IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v93y2014icp7-13.html
   My bibliography  Save this article

Nonparametric estimation of the spectral density of amplitude-modulated time series with missing observations

Author

Listed:
  • Efromovich, Sam

Abstract

Consider a real-valued and second-order stationary time series with mean zero. The aim is to estimate its spectral density. A minimax solution of this problem is known when either the time series is observed directly, or some observations are missed according to an independent Bernoulli process, or for some special cases when the time series is multiplied by an amplitude-modulating time series with known distribution. It is shown that if a time series of interest, a Bernoulli time series defining missing mechanism, and an amplitude-modulating time series are mutually independent, then the shape of spectral density of an underlying time series of interest can be estimated with the minimax rate known for the case of direct observations. Furthermore, in some special cases the spectral density can be estimated with the minimax rate known for directly observed time series of interest.

Suggested Citation

  • Efromovich, Sam, 2014. "Nonparametric estimation of the spectral density of amplitude-modulated time series with missing observations," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 7-13.
    • Handle: RePEc:eee:stapro:v:93:y:2014:i:c:p:7-13
    DOI: 10.1016/j.spl.2014.06.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715214002156
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2014.06.013?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. Jiancheng Jiang & Y. Hui, 2004. "Spectral density estimation with amplitude modulation and outlier detection," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(4), pages 611-630, December.
    2. Politis, Dimitris N., 2011. "Higher-Order Accurate, Positive Semidefinite Estimation Of Large-Sample Covariance And Spectral Density Matrices," Econometric Theory, Cambridge University Press, vol. 27(4), pages 703-744, August.
    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. Sam Efromovich, 2020. "Missing not at random and the nonparametric estimation of the spectral density," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(5), pages 652-675, 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. Amira Elayouty & Marian Scott & Claire Miller, 2022. "Time-Varying Functional Principal Components for Non-Stationary EpCO $$_2$$ 2 in Freshwater Systems," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(3), pages 506-522, September.
    2. Bai, Shuyang & Taqqu, Murad S. & Zhang, Ting, 2016. "A unified approach to self-normalized block sampling," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2465-2493.
    3. La Vecchia, Davide & Moor, Alban & Scaillet, Olivier, 2023. "A higher-order correct fast moving-average bootstrap for dependent data," Journal of Econometrics, Elsevier, vol. 235(1), pages 65-81.
    4. A. Elhassanein, 2014. "On the theory of continuous time series," Indian Journal of Pure and Applied Mathematics, Springer, vol. 45(3), pages 297-310, June.
    5. Hassan Doosti & Peter Hall, 2016. "Making a non-parametric density estimator more attractive, and more accurate, by data perturbation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 445-462, March.
    6. Federico Belotti & Alessandro Casini & Leopoldo Catania & Stefano Grassi & Pierre Perron, 2023. "Simultaneous bandwidths determination for DK-HAC estimators and long-run variance estimation in nonparametric settings," Econometric Reviews, Taylor & Francis Journals, vol. 42(3), pages 281-306, February.
    7. Mihai C. Giurcanu, 2017. "Oracle M-Estimation for Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(3), pages 479-504, May.
    8. Berkes, István & Horváth, Lajos & Rice, Gregory, 2016. "On the asymptotic normality of kernel estimators of the long run covariance of functional time series," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 150-175.
    9. Hirukawa, Masayuki, 2023. "Robust Covariance Matrix Estimation in Time Series: A Review," Econometrics and Statistics, Elsevier, vol. 27(C), pages 36-61.
    10. Jungbin Hwang, 2017. "Simple and Trustworthy Cluster-Robust GMM Inference," Working papers 2017-19, University of Connecticut, Department of Economics, revised Aug 2020.
    11. Casini, Alessandro, 2023. "Theory of evolutionary spectra for heteroskedasticity and autocorrelation robust inference in possibly misspecified and nonstationary models," Journal of Econometrics, Elsevier, vol. 235(2), pages 372-392.
    12. Qihui Chen & Zheng Fang, 2018. "Improved Inference on the Rank of a Matrix," Papers 1812.02337, arXiv.org, revised Mar 2019.
    13. Min Seong Kim, 2021. "Robust Inference for Diffusion-Index Forecasts with Cross-Sectionally Dependent Data," Working papers 2021-04, University of Connecticut, Department of Economics.
    14. Rasmus Tangsgaard Varneskov, 2011. "Generalized Flat-Top Realized Kernel Estimation of Ex-Post Variation of Asset Prices Contaminated by Noise," CREATES Research Papers 2011-31, Department of Economics and Business Economics, Aarhus University.
    15. Dimitrios Thomakos & Johannes Klepsch & Dimitris N. Politis, 2020. "Model Free Inference on Multivariate Time Series with Conditional Correlations," Stats, MDPI, vol. 3(4), pages 1-26, November.
    16. Politis, Dimitris, 2014. "High-dimensional autocovariance matrices and optimal linear prediction," University of California at San Diego, Economics Working Paper Series qt3k58p0xr, Department of Economics, UC San Diego.
    17. Kim, Min Seong & Sun, Yixiao, 2013. "Heteroskedasticity and spatiotemporal dependence robust inference for linear panel models with fixed effects," Journal of Econometrics, Elsevier, vol. 177(1), pages 85-108.
    18. Gregory Rice & Han Lin Shang, 2017. "A Plug-in Bandwidth Selection Procedure for Long-Run Covariance Estimation with Stationary Functional Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(4), pages 591-609, July.
    19. Pierre Perron & Eduardo Zorita & Arthur P. Guillaumin & Adam M. Sykulski & Sofia C. Olhede & Jeffrey J. Early & Jonathan M. Lilly, 2017. "Analysis of Non-Stationary Modulated Time Series with Applications to Oceanographic Surface Flow Measurements," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(5), pages 668-710, September.
    20. Ying Liu & Dootika Vats & James M. Flegal, 2022. "Batch Size Selection for Variance Estimators in MCMC," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 65-93, March.

    More about this item

    Keywords

    Adaptation; ARMA; Minimax; MISE; Shape;
    All these keywords.

    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:eee:stapro:v:93:y:2014:i:c:p:7-13. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.