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You noted two other anomalies:
The only periods that this extreme a difference appears for expiration dates at least 5 months out are Oct. 2008 and Feb. 2018

Oct 2008 had a huge S&P drop.
Feb 2018 had a huge vol spike (out of historical proportion to the S&P drop).

I was wondering when the Oct 2008 and the Feb 2018 anomalies in the term structure were noted?

You seem to be suggesting that the change in term structure is predictive.
I'm aware that some people look at VIX term structure, e.g. the 1 month (^VIX) compared to the 3 month (^VXV), to decide whether to buy a short vol fund or not.
Backtest results seem mixed, depending on implementation.
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