Statistical Prediction of Dst Index by Solar Wind Data and <inline-formula> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula>-Distributions

Abstract

The disturbance storm time (Dst) index is a measure of the geomagnetic storm strength that can be caused by solar wind plasma ejecta and/or high-speed streams. The research aims to predict the Dst index hours ahead using statistical regression models based on solar wind measurements. It is shown that the distribution of Dst index data has heavy tails. This implies that the data cannot be well approximated with Gaussian distribution. Instead, we use $t$ -distributions to model the Dst index data. By considering the Sun–earth plasma coupling process as a stochastic dynamical system, we construct $t$ -distribution-based autoregressive models with the solar wind proton density, solar wind speed, and interplanetary magnetic field $B_{z}$ as exogenous variables. The Dst index is also regressed to the solar wind measurements as well as the past observations of the Dst index. Furthermore, the scale and degree of freedom of the $t$ -distributions are regressed using generalized linear models. The Bayesian information criterion is used to select the optimal model structures. The results for real data indicate that the proposed model is very effective at describing the time-dependent features of the Dst index.