IDEAS home Printed from https://ideas.repec.org/a/spr/sistpr/v20y2017i3d10.1007_s11203-017-9155-7.html
   My bibliography  Save this article

Time series regression models with locally stationary disturbance

Author

Listed:
  • Junichi Hirukawa

    (Niigata University)

Abstract

Time series linear regression models with stationary residuals are a well studied topic, and have been widely applied in a number of fields. However, the stationarity assumption on the residuals seems to be restrictive. The analysis of relatively long stretches of time series data that may contain changes in the spectrum is of interest in many areas. Locally stationary processes have time-varying spectral densities, the structure of which smoothly changes in time. Therefore, we extend the model to the case of locally stationary residuals. The best linear unbiased estimator (BLUE) of vector of regression coefficients involves the residual covariance matrix which is usually unknown. Hence, we often use the least squares estimator (LSE), which is always feasible, but in general is not efficient. We evaluate the asymptotic covariance matrices of the BLUE and the LSE. We also study the efficiency of the LSE relative to the BLUE. Numerical examples illustrate the situation under locally stationary disturbances.

Suggested Citation

  • Junichi Hirukawa, 2017. "Time series regression models with locally stationary disturbance," Statistical Inference for Stochastic Processes, Springer, vol. 20(3), pages 329-346, October.
    • Handle: RePEc:spr:sistpr:v:20:y:2017:i:3:d:10.1007_s11203-017-9155-7
    DOI: 10.1007/s11203-017-9155-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11203-017-9155-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11203-017-9155-7?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. Suhasini Subba Rao, 2004. "On multiple regression models with nonstationary correlated errors," Biometrika, Biometrika Trust, vol. 91(3), pages 645-659, September.
    2. 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.
    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. 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.

    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. Casini, Alessandro & Perron, Pierre, 2024. "Change-point analysis of time series with evolutionary spectra," Journal of Econometrics, Elsevier, vol. 242(2).
    3. 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.
    4. Yayi Yan & Jiti Gao & Bin Peng, 2021. "On Time-Varying VAR Models: Estimation, Testing and Impulse Response Analysis," Papers 2111.00450, arXiv.org.
    5. Aloy Marcel & Dufrénot Gilles & Tong Charles Lai & Peguin-Feissolle Anne, 2013. "A smooth transition long-memory model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(3), pages 281-296, May.
    6. Baruník, Jozef & Ellington, Michael, 2024. "Persistence in financial connectedness and systemic risk," European Journal of Operational Research, Elsevier, vol. 314(1), pages 393-407.
    7. Dew-Becker, Ian & Nathanson, Charles G., 2019. "Directed attention and nonparametric learning," Journal of Economic Theory, Elsevier, vol. 181(C), pages 461-496.
    8. 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.
    9. Beran, Jan, 2007. "On parameter estimation for locally stationary long-memory processes," CoFE Discussion Papers 07/13, University of Konstanz, Center of Finance and Econometrics (CoFE).
    10. Stefan Birr & Stanislav Volgushev & Tobias Kley & Holger Dette & Marc Hallin, 2017. "Quantile spectral analysis for locally stationary time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1619-1643, November.
    11. Arif Dowla & Efstathios Paparoditis & Dimitris Politis, 2013. "Local block bootstrap inference for trending time series," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(6), pages 733-764, August.
    12. Roueff, François & von Sachs, Rainer & Sansonnet, Laure, 2016. "Locally stationary Hawkes processes," Stochastic Processes and their Applications, Elsevier, vol. 126(6), pages 1710-1743.
    13. Jiti Gao & Bin Peng & Wei Biao Wu & Yayi Yan, 2022. "Time-Varying Multivariate Causal Processes," Monash Econometrics and Business Statistics Working Papers 8/22, Monash University, Department of Econometrics and Business Statistics.
    14. Last, Michael & Shumway, Robert, 2008. "Detecting abrupt changes in a piecewise locally stationary time series," Journal of Multivariate Analysis, Elsevier, vol. 99(2), pages 191-214, February.
    15. Jozef Barunik & Michael Ellington, 2020. "Dynamic Network Risk," Papers 2006.04639, arXiv.org, revised Jul 2020.
    16. Fu, Zhonghao & Hong, Yongmiao, 2019. "A model-free consistent test for structural change in regression possibly with endogeneity," Journal of Econometrics, Elsevier, vol. 211(1), pages 206-242.
    17. Kley, Tobias & Preuss, Philip & Fryzlewicz, Piotr, 2019. "Predictive, finite-sample model choice for time series under stationarity and non-stationarity," LSE Research Online Documents on Economics 101748, London School of Economics and Political Science, LSE Library.
    18. Giurcanu Mihai & Spokoiny Vladimir, 2004. "Confidence estimation of the covariance function of stationary and locally stationary processes," Statistics & Risk Modeling, De Gruyter, vol. 22(4), pages 283-300, April.
    19. Chen, Bin & Hong, Yongmiao, 2016. "Detecting For Smooth Structural Changes In Garch Models," Econometric Theory, Cambridge University Press, vol. 32(03), pages 740-791, June.
    20. 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.

    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:spr:sistpr:v:20:y:2017:i:3:d:10.1007_s11203-017-9155-7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.