Jan, I use the second derivative because that exposes more directly the forcing factor, F(t)

$ f''(t) + \omega_0^2 f(t) = F(t) $

The factors matrix is flat with these periods (in years) all contributing equal potential power, but the regression returns a weighting and phase.

s9 is 9.08 -- metonic cycle
di is 18.63 -- diurnal tide
q4 is 4.06 -- close to aliased Anomalistic month 3.93
qm is 2.245 -- strong sideband of main QBO period of 2.33 years
q1 is 1.745 -- close to 1/(1-1/2.33) aliasing residue
cw is 6.48 -- Chandler wobble period
sd is 8.848/2 -- semidiurnal tide
qs is 2.763 -- close to aliased Synodic cycle 2.71
sp is 2.9 -- spin-orbit coupling cycle Moon and Earth
q2 is 2.09 --
q3 is 3.52 -- the third strongest tide after diurnal and semidiurnal
qb is 2.329 -- close to aliased Draconic cycle
ms is 1.93 -- MSm tide

I quickly made this chart just for you, so you can see the final weightings of the factors.


s9 and di have very low weightings for the second derivative but are much more important for the f(t).

The concept of lags may not mean anything at this point because there is no reference point to attach it to. Ideally, what I would want to have is a fully calculated luni-solar gravitational pull time series that comes from the JPL ephemeris calculations. What I am doing above is trying to create a first-order approximation to this time series. which will hopefully identify the primary factors,

Yes, I have seen many of the papers linking QBO and ENSO, but that's as far as it goes.