Climatic Change

, Volume 107, Issue 3–4, pp 247–265 | Cite as

Long memory in temperature reconstructions

  • William Rea
  • Marco RealeEmail author
  • Jennifer Brown


Ever since H. E. Hurst brought the concept of long memory time series to prominence in his study of river flows the origins of the so-called Hurst phenomena have remained elusive. Two sets of competing models have been proposed. The fractional Gaussian noises and their discrete time counter-part, the fractionally integrated processes, possess genuine long memory in the sense that the present state of a system has a temporal dependence on all past states. The alternative to these genuine long memory models are models which are non-stationary in the mean but for physical reasons are constrained to lie in a bounded range, hence on visual inspection appear to be stationary. In these models the long memory is merely an artifact of the method of analysis. There are now a growing number of millenial scale temperature reconstructions available. In this paper we present a new way of looking at long memory in these reconstructions and proxies, which gives support to them being described by the non-stationary models. The implications for climatic change are that the temperature time series are not mean reverting. There is no evidence to support the idea that the observed rise in global temperatures are a natural fluctuation which will reverse in the near future.


Structural Break Spectral Estimate Temperature Time Series Time Series Plot Colorado Plateau 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.University of CanterburyChristchurchNew Zealand

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