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On trend estimation under monotone Gaussian subordination with long-memory: application to fossil pollen series

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  • Patricia Menéndez
  • Sucharita Ghosh
  • Hans R. Künsch
  • Willy Tinner

Abstract

Fossil pollen data from stratigraphic cores are irregularly spaced in time due to non-linear age-depth relations. Moreover, their marginal distributions may vary over time. We address these features in a nonparametric regression model with errors that are monotone transformations of a latent continuous-time Gaussian process Z ( T ). Although Z ( T ) is unobserved, due to monotonicity, under suitable regularity conditions, it can be recovered facilitating further computations such as estimation of the long-memory parameter and the Hermite coefficients. The estimation of Z ( T ) itself involves estimation of the marginal distribution function of the regression errors. These issues are considered in proposing a plug-in algorithm for optimal bandwidth selection and construction of confidence bands for the trend function. Some high-resolution time series of pollen records from Lago di Origlio in Switzerland, which go back ca. 20,000 years are used to illustrate the methods.

Suggested Citation

  • Patricia Menéndez & Sucharita Ghosh & Hans R. Künsch & Willy Tinner, 2013. "On trend estimation under monotone Gaussian subordination with long-memory: application to fossil pollen series," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(4), pages 765-785, December.
    • Handle: RePEc:taf:gnstxx:v:25:y:2013:i:4:p:765-785
    DOI: 10.1080/10485252.2013.826357
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    Cited by:

    1. Jan Beran & Sucharita Ghosh, 2020. "Estimating the Mean Direction of Strongly Dependent Circular Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 210-228, March.
    2. Jan Beran & Yuanhua Feng & Sucharita Ghosh, 2015. "Modelling long-range dependence and trends in duration series: an approach based on EFARIMA and ESEMIFAR models," Statistical Papers, Springer, vol. 56(2), pages 431-451, May.
    3. Ryan Janicki & Tucker S. McElroy, 2016. "Hermite expansion and estimation of monotonic transformations of Gaussian data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 207-234, March.

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