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On nonparametric regression for bivariate circular long-memory time series

Author

Listed:
  • Jan Beran

    (University of Konstanz)

  • Britta Steffens

    (University of Konstanz)

  • Sucharita Ghosh

    (Swiss Federal Research Institute WSL)

Abstract

We consider nonparametric regression for bivariate circular time series with long-range dependence. Asymptotic results for circular Nadaraya–Watson estimators are derived. Due to long-range dependence, a range of asymptotically optimal bandwidths can be found where the asymptotic rate of convergence does not depend on the bandwidth. The result can be used for obtaining simple confidence bands for the regression function. The method is illustrated by an application to wind direction data.

Suggested Citation

  • Jan Beran & Britta Steffens & Sucharita Ghosh, 2022. "On nonparametric regression for bivariate circular long-memory time series," Statistical Papers, Springer, vol. 63(1), pages 29-52, February.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:1:d:10.1007_s00362-021-01228-1
    DOI: 10.1007/s00362-021-01228-1
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    References listed on IDEAS

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    1. Davidson, James & Sibbertsen, Philipp, 2005. "Generating schemes for long memory processes: regimes, aggregation and linearity," Journal of Econometrics, Elsevier, vol. 128(2), pages 253-282, October.
    2. Sungsu Kim & Ashis SenGupta, 2013. "A three-parameter generalized von Mises distribution," Statistical Papers, Springer, vol. 54(3), pages 685-693, August.
    3. Wenceslao González‐Manteiga & Rosa M. Crujeiras & Danny Modlin & Montserrat Fuentes & Brian Reich, 2012. "Circular conditional autoregressive modeling of vector fields," Environmetrics, John Wiley & Sons, Ltd., vol. 23(1), pages 46-53, February.
    4. Bai, Z. D. & Rao, C. Radhakrishna & Zhao, L. C., 1988. "Kernel estimators of density function of directional data," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 24-39, October.
    5. Fangpo Wang & Alan E. Gelfand, 2014. "Modeling Space and Space-Time Directional Data Using Projected Gaussian Processes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1565-1580, December.
    6. Robert, Christian, 1990. "Modified Bessel functions and their applications in probability and statistics," Statistics & Probability Letters, Elsevier, vol. 9(2), pages 155-161, February.
    7. Macro Di Marzio & Agnese Panzera & Charles C. Taylor, 2012. "Non-parametric smoothing and prediction for nonlinear circular time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(4), pages 620-630, July.
    8. Tsuruta, Yasuhito & Sagae, Masahiko, 2017. "Higher order kernel density estimation on the circle," Statistics & Probability Letters, Elsevier, vol. 131(C), pages 46-50.
    9. Yasuhito Tsuruta & Masahiko Sagae, 2020. "Theoretical properties of bandwidth selectors for kernel density estimation on the circle," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(2), pages 511-530, April.
    10. Taylor, Charles C., 2008. "Automatic bandwidth selection for circular density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3493-3500, March.
    11. Shogo Kato, 2010. "A Markov process for circular data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(5), pages 655-672, November.
    12. Hankin, Robin K. S., 2015. "Circular Statistics in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 66(b05).
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