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tldr of nature article:
mr wizards have been interested in solar behavior due to role in affecting magnetic phenomenon on earth.
authors looked at solar event data and relationship to magnetism on earth. existing stat models to account for relationship so far was regression models, and the particular models mentioned in article didnt predict at all how current solar cycle actually played out.
authors proposed an alternativr model they felt would account for more of the changes in historic data and do better job extrapolating model forward for prediction.
their model employs PCA and indeed fit historic data and current cycle better than existing models.
so they went on ahead and modeled it forward to see what this model suggests for a century or two forward. and present their findings.