## Modeling and prediction of sunspot cycles

##### Author(s)

He, Li, 1977-
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##### Other Contributors

Massachusetts Institute of Technology. Dept. of Mathematics.

##### Advisor

Richard M. Dudley.

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Solar activity, as indexed by sunspots, has a cycle of length varying from about 9 to 13 years. Statisticians have fitted several models to predict sunspot numbers one year ahead. We instead focus on predicting the magnitudes of the next cycle maximum, the next cycle minimum, the time from the initial minimum of a cycle to its maximum, called the rise time, and the time from a cycle maximum to the next cycle minimum, called the fall time. The predictions are based on sunspot numbers just far enough into a new cycle to establish that a cycle has started. We propose parsimonious regression models for the maximum and rise time. For the fall time and minimum we propose crude models, based on the sample means and variances for all past cycles. We compare our models to simulation results for many models we found in the literature including autoregressive (AR) models, subset AR (SAR) models, and related nonlinear models including a threshold AR model, transformed by squaring (TTAR model), a bilinear model, a so-called ASTAR model, and a neural network (CNAR) model. We also consider a model proposed by solar physicists, based on a functional form for cycles. (cont.) Numerical results show that among all the models considered for sunspot numbers, our regression models give the smallest MSEs (mean-square errors) for the maxima, and our crude models give the smallest MSEs for the minima. For fall times our crude model has the second-smallest MSE after CNAR. ASTAR does very well for modeling the rise times. Observations of the sun have become progressively more accurate, but we found that giving higher weight to more recent observations gave worse results. Among the model selection criteria we tried for the autoregressive and regression models, the two that worked best as judged by cross-validations were the well-known Akaike Information Criterion and a modification of the G. Schwarz BIC criterion called BIC* due to D. and J. Haughton and A. Izenman.

##### Description

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001. Includes bibliographical references (p. 161-165).

##### Date issued

2001##### Department

Massachusetts Institute of Technology. Dept. of Mathematics.##### Publisher

Massachusetts Institute of Technology

##### Keywords

Mathematics.