Answers the question three ways, because "align" conflates three different
claims with three different answers.
Move together: not always, and it depends entirely on the window. Day to day
there is no relationship at all -- signs agree 48.9% of the time, 95% CI
[46.9%, 50.9%], indistinguishable from a coin flip. On 7-day trends they agree
74.8% of the time at r = +0.602.
Which leads: price does, by one day. Cross-correlation peaks at k = +1 at
r = +0.588 while every lag in which sentiment would lead price sits at
|r| <= 0.013. Granger tests are one-sided: price explains sentiment with
F = 254.2, p = 1.4e-293, cutting residual sum of squares 38.83%, while
sentiment explains price with F = 0.29, p = 0.96 and a 0.07% reduction.
Stability: the 90-day rolling correlation of the trends averages +0.665 and is
never negative in any window from 2019 to 2026.
Divergences carry no signal: aligned days are followed by +0.91% over the next
week against +0.49% for diverging days, t = 1.17, p = 0…
