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STUDY ABOUT AUTO-REGRESSIVE INTEGRATED MOVING AVERAGE (ARIMA) MODEL USED FOR FORECAST OF STRONG GEOMAGNETIC DISTURBANCES
Abstract
The Auto-Regressive Integrated Moving Average (ARIMA) model is widely used to forecast non-stationary time series data. In a model of ARIMA (p, d, q), AR is autoregressive, p is the number of regression terms, MA is the moving average, q is the number of moving average terms, and d is the difference time to make the data a stationary series. It can be used to forecast the trend of geomagnetic disturbances. Firstly, the non-stationary historical data xt is processed by the d difference to develop the stable historical data yt, fitted to the ARMA (p, q) model to predict geomagnetic activity, and then the original data xt is obtained by d times contrast difference. In this paper we used planetary geomagnetic indices, hourly values, available on specialized sites. The Auroral Electrojet (AE) index is derived from geomagnetic variations in the horizontal component observed at selected observatories along the auroral zone in the northern hemisphere. To normalize the data a base value for each station is first calculated for each month by averaging all the data from the station on the five international quietest days. This base value is subtracted from each value of one-minute data obtained at the station during that month. The disturbance storm time (DST) index is a measure of the ring current around Earth caused by solar protons and electrons, in the context of space weather. The ring current around Earth produces a magnetic field that is directly opposite Earth's magnetic field, i.e. if the difference between solar electrons and protons gets higher, then Earth's magnetic field becomes weaker. A negative DST value means that Earth's magnetic field is weakened. This is particularly the case during solar storms. Our study, presented in the paper, refers to the realization of the ARIMA model for two important geomagnetic storms in the last Solar Cycle, based on DST and AE indices.
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