**1. Introduction**

130 Solar Radiation

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This work is focused on the investigation of correlations and memory effects in daily global solar radiation data series and in the capture of underlying multifractality. It is well known that the behaviour of the climatological variables affect directly crucial aspects of the people's daily lives. Typically measurements of these variables are a sequence of values that constitute a time series, and time series analysis tools can contribute effectively to the study of such variables. An interesting investigation that can be done on the series is to identify the occurrence of correlation in the records of the sequence and to detect an effect of longterm memory in this data set over time. One possible approach is to estimate how a particular measure of fluctuations in the series scales with the size *s* of the time window considered. A specific method for this analysis is the Detrended Fluctuation Analysis – DFA, a well-established method for the detection of long-range correlations. Usually, trends may mask the effect of correlations. DFA can systematically eliminate trends of polynomial of different orders. This method was proposed in (Peng et al., 1994) and has successfully been applied to many different fields, and particularly in the study of data series of variables associated with the weather and climate. The fluctuation function behaves as a power law with the values chosen for *s.* The exponent can be identified as the Hurst exponent (H). The DFA method gives the Hurst exponent, and estimating such exponent from a given data set is an effective way to determine the nature of correlation in it. Values of H in the range (0, 0.5) characterize anti-persistence, whereas those in the range (0.5,1) characterize persistence, long-range correlations. The value *H=0.5* is associated with uncorrelated noise. Temperature and precipitation have characteristic values of H (Koscielny-Bunde *et al*., 1998; Bunde & Havlin, 2002) although some claim that the scaling exponent is not universal for temperature data (Király & Jánosi, 2005; Rybski *et al*. 2008). Relative humidity shows stronger persistence (Chen *et al*., 2007; Lin *et al*., 2007), and wind speed also exhibit behaviour with long-range correlation (Govindan & Kantz, 2004; Kavasseri & Nagarajan, 2005; Koçak, 2009; Feng *et al*., 2009). One can be sure of the universality of the correlations in climatological time series but its exponents can be related to local patterns.

The variation of the Hurst exponent in time for a given series indicates the existence of nonstationary fluctuations, pointing to a multi-fractal. Thus, when the series points to the existence of more than one exponent for its characterization we are dealing with multifractal behaviour. Multifractal signals are far more complex than monofractal signals and require more exponents (theoretically infinite) to characterize their scaling properties. In this work multifractality in time series data of global solar radiation is studied by applying the Multifractal Detrended Fluctuation Analysis (MF-DFA) proposed in (Kantelhardt *et al*., 2002). It is a modified version of DFA to detect multifractal properties of time series and provides a systematic tool to identify and quantify the multiple scaling exponents in the data. This method was applied in several cases, in particular in climatological data series as presented in (Kantelhardt *et al*. 2003; Alvarez-Ramirez *et al*., 2008; Pedron, 2010; Zhang, 2010).
