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Cycles in the Annual Changes in Average Global Temperature

The temperature of a body is the cumulation of the net inflows of energy. Therefore the
statistical properties of temperatures differ from variables which are not the cumulation of
random disturbances. In particular, variables which are the cumulation of random influences will
tend to have the appearances of trends even when no long term trends exist. Therefore it is
appropriate to carry out the statistical analysis of temperature variables in terms of the
annual changes.

Some successful analyses of cycles and trends in global temperatures have been carried out using
the data from the National Oceanic and Atmospheric Administration (NOAA), the Hadley Climate Research
Unit (Hadley CRU), and NASA's Goddard Institute for Space Science
(GISS). In all three cases it was found that there is long term upward
trend in average global temperature of about 0.5°C per century. Furthermore there is a cycle
of upswings and downswings of about 32 years in duration that goes back to the beginning of the data.
This cycle prevails for the 128 years of the data for NOAA and GISS and the 158 years of the data
from Hadley CRU.

Annual Changes in Average Global Temperature

A cyclic pattern in average global temperature (AGT) would manifest itself in the form shown below.

Such a piecewise flat regression can be estimated using variables that change from 0 to 1 at
designated transition points. When the annual changes in the NOAA data were used and transition
points set at 1910, 1