  Multifractal structure of global monthly mean temperature anomaly time series
over the period of 1850-2012 are studied in terms of the multifractal detrended
moving average (MFDMA) analysis. We try to address the possible source(s) and
the nature of multifractality in the time series data by comparing the results
derived from the actual series with those from a set of shuffled and surrogate
series. It is seen that the MFDMA method predicts a multifractal structure of
the temperature anomaly records that is more or less similar to what was
obtained from the multifractal detrended analysis for the same set of data. In
our analysis the major contribution of multifractality in the data is found to
be due to the long-range temporal correlation among the measurements, however
the contribution of a fat-tail distribution function of the variables is not
negligible. The existence of long-range correlation is also confirmed by the
constancy of the local slopes of the fluctuation function over a sufficient
scale intervals. The results of the moving average analysis are found to depend
upon the location of the detrending window and tend to the observations of the
multifractal detrended analysis for a specific choice of the location of the
detrending window.
