Stochastic approach to Markovian interrelationship assessment of solar activity indices

Abstract

This paper employs a discrete-time Markov chain (DTMC) stochastic process to investigate a state/event based Markovian interrelationship between various solar activity indices (SAI) (including 10.7 cm solar radio flux (SF10.7), coronal index (CI), solar flare index (SFI) and total solar irradiance (TSI)) in relation to sunspot number (SSN). First, we applied the first order DTMC model as a first approximation to the total number of transitions between different states of SAI in order to estimate the probability of occurrence corresponding with each transition. Next, several DTMC descriptors like persistency, state dependency, stationarity, mean first passage time and entropy are derived from estimated transition probability matrices. These descriptors are very useful as they related to time series characteristics (like randomness, nature of cycles and predictability) within a stochastic dynamical system as well as crucial for checking the applicability of Markov chain method. Therefore, via the DTMC analysis and derived descriptors, this study found remarkable similarities in the formation of transition matrices and diagrams, significant 2-dimensional correlation values, robust self-communication behaviour among states, existence of dependent successive transitions and stationary nature of data throughout the space. Further, the resemblance in the average transit time from one state to another, probabilistically disordered symmetrical time series and existence of randomness in transition states has been observed. Therefore, results obtained in this paper provide a new insight to increase the level of knowledge of the possible linkage between underlying SAI that could be helpful in enhanced understanding of the potential future climate changes and other solar energy-related objectives.