A new class of near-rational sunspot equilibria is identified in economies expressed as non-linear forward-looking models. The new equilibria are natural extensions of the usual sunspot equilibria associated to the linearized version of the economy, and are near-rational in that agents use the optimal linear forecasting model when forming expectations. A generic existence result is established....

The authors show how the influence of extrinsic random signals depends on the noise structure of these signals. They present an experiment on a coordination game in which extrinsic random signals may generate sunspot equilibria. They measure how these signals affect behavior. Sunspot equilibria emerge naturally if there are salient public signals. Highly correlated private signals may also caus...

We analyze a simple sunspot model that represents a standard securities market without sidebets on an exogenous sunspot event. The multiple self–fulfilling equilibria that arise in the model are based on investors’ uncertainty about other investors’ beliefs. Hence, these multiple equilibria are “endogenous sunspots.” We show that endogenous sunspots can arise even with complete markets to which...

The low ionization state in parts of a sunspot may play an important role in its evolution and dynamical state. The cool magnetic interior region of the sunspot develops a substantial neutral atomic and molecular hydrogen osmotic pressure which can drive a wind outward from the umbra. Ambipolar diffusion against the magnetically pinned ionized plasma component can also distort the umbral magnet...

We consider the statistical relationship between the growth rate of activity in the early phase of a solar cycle with its subsequent amplitude on the basis of four datasets of global activity indices (Wolf sunspot number, group sunspot number, sunspot area, and 10.7-cm radio flux). In all cases, a significant correlation is found: stronger cycles tend to rise faster. Owing to the overlapping of...

Chaotic time-series is a dynamic nonlinear system whose features can not be fully reflected by Linear Regression Model or Static Neural Network. While Nonlinear Autoregressive with eXogenous input includes feedback of network output, therefore, it can better reflect the system’s dynamic feature. Take annual active times of sunspot as an example, after verifying the chaos of sunspot time-series ...

Although most of the magnetic flux observed on the sun originates in the low-latitude sunspot belts, this flux is gradually dispersed over a much wider range of latitudes by supergranular convective motions and meridional circulation. Numerical simulations show how these transport processes interact over the 11-year sunspot cycle to produce a strong "topknot" polar field, whose existence near s...

This paper considers the necessity and sufficiency of multiple certainty equilibria for sunspot effects, and shows that neither implication is valid. This claim is made for models with incomplete markets and numeraire assets. First, I prove that a multiplicity of certainty equilibria is neither necessary nor sufficient for sunspot effects by way of two counter-examples. Second, I verify over an...

Because of the lack of reliable sunspot observation, the quality of sunspot number series is poor in the late 18th century, leading to the abnormally long solar cycle (1784–1799) before the Dalton minimum. Using the newly recovered solar drawings by the 18–19th century observers Staudacher and Hamilton, we construct the solar butterfly diagram, i.e. the latitudinal distribution of sunspots in t...

The sun is the unlimited energy source for life on the earth. However, besides as the energy source, the sun also gives disruptions to the universe around the earth and also to the life on the earth. Sources of the disruptions from the sun are flares and Coronal Mass Ejection/CME. Both of those disruptions in general come from group of sunspots. With the growing of dependency of human life with...