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

  • OlaOluwa S. YayaEmail author
  • Olalekam J. Akintande
Original Paper


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.



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

Compliance with ethical standards

Conflict of interests

The authors declare that they have no conflict of interests.


The datasets and the materials used in the paper are referenced appropriately.


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© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Statistics, Computational Statistics UnitUniversity of IbadanIbadanNigeria
  2. 2.Department of Statistics, Laboratory for Interdisciplinary Statistical Analysis (UI-LISA)University of IbadanIbadanNigeria

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