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Cyclical Time Series: An Empirical Analysis of Temperatures in Central England Over Three Centuries

Author

Listed:
  • Liudas Giraitis

    (Queen Mary University of London)

  • Fulvia Marotta

    (De Nederlandsche Bank, University of Oxford)

  • Peter C B Phillips

    (Yale University)

Abstract

This paper builds on methodology that corrects for irregular spacing between realizations of unevenly spaced time series and provides appropriately corrected estimates of autoregressive model parameters. Using these methods for dealing with missing data, we develop time series tools for forecasting and estimation of autoregressions with cyclically varying parameters in which periodicity is assumed. To illustrate the robustness and flexibility of the methodology, an application is conducted to model daily temperature data. The approach helps to uncover cyclical (daily as well as annual) patterns in the data without imposing restrictive assumptions. Using the Central England Temperature (CET) time series (1772 - present) we find with a high level of accuracy that temperature intra-year averages and persistence have increased in the later sample 1850-2020 compared to 1772 - 1850, especially for the winter months, whereas the estimated variance of the random shocks in the autoregression seems to have decreased over time.

Suggested Citation

  • Liudas Giraitis & Fulvia Marotta & Peter C B Phillips, 2024. "Cyclical Time Series: An Empirical Analysis of Temperatures in Central England Over Three Centuries," Cowles Foundation Discussion Papers 2409, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:2409
    as

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    File URL: https://cowles.yale.edu/sites/default/files/2024-10/d2409.pdf
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    References listed on IDEAS

    as
    1. Tommaso Proietti & Eric Hillebrand, 2017. "Seasonal changes in central England temperatures," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(3), pages 769-791, June.
    2. Gerard D. McCarthy & Ivan D. Haigh & Joël J.-M. Hirschi & Jeremy P. Grist & David A. Smeed, 2015. "Ocean impact on decadal Atlantic climate variability revealed by sea-level observations," Nature, Nature, vol. 521(7553), pages 508-510, May.
    3. Jingyuan Li & David W. J. Thompson, 2021. "Widespread changes in surface temperature persistence under climate change," Nature, Nature, vol. 599(7885), pages 425-430, November.
    4. Terence C. Mills & David I. Harvey, 2003. "Modelling trends in central England temperatures," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 22(1), pages 35-47.
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