semiparametric Estimation of Locally Stationary Diffusion Models," STICERD - Econometrics Paper Series 551, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    3. Michael Vogt, 2012. "Nonparametric regression for locally stationary time series," CeMMAP working papers CWP22/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. 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.
    5. Abdelkamel Alj & Christophe Ley & Guy Melard, 2015. "Asymptotic Properties of QML Estimators for VARMA Models with Time-Dependent Coefficients: Part I," Working Papers ECARES ECARES 2015-21, ULB -- Universite Libre de Bruxelles.
    6. David T. Frazier & Bonsoo Koo, 2020. "Indirect Inference for Locally Stationary Models," Monash Econometrics and Business Statistics Working Papers 30/20, Monash University, Department of Econometrics and Business Statistics.
    7. Sun, Yuying & Hong, Yongmiao & Lee, Tae-Hwy & Wang, Shouyang & Zhang, Xinyu, 2021. "Time-varying model averaging," Journal of Econometrics, Elsevier, vol. 222(2), pages 974-992.
    8. Yayi Yan & Jiti Gao & Bin Peng, 2021. "On Time-Varying VAR models: Estimation, Testing and Impulse Response Analysis," Monash Econometrics and Business Statistics Working Papers 17/21, Monash University, Department of Econometrics and Business Statistics.
    9. Mykola Babiak & Jozef Barunik, 2021. "Volatility Shocks and Currency Returns," Papers 2101.09738, arXiv.org, revised Mar 2026.
    10. Krampe, J. & Kreiss, J.-P. & Paparoditis, E., 2015. "Hybrid wild bootstrap for nonparametric trend estimation in locally stationary time series," Statistics & Probability Letters, Elsevier, vol. 101(C), pages 54-63.
    11. Junichi Hirukawa & Sangyeol Lee, 2021. "Asymptotic properties of mildly explosive processes with locally stationary disturbance," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(4), pages 511-534, May.
    12. Gao, Jiti & Peng, Bin & Yan, Yayi, 2025. "Time-varying vector error-correction models: Estimation and inference," Journal of Econometrics, Elsevier, vol. 251(C).
    13. Baruník, Jozef & Vácha, Lukáš, 2024. "Predicting the volatility of major energy commodity prices: The dynamic persistence model," Energy Economics, Elsevier, vol. 140(C).
    14. Baruník, Jozef & Ellington, Michael, 2024. "Persistence in financial connectedness and systemic risk," European Journal of Operational Research, Elsevier, vol. 314(1), pages 393-407.
    15. Hafner, Christian M. & Reznikova, Olga, 2010. "Efficient estimation of a semiparametric dynamic copula model," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2609-2627, November.
    16. Yayi Yan & Jiti Gao & Bin Peng, 2020. "A Class of Time-Varying Vector Moving Average Models: Nonparametric Kernel Estimation and Application," Papers 2010.01492, arXiv.org.
    17. Baruník, Jozef & Bevilacqua, Mattia & Faff, Robert, 2024. "Dynamic industry uncertainty networks and the business cycle," Journal of Economic Dynamics and Control, Elsevier, vol. 159(C).
    18. Yousuf, Kashif & Ng, Serena, 2021. "Boosting high dimensional predictive regressions with time varying parameters," Journal of Econometrics, Elsevier, vol. 224(1), pages 60-87.
    19. Donald W. K. Andrews & Ming Li, 2024. "Inference in a Stationary/Nonstationary Autoregressive Time-Varying-Parameter Model," Papers 2411.00358, arXiv.org.
    20. Mykola Babiak & Jozef Barunik, 2021. "Uncertainty Network Risk and Currency Returns," CERGE-EI Working Papers wp687, The Center for Economic Research and Graduate Education - Economics Institute, Prague.

    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:jtsera:v:24:y:2003:i:4:p:483-504. 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=0143-9782 .

    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.