<blockquote>I have not heard or seen of a statistical treatment such as this and it seems a perfectly understandable and legitimate approach, even at the ‘informed layperson’ level.</blockquote>
These papers are not at the layperson level but are more akin to the way I would think of the problem, and were in fact discovered after I worked out a "layperson treatment" on my blog.
<a href="http://arxiv.org/PS_cache/arxiv/pdf/1105/1105.3118v1.pdf" rel="nofollow">A Stochastic Energy Budget Model Using Physically Based Red Noise</a> 2011
<a href="http://arxiv.org/PS_cache/arxiv/pdf/1007/1007.1376v4.pdf" rel="nofollow">Climate tipping as a noisy bifurcation: a predictive technique</a> 2010
These are very far removed from Ludecke's approach but in fact contain the elements needed to reason about stochastic time series, which must first and foremost consider fundamental statistical physics.
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