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Parsimonious time series modeling for high frequency climate data

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  • Paul L. Anderson
  • Farzad Sabzikar
  • Mark M. Meerschaert

Abstract

Climate data often provides a periodically stationary time series, due to seasonal variations in the mean and covariance structure. Periodic ARMA models, where the parameters vary with the season, capture the nonstationary behavior. High frequency data collected weekly or daily results in a large number of model parameters. In this article, we apply discrete Fourier transforms to the parameter vectors, and develop a test for the statistically significant harmonics. An example of daily high temperatures illustrates the method, whereby a periodic autoregressive model with 1095 parameters is reduced to a parsimonious 12 parameter version without any apparent loss of fidelity.

Suggested Citation

  • Paul L. Anderson & Farzad Sabzikar & Mark M. Meerschaert, 2021. "Parsimonious time series modeling for high frequency climate data," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(4), pages 442-470, July.
    • Handle: RePEc:bla:jtsera:v:42:y:2021:i:4:p:442-470
    DOI: 10.1111/jtsa.12579
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    References listed on IDEAS

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    1. Yonas Gebeyehu Tesfaye & Paul L. Anderson & Mark M. Meerschaert, 2011. "Asymptotic results for Fourier‐PARMA time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(2), pages 157-174, March.
    2. French, Joshua & Kokoszka, Piotr & Stoev, Stilian & Hall, Lauren, 2019. "Quantifying the risk of heat waves using extreme value theory and spatio-temporal functional data," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 176-193.
    3. P. L. Anderson & A. V. Vecchia, 1993. "Asymptotic Results For Periodic Autoregressive Moving‐Average Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(1), pages 1-18, January.
    4. Paul L. Anderson & Mark M. Meerschaert, 2005. "Parameter Estimation for Periodically Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(4), pages 489-518, July.
    5. repec:bla:jtsera:v:25:y:2004:3:p:359-372 is not listed on IDEAS
    6. Dag Tjøstheim & Jostein Paulsen, 1982. "Empirical Identification Of Multiple Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 3(4), pages 265-282, July.
    7. Robert Lund & I. V. Basawa, 2000. "Recursive Prediction and Likelihood Evaluation for Periodic ARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(1), pages 75-93, January.
    8. Philip Hans Franses & Richard Paap, 2011. "Random‐coefficient periodic autoregressions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 65(1), pages 101-115, February.
    9. Taylan A. Ula, 1993. "Forecasting Of Multivariate Periodic Autoregressive Moving‐Average Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(6), pages 645-657, November.
    10. Qin Shao & Robert Lund, 2004. "Computation and Characterization of Autocorrelations and Partial Autocorrelations in Periodic ARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(3), pages 359-372, May.
    11. Basawa, I. V. & Lund, Robert & Shao, Qin, 2004. "First-order seasonal autoregressive processes with periodically varying parameters," Statistics & Probability Letters, Elsevier, vol. 67(4), pages 299-306, May.
    12. Anderson, Paul L. & Meerschaert, Mark M. & Vecchia, Aldo V., 1999. "Innovations algorithm for periodically stationary time series," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 149-169, September.
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    Cited by:

    1. Webel, Karsten, 2022. "A review of some recent developments in the modelling and seasonal adjustment of infra-monthly time series," Discussion Papers 31/2022, Deutsche Bundesbank.

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