Abstract
We study the dynamic evolution of the time series describing the plage regions areas observed daily at the Observatório Astronómico da Universidade de Coimbra, in each one of the solar hemispheres during solar cycles 21 – 23. The classical ARMA model has proven to be insufficient to describe the time variations seen in the data because of the strong conditional variability. We found that the data are well fitted by ARMA mixed with power-δ TGARCH error models. The power index δ is non-integer; this property has recently been introduced in the literature on time-series analyses and indicates the presence of strong volatility and long memory in the data series. We also detected dynamic asymmetry in the plage region areas observed in the two hemispheres when two different temporal models were obtained to fit them. The finding of a dynamic asymmetry is also supported by the dynamic evolution of the daily difference (north–south) time series, which is significantly different from white noise. This statistical modeling of time series, taking into account new and different characteristics of the solar activity, will be very useful in subsequent forecast developments.
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Notes
This parameter has the same units as the plage region area.
The indicatrix function is defined as \(\mathbb{I}_{A}=\big\{ \begin{array}{l} 1, \text{if } A \text{ happens}, \\ 0, \text{otherwise}. \end{array} \)
The partial autocorrelation of lag k is the correlation between observations X t and X t−k after removing the linear relations among X t−1,…,X t−k+1.
The AR parameter values are estimated by the classical least-squares method, while in the δ-TGARCH parameters the maximum-likelihood estimation is used (Francq and Zakoian 2010).
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We are grateful to the anonymous referee for advice that helped us to significantly improve this article.
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Gonçalves, E., Mendes-Lopes, N., Dorotovič, I. et al. North and South Hemispheric Solar Activity for Cycles 21 – 23: Asymmetry and Conditional Volatility of Plage Region Areas. Sol Phys 289, 2283–2296 (2014). https://doi.org/10.1007/s11207-013-0448-8
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DOI: https://doi.org/10.1007/s11207-013-0448-8