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Tempered linear and non-linear time series models and their application to heavy-tailed solar flare data.
- Source :
-
Chaos . Nov2021, Vol. 31 Issue 11, p1-12. 12p. - Publication Year :
- 2021
-
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]
Details
- Language :
- English
- ISSN :
- 10541500
- Volume :
- 31
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- Chaos
- Publication Type :
- Academic Journal
- Accession number :
- 153907453
- Full Text :
- https://doi.org/10.1063/5.0061754