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Time series modelling of two millennia of northern hemisphere temperatures: long memory or shifting trends?

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  • Terence C. Mills

Abstract

Summary. The time series properties of the temperature reconstruction of Moberg and co‐workers are analysed. It is found that the record appears to exhibit long memory characteristics that can be modelled by an autoregressive fractionally integrated moving average process that is both stationary and mean reverting, so that forecasts will eventually return to a constant underlying level. Recent research has suggested that long memory and shifts in level and trend may be confused with each other, and fitting models with slowly changing trends is found to remove the evidence of long memory. Discriminating between the two models is difficult, however, and the strikingly different forecasts that are implied by the two models point towards some intriguing research questions concerning the stochastic process driving this temperature reconstruction.

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  • Terence C. Mills, 2007. "Time series modelling of two millennia of northern hemisphere temperatures: long memory or shifting trends?," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(1), pages 83-94, January.
    • Handle: RePEc:bla:jorssa:v:170:y:2007:i:1:p:83-94
    DOI: 10.1111/j.1467-985X.2006.00443.x
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    Cited by:

    1. J. Eduardo Vera-Valdés, 2021. "Nonfractional Long-Range Dependence: Long Memory, Antipersistence, and Aggregation," Econometrics, MDPI, vol. 9(4), pages 1-18, October.
    2. Beenstock, Michael & Reingewertz, Yaniv & Paldor, Nathan, 2016. "Testing the historic tracking of climate models," International Journal of Forecasting, Elsevier, vol. 32(4), pages 1234-1246.
    3. William Rea & Marco Reale & Jennifer Brown, 2011. "Long memory in temperature reconstructions," Climatic Change, Springer, vol. 107(3), pages 247-265, August.
    4. Luis A. Gil-Alana, 2015. "Linear and segmented trends in sea surface temperature data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(7), pages 1531-1546, July.
    5. Terence C. Mills, 2012. "Semi-parametric modelling of temperature records," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 361-383, May.
    6. Gilles Dufrénot & William Ginn & Marc Pourroy, 2021. "The Effect of ENSO Shocks on Commodity Prices: A Multi-Time Scale Approach," Working Papers halshs-03225070, HAL.
    7. J. Eduardo Vera-Valdés, 2021. "Temperature Anomalies, Long Memory, and Aggregation," Econometrics, MDPI, vol. 9(1), pages 1-22, March.
    8. Michael Mann, 2011. "On long range dependence in global surface temperature series," Climatic Change, Springer, vol. 107(3), pages 267-276, August.
    9. John K. Dagsvik & Mariachiara Fortuna & Sigmund Hov Moen, 2020. "How does temperature vary over time?: evidence on the stationary and fractal nature of temperature fluctuations," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(3), pages 883-908, June.
    10. Contreras-Reyes, Javier E., 2022. "Rényi entropy and divergence for VARFIMA processes based on characteristic and impulse response functions," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

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