1. Tempered linear and non-linear time series models and their application to heavy-tailed solar flare data.
- Author
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Susan Kabala, Jinu, Burnecki, Krzysztof, and Sabzikar, Farzad
- Subjects
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SOLAR flares , *TIME series analysis , *HIDDEN Markov models , *MOVING average process , *SOFT X rays - Abstract
In this paper, we introduce two tempered linear and non-linear time series models, namely, an autoregressive tempered fractionally integrated moving average (ARTFIMA) with α -stable noise and ARTFIMA with generalized autoregressive conditional heteroskedasticity (GARCH) noise (ARTFIMA-GARCH). We provide estimation procedures for the processes and explain the connection between ARTFIMA and their tempered continuous-time counterparts. Next, we demonstrate an application of the processes to modeling of heavy-tailed data from solar flare soft x-ray emissions. To this end, we study the solar flare data during a period of solar minimum, which occurred most recently in July, August, and September 2017. We use a two-state hidden Markov model to classify the data into two states (lower and higher activity) and to extract stationary trajectories. We do an end-to-end analysis and modeling of the solar flare data using both ARTFIMA and ARTFIMA-GARCH models and their non-tempered counterparts. We show through visual inspection and statistical tests that the ARTFIMA and ARTFIMA-GARCH models describe the data better than the ARFIMA and ARFIMA-GARCH, especially in the second state, which justifies that tempered processes can serve as the state-of-the-art approach to model signals originating from a power-law source with long memory effects. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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