Regarding orderly sequences embedded within longer stochastic sequences; these are called Feynman Points, after the famous sequence of six nines starting at position 768 of pi. Any partial data set corresponding to a Feynman Point is going to badly underestimate total entropy.
Directly-observed atmospheric data sets are quite short compared to ice-core records. Beginning literature-search of QBO signal in ice-cores, to help resolve questions of tidal-forcing. Seeing initially that annual solar signal and stochastic storm and wind timing swamps tidal signals, such that a huge ice-core sequence needs to be crunched for tidal-forcing to appear. QBO itself is easily detected in ice-cores [https://doi.org/10.5194/acp-12-4107-2012].
Another harmonic principle applies. At high energies of an oscillator, all frequencies are expressed. As energy decays, slowest fundamental frequencies persist the longest, however, as they finally decay, they do so into smaller transient frequencies. This is a further source of ENSO-QBO chaos. We may not best just cry "chaos", but also "multi-chaos" or "fractal-chaos".
Tree-ring data does seem to contain clear decadal-scale signals of "intermittent periodicity"- [Rogozo et al 2008] https://doi.org/10.1016/j.jastp.2008.02.002
Disregarding relative bio-amplification of cyclic solar effects, we can conjecture >0 atmospheric oscillation forcing tendency.