FARIMA MODELING OF SOLAR FLARE ACTIVITY FROM EMPIRICAL TIME SERIES OF SOFT X-RAY SOLAR EMISSION

Atime series of soft X-ray emission observed by the Geostationary Operational Environment Satellites from 1974 to 2007 is analyzed. We show that in the solar-maximum periods the energy distribution of soft X-ray solar flares for C, M, and X classes is well described by a fractional autoregressive integrated moving average model with Pareto noise. The model incorporates two effects detected in our empirical studies. One effect is a long-term dependence (long-term memory), and another corresponds to heavy-tailed distributions. The parameters of the model: self-similarity exponent H, tail index a, and memory parameter d are statistically stable enough during the periods 1977-1981, 1988-1992, 1999-2003. However, when the solar activity tends to minimum, the parameters vary. We discuss the possible causes of this evolution and suggest a statistically justified model for predicting the solar flare activity.