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Long-range dependence, nonlinear trend, and breaks in historical sea surface and land air surface global and regional temperature anomalies

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Abstract

The global temperature series is a major indicator of climate change, whereas this indicator has undergone shift in trend over the twentieth century, changing from linear trend to nonlinear trend as a result of structural breaks. This paper investigates global and regional sea surface (SS) and land air surface (LS) temperature series from 1880 to 2016 by means of fractional integration technique. The results show that temperature series are described by trend stationary process, mostly in long memory range in the case of LS temperature while in the case of SS temperature, temperature series are in nonstationary mean reverting range for global and hemispheric temperature as well as for three other regional locations. By applying the multiple structural break test, the trend line is found breaking in many dates, locking up into many regimes which can be described using nonlinear trend structure. Nonlinear trend, based on Chebyshev inequality in the fractional integration framework, shows that global and regional temperature series can be represented using nonlinear trend up to the third order since this further lowers the integration order to long memory range in both SS and LS temperature series.

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Notes

  1. Other approaches to analysis of global and regional sea surface and land air surface temperature series are found in Rayner et al. (2003), Franzke (2011), Friedel (2012), Jiang et al. (2016), Campra and Morales (2016), Rugenstein et al. (2016), among others.

  2. Similar definition is given based on time domain approach in time series analysis (see Palma 2007).

  3. GISTEMP: GISS Surface Temperature Analysis. This is an estimate of global temperature change.

  4. The absolute temperature may not really make more applicability sense since this varies markedly in short distances, while temperature anomalies are strongly correlated out to long distance span (Hansen and Lebedeff 1987; Gil-Alana et al. 2014).

  5. Noting that the emphasis in this paper is on model fitness, thus for future research along this line, one can investigate forecast performance using criteria such root mean square error (RMSE), mean absolute percentage error (MAPE), and Diebold-Mariano (DM) test of Diebold and Mariano (1995) as well as its modified version (M-DM) by Harvey et al. (1997).

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Acknowledgements

The authors gratefully acknowledged the comments from the Editor and anonymous reviewers.

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Authors and Affiliations

  1. Department of Statistics, Computational Statistics Unit, University of Ibadan, Ibadan, Nigeria

    OlaOluwa S. Yaya

  2. Department of Statistics, Laboratory for Interdisciplinary Statistical Analysis (UI-LISA), University of Ibadan, Ibadan, Nigeria

    Olalekam J. Akintande

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  1. OlaOluwa S. Yaya
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  2. Olalekam J. Akintande
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Correspondence to OlaOluwa S. Yaya.

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Yaya, O.S., Akintande, O.J. Long-range dependence, nonlinear trend, and breaks in historical sea surface and land air surface global and regional temperature anomalies. Theor Appl Climatol 137, 177–185 (2019). https://doi.org/10.1007/s00704-018-2592-4

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  • DOI: https://doi.org/10.1007/s00704-018-2592-4