In this paper we describe the statistical properties of the EUV solar flux sudden variation. The solar flux variation is modeled as a time series characterized by the subsolar Vertical Total Electron Content double difference in time, computed with dual‐frequency GNSS (Global Navigation Satellite Systems) measurements in the daylight hemisphere (GNSS solar flare indicator rate parameter). We propose a model that explains its characteristics and the forecasting limitations. The sudden overionization pattern is assumed to be of solar origin, and the data used in this study was collected during the last solar cycle. The two defining characteristics of this time series are an extreme variability (i.e., in a solar cycle one can find events at 400σ from the mean value) and a temporal correlation that is independent of the timescale. We give a characterization of a model that explains the empirical results and properties such as (a) the persistence and presence of bursts of solar flares and (b) their long tail peak values of the solar flux variation. We show that the solar flux variation time series can be characterized by a fractional Brownian model for the long‐term dependence, and a power law distribution for the extreme values that appear in the time series. Key PointsStatistical properties of the EUV solar flux sudden variation as a time seriesSudden overionization studied during one solar cycle from GNSS signalsThe solar flux rate follows the Levy‐Mandelbrot and fractional Brownian models