Solar X-ray variability in terms of a fractional heteroskedastic time series model

Анотація

The Sun is variable in activity with changes on time-scales as short as minutes to as long as a solar cycle. Although the most accurate measurements are limited to the satellite era, the past four decades, looking at the solar variability over this period provides a possible link between complex dynamics of the Sun and the accompanying radiation. Measurements of the latter and their analysis by sophisticated time series methods encourage forecasting future values of the time series. Our data analysis work focuses on the soft X-ray emission observed at the current solar minimum, in 2017 September July. We have found two different (active and inactive) states of the solar activity using a Hidden Markov Model, and we show that in the periods of high-solar activity the energy distribution of soft X-ray solar flares is well described by an ARFIMA-GARCH model, whereas in the case of low-solar activity an ARFIMA model is best fitted. Switching from the inactive state to the active one is caused by explosive phenomena in the Sun. The model describes three effects detected in our empirical studies. One of them is a long-term dependence, the second is variance changing in time, and the third corresponds to heavy-tailed distributions of the X-ray data. Moreover, the model takes into account memory effects in soft X-ray emission due to the Sun’s magnetic field evolution. All this together allows us to suggest a statistically justified model for explaining the solar activity variability at the current solar minimum.

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