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Time-Varying Functional Principal Components for Non-Stationary EpCO $$_2$$ 2 in Freshwater Systems

Author

Listed:
  • Amira Elayouty

    (University of Glasgow
    Cairo University)

  • Marian Scott

    (University of Glasgow)

  • Claire Miller

    (University of Glasgow)

Abstract

Outgassing of carbon dioxide (CO $$_2$$ 2 ) from river surface waters, estimated using partial pressure of dissolved CO $$_2$$ 2 , has recently been considered an important component of the global carbon budget. However, little is still known about the high-frequency dynamics of CO $$_2$$ 2 emissions in small-order rivers and streams. To analyse such highly dynamic systems, we propose a time-varying functional principal components analysis (FPCA) for non-stationary functional time series (FTS). This time-varying FPCA is performed in the frequency domain to investigate how the variability and auto-covariance structures in a FTS change over time. This methodology, and the associated proposed inference, enables investigation of the changes over time in the variability structure of the diurnal profiles of the partial pressure of CO $$_2$$ 2 and identification of the drivers of those changes. By means of a simulation study, the performance of the time-varying dynamic FPCs is investigated under different scenarios of complete and incomplete FTS. Although the time-varying dynamic FPCA has been applied here to study the daily processes of consuming and producing CO $$_2$$ 2 in a small catchment of the river Dee in Scotland, this methodology can be applied more generally to any dynamic time series.Supplementary materials accompanying this paper appear online.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jagbes:v:27:y:2022:i:3:d:10.1007_s13253-022-00494-2
    DOI: 10.1007/s13253-022-00494-2
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    References listed on IDEAS

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    1. Horváth, Lajos & Kokoszka, Piotr & Rice, Gregory, 2014. "Testing stationarity of functional time series," Journal of Econometrics, Elsevier, vol. 179(1), pages 66-82.
    2. Panaretos, Victor M. & Tavakoli, Shahin, 2013. "Cramér–Karhunen–Loève representation and harmonic principal component analysis of functional time series," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2779-2807.
    3. 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.
    4. Daniel Peña & Victor J. Yohai, 2016. "Generalized Dynamic Principal Components," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1121-1131, July.
    5. Ombao, Hernando & Ringo Ho, Moon-ho, 2006. "Time-dependent frequency domain principal components analysis of multichannel non-stationary signals," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2339-2360, May.
    6. Fangrong Yan & Xiao Lin & Ruosha Li & Xuelin Huang, 2018. "Functional principal components analysis on moving time windows of longitudinal data: dynamic prediction of times to event," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(4), pages 961-978, August.
    7. Siegfried Hörmann & Łukasz Kidziński & Marc Hallin, 2015. "Dynamic functional principal components," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 319-348, March.
    8. Clara Happ & Sonja Greven, 2018. "Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 649-659, April.
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