Using fractal dimension to quantify long-range persistence in global solar radiation

The basic characteristic of a self-affine time series is that the persistence (or long-term memory) is scale invariant and long-range. The persistence measures the correlation between adjacent values within the time series. Values of a time series can affect other values in the time series that are not only nearby in time but also far away in time. A number of statistical approaches are currently in use to quantify persistence in time series. In this paper, we examine the persistence of daily and annually global solar irradiation data with many years of record using the fractal dimension. For this purpose, a new method to measure the fractal dimension of temporal discrete signals is presented. The fractal dimension is then used as criterion in an approach we have elaborated to detect the long-term correlation in solar irradiation series. The results show that daily and annual solar irradiations are anti-persistent.