Prediction performance of Hidden Markov modelling for solar flares

Solar flares are large explosions in the sun's atmosphere. They can damage satellites and overload electrical systems. To manage that risk, finding methods of efficiently predicting future events is very important. In this paper we introduce a full-Sun flare prediction method based on the Hidden Markov modelling with two hidden states. We concentrate on the soft X-ray emission data near the minimum of solar cycle and consider two different driving dynamics for both states, namely the independent identically distributed (IID) random variables and the autoregressive (AR) processes, the latter introducing a memory structure. We compare prediction performance for the IID and AR approaches and also with a naive prediction equal to the last observation. The solar X-flux dynamics is predicted by using the day-ahead forecasts. We calculate point and interval forecasts and perform relevant statistical tests to choose the best method. It appears that the AR approach is clearly superior to the IID and naive both by means of point and interval forecasts. Moreover, it can well detect the higher state which can lead to very strong energy releases. Significant development of the model would be necessary to forecast solar flares over an entire solar cycle.