Statistical Modeling of Solar Flare Activity from Empirical Time Series of Soft X-ray Solar Emission

TL;DR

This paper models solar flare energy distribution during high activity periods using FARIMA with Pareto innovations, revealing long-term memory and heavy tails, and discusses changes during solar minima for prediction purposes.

Contribution

It introduces a statistical FARIMA-based model with Pareto innovations for solar flare energy, capturing long-range dependence and heavy tails, and analyzes parameter stability across solar activity cycles.

Findings

Energy statistics fit FARIMA with Pareto innovations during high activity periods.

Parameters are stable during high activity but change during minima.

Proposes a model for predicting flare energy statistics based on observed evolution.

Abstract

A time series of soft X-ray emission observed on 1974-2007 years (GOES) is analyzed. We show that in the periods of high solar activity 1977-1981, 1988-1992, 1999-2003 the energy statistics of soft X-ray solar flares for class M and C is well described by a FARIMA time series with Pareto innovations. The model is characterized by two effects. One of them is a long-range dependence (long-term memory), and another corresponds to heavy-tailed distributions. Their parameters are statistically stable enough during the periods. However, when the solar activity tends to minimum, they change essentially. We discuss possible causes of this evolution and suggest a statistical model for predicting the flare energy statistics.