Bid-ask bounce
A Gaussian Roll model: negatively autocorrelated errors are anti-redundant evidence.
In Roll's model of the effective spread, trades bounce between bid and ask, so observed prices carry negatively autocorrelated errors around the efficient price $\mu$. Here is a Gaussian stand-in: $y_t = \mu + e_t$ with AR(1) errors $e_t = a\,e_{t-1} + \sqrt{1-a^2}\,\eta_t$ of unit marginal variance. Bounce is $a < 0$; stale, smoothed quotes are $a > 0$; $a = 0$ is the iid case.
Correlated errors couple the observations to each other, but for estimating a single $\mu$ the coupling collapses into a re-weighting of the masses: the GLS weights are the row sums of the error precision matrix, which for AR(1) come out in closed form as $\tfrac{1}{1+a}$ for the first and last trade and $\tfrac{1-a}{1+a}$ for every interior trade. Slide $a$ negative and watch every body on the rail grow — bouncing errors cancel, so the evidence is worth more than its naive iid weight and the masses more than add. Slide $a$ positive and the interior trades shrivel to near nothing: redundant evidence. The particle settles at the GLS estimate; the grey line is the naive sample mean, which ignores the bounce. Drag any trade to see the two estimators disagree.
The same trades, weighed twice. With $a=-0.6$ the total mass is more than triple the naive count $n$ — the posterior is far tighter than the iid analysis admits — while with $a=0.9$ twenty-four trades carry the mass of about two. Roll's estimator itself recovers the spread from exactly this signature, the negative first-order autocovariance of price changes: $s = 2\sqrt{-\mathrm{cov}(\Delta p_t, \Delta p_{t-1})}$. See Roll (1984) in the reading list, and the dictionary for where correlated residuals sit in the mechanics.